Category Archives: Teaching

General thoughts on teaching…

Colons and semicolons

Using colons and semicolons is often an easy way to get a tick in your homework, but it still involves taking a bit of a risk. If you get it right, you get the tick, but if you get it wrong, you’ll get a cross. This article will explain how to use both colons and semicolons so that you can be confident of getting far more ticks than crosses!

Colons (:)

Colons can only be used to introduce a list where the introductory phrase could form a sentence on its own. If not, you shouldn’t use any punctuation at all.

I went to the supermarket and bought the following items: apples, pears and bananas.

Or:

I went to the supermarket and bought apples, pears and bananas.

Note that you can still use colons even if there’s only one item in the list:

I only wanted one thing from my men: courage!

Sample questions

Have a go at the following questions and see if you can add the right punctuation. It’ll either be a colon, a semicolon, a comma or nothing at all.

  1. I love chocolate biscuits and milkshakes.
  2. He said “I always go the gym on Wednesdays.”
  3. There were three items on her shopping list flour, sugar and eggs.
  4. He prized only one quality in his players teamwork.
  5. He stayed in his room it was far too hot to go outside.

Semicolons (;)

Semicolons can be used either to separate two main clauses if one explains the other or to separate items in a list that are long and/or contain commas.

He was very careful not to make any spelling mistakes; his teacher was always having a go at him for bad spelling.

Or:

The entries to the competition came from London, England; Paris, France; and Berlin, Germany.

Note that the semicolon before the ‘and’ is optional. We don’t generally use commas before ‘and’ in a normal list, but some people think using a semicolon in the same situation makes things clearer.

Sample questions

Have a go at the following questions and see if you can add the right punctuation. It’ll either be a semicolon, a colon, a comma or nothing at all.

  1. I love chocolate biscuits and milkshakes I used to have them all the time as a kid.
  2. She said, “I always go the pool on Saturdays it’s the only day I get enough time.”
  3. There was only one thing she wanted to do go and get her hair cut.
  4. His team always scored great goals the other team just scored more.
  5. I never cook chicken I’m afraid of making myself sick.

Explaining humour

Explaining humourOne of the things that children taking Common Entrance exams at either 11+ or 13+ find most difficult to explain is humour. Here’s a quick guide to various different types with explanations, examples and a short quiz at the end.

Slapstick comedy or farce

This is a type of physical comedy that relies on the fact that we find it funny when other people hurt themselves. It’s called ‘Schadenfreude’ in German, and it really shouldn’t be funny…but it is!

Example: A man slips on a banana skin and falls over.

Deadpan or dry humour

This is any joke that’s told with a very matter-of-fact tone.

Example: “It can hardly be a coincidence that no language on earth has ever produced the expression ‘As pretty as an airport’.”
The Long Dark Tea-time of the Soul, by Douglas Adams

Self-deprecation

This means putting oneself down in a self-mocking way.

Example: “If a book about failures doesn’t sell, is it a success?”
Jerry Seinfeld

Toilet and bodily humour

What we do in the toilet or in the bedroom has given rise to a LOT of jokes over the years…

Example: “It’s just a penis, right? Probably no worse for you than smoking.”
When You Are Engulfed in Flames, by David Sedaris

Puns, wit and wordplay

These are jokes based on double meanings or a play on words.

Example: “If not actually disgruntled, he was far from being gruntled.”
The Code of the Woosters, by P.G. Wodehouse

Epigrams

An epigram is just a saying, and some sayings can be very funny – whether deliberately or not!

Example: “Always go to other people’s funerals, otherwise they won’t come to yours.”
Yogi Berra

Dark humour

Dark humour is usually about death or the gloomier aspects of life.

Example: I come from Des Moines. Somebody had to.”
The Lost Continent: Travels in Small-Town America, by Bill Bryson

Sarcasm and irony

Sarcasm is saying exactly the opposite of what you mean, but irony is much richer and more popular because the meaning for the reader can be anything from the literal truth of the statement to its exact opposite. It’s up to you…

Example: “It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife.”
Pride and Prejudice, by Jane Austen

Innuendo

Finding a rude double meaning in a word or phrase is called innuendo.

Example: “Headline?” he asked.
“‘Swing Set Needs Home,'” I said.
“‘Desperately Lonely Swing Set Needs Loving Home,'” he said.
“‘Lonely, Vaguely Pedophilic Swing Set Seeks the Butts of Children,'” I said.”
The Fault in Our Stars, by John Green

Tongue-in-cheek

This expression just means the writer or speaker is being insincere in an ironic and/or mocking way.

Example: “In the beginning, the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.”
The Hitchhiker’s Guide to the Galaxy, by Douglas Adams

Exaggeration and hyperbole

Exaggeration can lead to a powerful punchline in a joke because it relies on shocking the reader with something unexpected.

Example: “In our family, there was no clear line between religion and fly fishing.”
A River Runs Through It, by Norman Maclean

Parody and mockery

Pretending to write in a certain style or copying the format of a particular writer or type of text can be done humorously – although the implied criticism may be affectionate.

Example: “It is a truth universally acknowledged that a zombie in possession of brains must be in want of more brains.”
Pride and Prejudice and Zombies, by Seth Grahame-Smith and Jane Austen

Satire

This is making fun of something usually in religion, politics or current affairs.

Example: “They say the world is flat and supported on the back of four elephants who themselves stand on the back of a giant turtle.”
The Fifth Elephant, by Terry Pratchett

The surreal

‘Surreal’ just means absurd, nightmarish or like a fantasy.

Example: “As Gregor Samsa awoke one morning from uneasy dreams he found himself transformed in his bed into a gigantic insect.”
The Metamorphosis, by Franz Kafka

Character humour

Like a lot of sit-coms this form of humour relies on the personality of the characters. Things are funny because they are so typical of a certain type of person – often a stereotype.

Example: “As a boy, I wanted to be a train.”
Machine Man, by Max Barry

Observational

A lot of stand-up comedy is based on observational humour, which means simply picking up on the typical habits of people in the world around us. We laugh because we recognise the behaviour and often the reason for it.

Example: “It’s a funny thing about mothers and fathers. Even when their own child is the most disgusting little blister you could ever imagine, they still think that he or she is wonderful.”
Matilda, by Roald Dahl

Insults

The shock value of an insult lends itself to humour.

Example: Two whales walk into a bar. The first whale says to the other, “WOOOOOO. WEEEEEEEEOOOOO. WEEEEEEEEEEEEOOOOOOOOO.” The second whale says, “Shut up Steve, you’re drunk.”

Awkward situations

If a situation is particularly cringeworthy or awkward, then it will often generate nervous laughter.

Example: “I don’t know how other men feel about their wives walking out on them, but I helped mine pack.”
Breaking Up, by Bill Manville

Blue or off-colour jokes

Using rude words or swear words has the shock value that can generate humour.

Example: “If this typewriter can’t do it, then f*** it, it can’t be done.”
Still Life With Woodpecker, by Tom Robbins

Sample questions

How would you explain the humour in these lines?

  1. “An unhappy alternative is before you, Elizabeth. From this day, you must be a stranger to one of your parents. your mother will never see you again if you do not marry Mr Collins, and I will never see you again if you do.”
    Pride & Prejudice, by Jane Austen
  2. “There’s a door,” he whispered.
    “Where does it go?”
    “It stays where it is, I think,” said Rincewind.
    Eric, by Terry Pratchett
  3. “It’s not because I want to make out with her.”
    “Hold on.”
    He grabbed a pencil and scrawled excitedly at the paper as if he’d just made a mathematical breakthrough and then looked back up at me.
    “I just did some calculations, and I’ve been able to determine that you’re full of s**t.”
    Looking for Alaska, by John Green
  4. “I came from a real tough neighborhood. Once a guy pulled a knife on me. I knew he wasn’t a professional: the knife had butter on it.”
    Rodney Dangerfield
  5. “A word to the wise ain’t necessary. It’s the stupid ones who need advice.”
    Bill Cosby
  6. “To win back my youth, Gerald, there is nothing I wouldn’t do – except take exercise, get up early or be a useful member of the community.”
    A Woman of No Importance, by Oscar Wilde
  7. “Some men are born mediocre, some men achieve mediocrity, and some men have mediocrity thrust upon them. With Major Major, it had been all three. Even among men lacking all distinction, he inevitably stood out as a man lacking more distinction than all the rest, and people were always impressed by how unimpressive he was.”
    Catch-22, by Joseph Heller
  8. “Build a man a fire, and he’ll be warm for a day. Set a man on fire, and he’ll be warm for the rest of his life.”
    Jingo, by Terry Pratchett
  9. “There are moments, Jeeves, when one asks oneself, ‘Do trousers matter?'”
    “The mood will pass, sir.”
    The Code of the Woosters, by PG Wodehouse
  10. “There was a boy called Eustace Clarence Scrubb, and he almost deserved it.”
    The Voyage of the Dawn Treader, by CS Lewis
  11. “I write this sitting in the kitchen sink.”
    I Capture the Castle, by Dodie Smith
  12. “You can lead a horticulture, but you can’t make her think.”
    Dorothy Parker
  13. “For a moment, nothing happened. Then, after a second or so, nothing continued to happen.”
    The Hitchhiker’s Guide to the Galaxy, by Douglas Adams
  14. “For the better part of my childhood, my professional aspirations were simple – I wanted to be an intergalactic princess.”
    Seven Up, by Janet Evanovich
  15. “It wasn’t until I had become engaged to Miss Piano that I began avoiding her.”
    Into Your Tent I’ll Creep, by Peter De Vries
  16. “To lose one parent, Mr. Worthing, may be regarded as a misfortune; to lose both looks like carelessness.”
    The Importance of Being Earnest, by Oscar Wilde

SOHCAHTOA

SOHCAHTOA (pronounced ‘soccer-toe-uh’) is a useful ‘mnemonic’ to remember the definitions of sines, cosines and tangents. Amazingly, I was never taught this at school, so I just had to look up all the funny numbers in a big book of tables without understanding what they meant. As a result, I was always a bit confused by trigonometry until I started teaching Maths and came across SOHCAHTOA quite by accident!

The reason it’s called SOHCAHTOA is because the letters of all three equations make up that word – if you ignore the equals signs…

First of all, let’s define our terms:

  • S stands for sine (or sin)
  • O stands for the opposite side of a right-angled triangle
  • H stands for the hypotenuse of a right-angled triangle
  • C stands for cosine (or cos)
  • A stands for the adjacent side of a right-angled triangle
  • T stands for tangent (or tan)
  • O stands for the opposite side of a right-angled triangle (again)
  • A stands for the adjacent side of a right-angled triangle (again)

Sines, cosines and tangents are just the numbers you get when you divide one particular side of a right-angled triangle by another. For a given angle, they never change – however big the triangle is.

Sine = Opposite ÷ Hypotenuse

Cosine = Adjacent ÷ Hypotenuse

Tangent = Opposite ÷ Adjacent

All these ratios were discovered by Indian and Arabic mathematicians some time before the 9th Century, but you can still use them today to help you work out the length of the sides of a right-angled triangle or one of the angles.

Each of these formulas can be rearranged to make two other formulas. (If it helps, you can put the three values in a number triangle with the one in the middle at the top). Let’s take the sine formula first:

Sine = Opposite ÷ Hypotenuse means:

  • Hypotenuse = Opposite ÷ Sine
  • Opposite = Hypotenuse x Sine

As long as you know the angle and the length of the opposite side or the hypotenuse, you can work out the length of the other one of those two sides.

  • Unknown: hypotenuse
    Known: opposite and angle
    • If one of the angles of a right-angled triangle is 45° and the opposite side is 5cm, the formula for the length of the hypotenuse must be opposite ÷ sin(45°). The sine of 45° is 0.707 (to three decimal places), so hypotenuse = 5 ÷ 0.707 = 7cm (to the nearest cm).
  • Unknown: opposite
    Known: hypotenuse and angle
    • If one of the angles of a right-angled triangle is 45° and the hypotenuse is 5cm, the formula for the length of the opposite side must be hypotenuse x sin(45°). The sine of 45° is 0.707 (to three decimal places), so opposite = 5 x 0.707 = 4cm (to the nearest cm).

Equally, as long as you know the the hypotenuse and opposite side lengths, you can work out the angle by using the ‘arcsine’ or ‘inverse sine’ function on your calculator, which works out the matching angle for a given sine and is written as sin-1, eg sin(45°) = 0.707, which means sin-1(0.707) = 45°.

  • Unknown: angle
  • Known: opposite and hypotenuse
    • If the opposite side of a right-angled triangle is 4cm and the hypotenuse is 5cm, the formula for the angle must be sin-1(4÷5), or the inverse sine of 0.8. The sine of 53° (to the nearest degree) is 0.8, so the angle must be 53°.

We can do the same kind of thing with the cosine formula, except this time we’re dealing with the adjacent rather than the opposite side.

Cosine = Adjacent ÷ Hypotenuse means:

  • Hypotenuse = Adjacent ÷ Cosine
  • Adjacent = Hypotenuse x Cosine

As long as you know the angle and the length of the adjacent side or the hypotenuse, you can work out the length of the other one of those two sides.

  • Unknown: hypotenuse
    Known: adjacent and angle
    • If one of the angles of a right-angled triangle is 45° and the adjacent side is 5cm, the formula for the length of the hypotenuse must be adjacent ÷ cos(45°). The cosine of 45° is 0.707 (to three decimal places), so hypotenuse = 5 ÷ 0.707 = 7cm (to the nearest cm).
  • Unknown: adjacent
    Known: hypotenuse and angle
    • If one of the angles of a right-angled triangle is 45° and the hypotenuse is 5cm, the formula for the length of the adjacent side must be hypotenuse x cos(45°). The sine of 45° is 0.707 (to three decimal places), so adjacent = 5 x 0.707 = 4cm (to the nearest cm).

Equally, as long as you know the the hypotenuse and adjacent side lengths, you can work out the angle by using the ‘arccosine’ or ‘inverse cosine’ function on your calculator, which works out the matching angle for a given cosine and is written as cos-1, eg cos(45°) = 0.707, which means cos-1(0.707) = 45°.

  • Unknown: angle
  • Known: adjacent and hypotenuse
    • If the adjacent side of a right-angled triangle is 4cm and the hypotenuse is 5cm, the formula for the angle must be cos-1(4÷5), or the inverse cosine of 0.8. The sine of 37° (to the nearest degree) is 0.8, so the angle must be 37°.

Finally, we can do the same kind of thing with the tangent formula, except this time we’re dealing with the opposite and adjacent sides.

Tangent = Opposite ÷ Adjacent means:

  • Adjacent = Opposite ÷ Tangent
  • Opposite = Adjacent x Tangent

As long as you know the angle and the length of the opposite or adjacent side, you can work out the length of the other one of those two sides.

  • Unknown: adjacent
    Known: opposite and angle
    • If one of the angles of a right-angled triangle is 45° and the opposite side is 5cm, the formula for the length of the adjacent must be opposite ÷ tan(45°). The tangent of 45° is 1, so adjacent = 5 ÷ 1 = 5cm.
  • Unknown: opposite
    Known: adjacent and angle
    • If one of the angles of a right-angled triangle is 45° and the adjacent side is 5cm, the formula for the length of the opposite side must be adjacent x tan(45°). The tangent of 45° is 1, so opposite = 5 x 1 = 5cm.

Equally, as long as you know the the opposite and adjacent side lengths, you can work out the angle by using the ‘arctangent’ or ‘inverse tangent’ function on your calculator, which works out the matching angle for a given tangent and is written as tan-1, eg tan(45°) = 0.707, which means tan-1(0.707) = 45°.

  • Unknown: angle
  • Known: adjacent and hypotenuse
    • If the adjacent side of a right-angled triangle is 5cm and the hypotenuse is 5cm, the formula for the angle must be tan-1(5÷5), or the inverse tangent of 1. The tangent of 45° is 1, so the angle must be 45°.

Long multiplication

You can use short multiplication if you’re multiplying one number by another that’s in your times tables (up to 12). However, if you want to multiply by a higher number, you need to use long multiplication.

  • Write down the numbers one on top of the other with the smaller number on the bottom and a times sign on the left (just as you would normally), then draw three lines underneath to hold three rows of numbers.
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  • Multiply the top number by the last digit of the bottom number as you would normally.
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  • Write a zero at the end of the next answer line (to show that you’re multiplying by tens now rather than units).
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  • Multiply the top number by the next digit of the bottom number, starting to the left of the zero you’ve just added.
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  • Add the two answer lines together to get the final answer.
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Notes:

  • Some people write the tens they’ve carried right at the top of the sum, but that can get very confusing with three lines of answers!
  • Don’t forget to add the zero to the second line of your answer. If it helps, you can try writing it down as soon as you set out the sum (and before you’ve even worked anything out).
  • At 11+ level, long multiplication will generally be a three-digit number multiplied by a two-digit number, but the method will work for any two numbers, so don’t worry. If you have to multiply two three-digit numbers, say, you’ll just have to add another line to your answer.

Sample questions:

Have a go at these questions. Make sure you show your working – just as you’d have to do in an exam.

  1. 216 x 43
  2. 17 x 423
  3. 23 x 648
  4. 782 x 28
  5. 127 x 92

How to add, subtract, multiply and divide

The most important things you need to do in Maths are to add, subtract, divide and multiply. If you’re doing an entrance exam, and there’s more than one mark for a question, it generally means that you have to show your working. Even if it’s easy enough to do in your head, you still have to write down the sum on paper. That way, the examiner knows that you didn’t just guess!

Here are the basic operations:

Addition

The standard way to add numbers is the ‘column method’.

  • Write down the numbers one on top of the other (however many there are), with two lines under them and a plus sign on the left.
  • Add the first column of numbers on the right and put the answer between the lines.
    • If the total is more than 9, ‘carry’ the tens by putting that number in small handwriting under the next space on the answer line.
  • Add the next column of numbers working from the right and put the answer between the lines, adding any numbers below the line that have been carried.
  • If you get to the final column of numbers and the total is more than 9, you can write both digits on the answer line.
  • If you have more than two columns of numbers and the total is more than 9, you’ll have to ‘carry’ any tens again by putting that number in small handwriting under the next space on the answer line.
  • You can then finish off as normal.

Notes:

  • You don’t need the second line if you don’t want to use it.
  • You can also choose to put the carried numbers above the top line of the sum, but that gets a bit messy if you’re doing long multiplication, so it’s best to get into the habit of using this method.

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 8 + 5
  2. 17 + 12
  3. 23 + 19
  4. 77 + 88
  5. 127 + 899

Subtraction

The standard way to subtract one number from another is again the ‘column method’, but this time it’s slightly different. For a start, you can only use this method with two numbers (not three or more), and you can’t use it for negative numbers.

  • Write down the two numbers one on top of the other, with the bigger one on top, the usual two lines under them and a minus sign on the left.
  • Working from the right, take away the first digit in the second number from the first digit in the first and write the answer on the answer line.
    • If you can’t do it because the digit on the top row is too small, you’ll have to ‘borrow’ a 10 from the digit in the next column.
      • Place a 1 above and to the left of the top right-hand digit to make a new number, in this case 12.
      • Cross out the digit you’re borrowing from, subtract 1 and write the new digit above and to the left of the old one.
      • You can now subtract as normal, so 12 – 7 = 5 in this case.
  • Working from the right, subtract the next digit in the bottom number from the next digit in the top number and put the answer between the lines.
  • Repeat this step until you’ve finished the sum.
    • Note that in this case you have to borrow 1 from the 2, leaving 1, and then borrow 1 from the 4, writing it next to the 1 so it makes 11. It may look like you’re borrowing 11, but you’re not. You’ve just had to write the two 1s next to each other.

If you can’t borrow from a digit because it’s a zero, just cross it out, write 9 above and to the left and borrow from the next digit to the left. If that’s a zero, too, just do the same again until you reach one that’s not zero.

Notes:

  • You don’t need the second line if you don’t want to use it.
  • If the answer to the sum in the last column on the left is zero, you don’t need to write it down, so your answer should be 17, say, not 017.
  • You don’t need to put commas in numbers that are more than 1,000.
  • You could cross out the numbers from top left to bottom right instead, but that leaves less room to write any little numbers above and to the left (where they have to go), so it’s best to get into the habit of using this method.

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 8 – 5
  2. 17 – 12
  3. 43 – 19
  4. 770 – 681
  5. 107 – 89

Multiplication (or short multiplication)

This is short multiplication, which is meant for multiplying one number by another that’s in our times tables (up to 12). If you want to multiply by a higher number, you need to use long multiplication.

  • Write down the numbers one on top of the other with the single-digit number on the bottom, two lines underneath and a times sign on the left.
  • Multiply the last digit of the top number by the bottom number and put the answer between the lines.
    • If the total is more than 9, ‘carry’ the tens by putting that number in small handwriting under the next space on the answer line.
  • Working from the right, multiply the next digit of the top number by the bottom number, adding any number below the answer line.
    • As with addition, if you get to the final column of numbers and the total is more than 9, you can write both digits on the answer line.

Notes:

  • You don’t need the second line if you don’t want to use it.
  • You can also choose to put the carried numbers above the top line of the sum, but that gets a bit messy if you’re doing long multiplication, so it’s best to get into the habit of using this method.

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 21 x 3
  2. 17 x 4
  3. 23 x 6
  4. 77 x 8
  5. 127 x 9

Division (or short division, or the ‘bus stop’ method)

This is short division, which is meant for dividing one number by another that’s in your times tables (up to 12). If you want to divide by a higher number, you need to use long division (see my article here). It’s called the ‘bus stop’ method because the two lines look a bit like the area where a bus pulls in at a bus stop.

  • Write down the number you’re dividing (the ‘dividend’), draw the ‘bus stop’ shape around it so that all the digits are covered and then write the number you’re dividing by (the ‘divisor’) on the left.
  • Try to divide the first digit of the dividend by the divisor. If it goes in exactly, write the answer on the answer line above the first digit of the dividend.
  • If it goes in, but there’s a remainder, write the answer on the answer line above the first digit of the dividend and then write the remainder above and to the left of the next digit in the dividend.
  • If it doesn’t go, then make a number out of the first two digits of the dividend and divide that number by the divisor, adding any remainder above and to the left of the next digit.
  • Repeat this process for each of the remaining digits, using any remainders to make a new number with the next digit.
  • If you divide one number by another in the middle of the dividend and it doesn’t go, then just put a zero on the answer line and combine the digit with the next one.

Notes:

  • If you have a remainder at the end of the sum, you can either show it as a remainder or you can put a decimal point above and below the line, add a zero to the dividend and carry on until you have no remainder left.
    • If the remainder keeps going, it’s likely to repeat the same digits over and over again. This is called a ‘recurring decimal’. Once you spot the pattern, you can stop doing the sum. Just put a dot over the digit that’s repeating or – if there’s more than one – put a dot over the first and last digit in the pattern.
  • If your handwriting is a bit messy, make sure you make the numbers quite large with a bit of space between them so that you can fit everything in!

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

  1. 36 ÷ 3
  2. 172 ÷ 4
  3. 222 ÷ 6
  4. 816 ÷ 8
  5. 126 ÷ 9

Who or whom, who’s or whose?

The ‘W’ words are useful if you’re trying to understand or summarise a story, but who, whom, who’s and whose tend to cause problems. Here’s a quick guide to what they all mean and how they can be used.

Who v whom

Who and whom are both relative pronouns, which mean they relate to the person you’ve just been talking about. Note that they don’t relate to animals or things, just people. The difference is just one letter, but it signals that one of them stands for the subject (in the nominative case if you’ve ever done Latin) while the other stands for the object (in the accusative).

  • The subject of a sentence is the noun or pronoun that controls the verb, in other words the person or thing that’s ‘doing the doing’.
  • The object of a sentence is the noun or pronoun that is suffering the action the verb, in other words the person or thing that’s having something done to it.

For example, in the following sentence, ‘the girl’ is the subject, and ‘the boy’ is the object:

The girl tapped the boy on the shoulder.

We could also use pronouns, in which case ‘she’ is the subject, and ‘him’ is the object.

She tapped him on the shoulder.

Note that we use ‘him’ rather than ‘he’ in this case. That tells us that the boy is the object and not the subject. It’s the same with ‘who’ and ‘whom’. In fact, it’s the same letter – the letter ‘m’ – that tells us that ‘him’ and ‘whom’ are both the objects of the sentence, and that might be a good way to remember the difference.

For example, in the following sentence, ‘the girl’ is still the subject, so we use ‘who’:

They saw the girl who had tapped the boy on the shoulder.

In the next sentence, the boy is still the object, so we use ‘whom’:

They saw the boy whom the girl had tapped on the shoulder.

Note that neither who nor whom needs a comma before it in these cases. That’s because we are defining which people we’re talking about. It’s a bit like ‘which’ and ‘that’: ‘which’ describes things and needs a comma, but ‘that’ defines things and doesn’t. If we already know who people are and simply want to describe them, then we do use a comma.

They saw Patricia Smith, who had tapped the boy on the shoulder.

They saw Paul Jones, whom the girl had tapped on the shoulder.

In these cases, we know who the children are – Patricia and Paul – so all we’re doing is describing something that has happened. There is only one Patricia Smith and one Paul Jones, so we don’t need to define them. That means we need to use a comma in both cases.

I hope that all makes sense. Here are a few practice questions. Just decide in each case whether you should use ‘who’ or ‘whom’.

  1. They talked to Jim, who/whom lived in Stoke.
  2. He played football with the boy who/whom had red hair.
  3. She was friends with the girl who/whom played volleyball.
  4. Who/whom do you think will win the egg and spoon race?
  5. Who/whom did they put in prison?

Who’s v whose

The words ‘who’s’ and ‘whose’ are homophones, which is another way of saying they sound the same but mean completely different things. ‘Who’s’ is short for ‘who is’ or ‘who has’ while ‘whose’ is a possessive pronoun that means ‘of whom the’ or ‘of which the’. For example, take these two sentences:

  • Who’s going to the cinema tonight?
  • He was a big man whose hands were larger than dinner plates.

The first means ‘Who is going to the cinema tonight?’ whereas the second means ‘He was a big man of whom the hands were larger than dinner plates’. The only reason we don’t say those things is that they’re a bit of a mouthful, so it’s easier to use ‘who’s’ or ‘whose’.

I hope that’s clear now. Here are a few practice questions. Just decide in each case whether you should use ‘who’s’ or ‘whose’.

  1. Who’s/whose in charge of the tennis rackets?
  2. Who’s/whose bag is this?
  3. He speaks to the woman who’s/whose behind the counter.
  4. She likes him to know who’s/whose boss.
  5. Who’s/whose been eating all the crisps?

Could or might?

Could and might mean different things, but a lot of people use them both to mean the same thing. Here’s a quick guide to avoid any confusion.

Here are two sentences that a lot of people think mean the same thing:

  • “I might [or may] go to the cinema tonight.”
  • “I could go to the cinema tonight.”

The first sentence means there is a possibility the speaker will go to the cinema that night. The second sentence doesn’t. I know this is a bit picky and pedantic, but ‘could’ – like ‘can’ – comes from the verb ‘to be able to’, so the second sentence either means “I was able to go to the cinema tonight” or “I would be able to go to the cinema tonight.” Neither of those is the same as the first sentence. Adults might get away with confusing ability with possibility, but if you’re taking an English exam any time soon, it’s probably a good idea learn the difference!

Homophones

Homophones are words that sound the same even though they’re spelt differently and mean different things. Getting them right can be tricky, but it’s worth it in the end.

The reason why homophones are important is not just to do with the general need to spell correctly. Many people think getting them wrong is a ‘worse’ mistake than simply mis-spelling a word because it means that you don’t really know what you’re doing. Anyone can make a spelling mistake, but using completely the wrong word somehow seems a lot worse. That may not sound fair, but that’s just how a lot of people think, so it’s worth learning the common homophones so you don’t get caught out.

Here’s a list of the main ones:

SpellingsMeanings
a lot/allotmuch/distribute
ad/addnotice/put together
ads/adds/adzenotices/puts together/type of axe
aid/aidehelp/assistant
ail/aletrouble (verb)/beer
air/heiratmospheric gas/inheritor
aisle/isle/I’llcorridor/island/I will
all ready/alreadyeverything set/by a certain time
all together/altogethereveryone in the same place/absolutely
all/awltotally/piercing tool
allowed/aloudpermitted/out loud
alter/altarchange/church table
ant/auntinsect/parent’s sister or brother’s wife
arc/arkpart of circle/Biblical boat
assent/ascentagreement/rise
assistance/assistantshelp/helper
ate/eightconsumed/8
aural/oralto do with hearing/to do with mouths
away/aweighoff/up (eg anchors aweigh)
ay/aye/eye/Iyes/yes/organ of sight/1st person
bail/balescoop water out/jump out
bait/batefood on hook/hold (eg bated breath)
ball/bawlsphere/
band/bannedgroup/illegal
bard/barredpoet/banned
bare/bearnaked/tolerate or grizzly
baron/barrenlord/arid
base/bassfoundation/low note
be/beeexist/flying insect
beach/beechsandy area/type of tree
beat/beethit/beetroot
beau/bowmale admirer/bend down or front
bell/bellemusical instrument/pretty girl
berry/buryfruit/inter
berth/birthsleeping place/arrival of baby
billed/buildinvoiced/construct
bite/bytenibble/unit of data
blew/blueforced air/colour
bloc/blockgroup of countries/cuboid
boar/borewild pig/boring person
board/boredflat object/weary
boarder/borderlodger/edge
bode/bowedimply/curved
bolder/boulderbraver/rock
born/bornecreated/tolerated
bough/bowbranch/bend down or front of ship
boy/buoymale child/floating marker
brake/breakslow down/shatter
breach/breechgap/part of gun
bread/bredfood made with yeast/brought up
brewed/broodfermented/family
brews/bruiseferments/scar
bridle/bridalleather strap/to do with brides
broach/broochopen (a question)/piece of jewellery
browse/browslook through/hair above the eyes
but/buttalthough/water tank
buy/by/byepurchase/by means of/goodbye
cache/cashhidden hoard/notes and coins
callous/callusheartless/blister
cannon/canongun/collection of artistic works
canvas/canvasssail fabric/ask questions of
capital/capitolupper case or city/government building
carat/carrot/caret/karatweight/vegetable/arrow/share of gold
carol/carrelsong/cubicle
cast/castethrown/social class
cede/seedgive up/reproductive unit
ceiling/sealingroof/making watertight
cell/sellpart of body/exchange for money
cellar/sellerbasement/person selling
censor/sensorban (film etc)/measurement device
cent/scent/sentUS penny/perfume/dispatched
cents/scentsUS pennies/perfumes
cereal/serialbreakfast dish/TV show
cession/sessiongiving up/period of course
chance/chantsluck/songs
chased/chastepursued/like a virgin
cheap/cheepinexpensive/bird sound
chews/choosenibbles/select
chilly/chillicold/hot food
choir/quiregroup of singers/unit of paper
chord/cordgroup of notes/string
chute/shootdisposal passage/take shot at goal
cite/sight/sitequote/seeing/location
clause/clawsparagraph/talons
coarse/courserough/track or route
colonel/kernelarmy rank/stone in fruit
complement/complimentgo well with/say something nice
coo/coupsound of dove/revolution
core/corpscentre/army unit
correspondence/correspondentsletters/letter-writers
council/counselgoverning body/advice
councillor/counsellorgovernor/advisor
creak/creekwhine/stream
crews/cruiseteams/voyage
cue/queuesnooker tool/line of people waiting
currant/currentdried fruit/electric flow
cymbal/symbolmusical instrument/icon
dam/damnriver barrier/damnation
days/daze24-hour periods/confuse
dear/deerexpensive/type of mammal
defused/diffusedmade safe/circulated
desert/dessertsandy zone/pudding
dew/do/duewater on grass/finish/owed
die/dyeexpire/colour (verb)
discreet/discretenot talkative/separate
doe/dough/dohfemale dear/unbaked bread/oh, no
done/dunfinished/grey-brown
draft/draughtpractise writing/on tap (eg beer)
dual/duelin two parts/fight with swords etc
earn/urn/ern or ernemake money/vase/type of bird
ewe/you/yewfemale sheep/2nd person/type of tree
faint/feintlose consciousness/fake attack
fair/farejust/food
fated/feteddestined/celebrated
faun/fawnrural god/beige or young deer
faze/phase disturb/stage
feat/feetachievement/plural of foot
find/finedseek/told to pay money
fir/furtype of tree/animal hide
flair/flaretalent/bullet making bright light
flea/fleetype of insect/run away
flew/flu/fluepast tense of fly/influenza/chimney
flocks/phloxherds/type of plant
flour/floweringredient for bread/plant
for/four/foreto the benefit of/4/in front
fort/fortecastle/speciality
forth/fourthforwards/4th
foul/fowldisgusting/birds
friar/fryer monk/pan
gait/gateway of walking/door outside
gene/jeanDNA unit/trousers
gild/guildcover in gold/organisation
gilt/guiltcovered in gold/having done wrong
gored/gourdholed/fruit or water container
gorilla/guerrillatype of ape/freedom fighter
grate/greatfireplace/grand
grease/Greecelubrication/a country
groan/grownmoan/past tense of grow
guessed/guestpast tense of guess/invitee
hail/halecelebrate/healthy
hair/harestrands growing on head/rabbit
hall/haulroom/pull
hangar/hangerstorage for aircraft/hook in wardrobe
hay/heydried grass/oy
heal/heel/he’llmake well/back of foot/he will
hear/herelisten/in this place
heard/herdpast tense of hear/group of animals
heed/he’dpay attention to/he would or he had
hertz/hurtsfrequency unit/causes pain
hew/hue/Hughcut/colour/a name
hi/highhello/raised
higher/hiremore raised/rent
him/hymna pronoun/religious song
hoard/hordecollection/mass of people
hoarse/horserough (of voices)/an animal
hoes/hosegarden tools/tube
hold/holedkeep or carry/past tense of hole
hole/wholespace/entire
holey/holy/whollywith holes/sacred/completely
hour/our60 minutes/a pronoun
humorous/humerusfunny/arm bone
idle/idollazy/religious statue
illicit/elicitillegal/draw out
in/inninside/hotel
instance/instantsexample/moments
intense/intentsfierce/purposes
it’s/itsit is/belonging to it
jam/jambfruit spread/door frame
kernel/colonelcore/army rank
knap/napcrest/doze
knead/kneed/needmix dough/hit with knee/require
knight/nightwarrior/dark time
knit/nitfit together/egg of louse
knot/nottied rope/negative
know/no/Nohbe aware of/negative/type of drama
knows/noseis aware of/facial feature
laid/ladepast tense of lay/load ship
lain/lanepast participle of lay/alley
lay/leiplace/flower necklace
leach/leechleak/blood-sucking worm
lead/ledheavy metal/past tense of lead
leak/leekdrop out/vegetable
leased/leastpast tense of lease/superlative of less
lee/leashadow of wind/meadow
lessen/lessonmake less/teaching session
levee/levyembankment/tax
liar/lyreperson who lies/musical instrument
license/licencepermit (verb)/permission
lichen/likenmould/compare
lie/lyefalsehood/alkali solution
links/lynxconnections/wild cat
load/lodeput into/vein of metal in ground
loan/lonelending/single
locks/loxsecures/smoked salmon (American)
loot/lutemoney/musical instrument
made/maidcreated/young woman
mail/malepost/masculine
main/mane/Mainechief/hair/state in USA
maize/mazecorn/labyrinth
manner/manorway/lord’s house
mantel/mantlementalpiece/coat
marshal/martialarmy rank/to do with war
massed/mastbrought together/upright post on ship
maybe/may beperhaps/might be
meat/meet/metetype of food/get together/distribute
medal/meddleaward/interfere
metal/mettleshiny material/spirit
might/mitemay/tiny spider
mince/mintsground beef/plural of mint
mind/minedbrain/dug up
miner/minor/mynahdigger/junior/type of bird
missed/mistpast tense of miss/fog
moan/mowngroan/past participle of mow
mode/mowedway/past tense of mow
moose/mousseelk/foam
morn/mournmorning/regret
muscle/musselpart of body/sea creature
mustard/musteredspicy dressing/broughted together
naval/navelto do with the navy/belly button
nay/neighno (dated)/sound of horse
none/nunnot one/female monk
oar/or/oreblade/alternatively/metal source
ode/owedpoem/due
oh/owe/oah/have a debt of/oh (poetic)
overseas/overseesforeign/manages
pail/palebucket/faint
pain/paneache/window panel
pair/pare/pearcouple/shave/type of fruit
palate/palette/palletpart of mouth/artist’s tray/platform
passed/pastpast tense of pass/in the past
patience/patientstolerance/people in hospital
pause/pawsbreak/animal hands and feet
pea/peevegetable/urinate
peace/pieceharmony/bit
peak/peek/piquesummit/look quickly/annoyance
peal/peelsound of bells/take skin off
pearl/purlprecious stone/knitting stitch
pedal/peddlefoot lever/sell
pedalled/peddledcycled/sold
peer/pierlook carefully/jetty
per/purrfor each/sound of a cat
pi/pie3.14/dish topped with pastry
plain/planeunexciting/2D object
pleas/pleaserequests (noun)/if it pleases you
plum/plumbtype of fruit/measure water depth
pole/pollrod/election or survey
pore/pourconcentrate on/flow
practice/practiserehearsal/rehearse
pray/preytalk to God/victim
presence/presentsbeing somewhere/gifts
prince/printsson of monarch/printed photographs
principal/principlemain/rule of conduct
profit/prophetmoney made/religious seer
rack/wrackwire tray/shipwreck
rain/reign/reinwater from clouds/rule/control strap
raise/rays/razelift/plural of ray/destroy
rap/wraphit/pack up (eg a present)
rapped/rapt/wrappedpast tense of rap/spellbound/past tense of wrap
read/redpast tense of read/scarlet
read/reedstudy/type of plant
real/reelgenuine/cylinder for fishing line etc
reek/wreaksmell bad/cause
rest/wrestrelax/wrench away
retch/wretchvomit/poor soul
review/revuelook over/stage performance
right/rite/writecorrect/ritual/form Leopardtters
ring/wringsound of bell/squeeze out water
road/rode/rowedstreet/past tense of ride/past tense of row
roe/rowfemale deer/use oars
role/rollpart in play/type of bread
root/routepart of plant/roads to take
rose/rowstype of flower/tiers
rote/wroterepetition/past tense of write
rough/ruffcoarse/Elizabethan collar
rung/wrungpast tense of ring/squeezed water out
rye/wrycereal plant/mocking
sail/salecanvas propulsion/selling
scene/seensituation/past tense of see
scull/skullrow alone/head of skeleton
sea/seeocean/be aware of
seam/seemsewn connection/appear
seas/sees/seizeoceans/is aware of/grab
serf/surfagricultural worker/waves
sew/so/sowconnect with thread/thus/plant
shear/sheercut/complete
shoe/shoofootwear/chase away
side/sighededge/past tense of sigh
sighs/sizebreathes out/dimensions
slay/sleighkill/sled
sleight/slightdeceptive skill/faint
soar/sorerise/painful
soared/swordpast tense of soar/bladed weapon
sole/soulonly/spirit
some/suma few/total
son/sunmale child/star in the sky
staid/stayedunadventurous/past tense of stay
stair/starestep/look hard
stake/steakwooden post/joint of meat
stationary/stationerymotionless/writing materials
steal/steelrun off with/metal compound
step/steppestair/European plains
stile/stylefence steps/manner
straight/straitnot bending/narrow strip of water
suite/sweethotel rooms/sugary
summary/summerybrief account/to do with summer
surge/sergerush/type of cloth
tacks/taxnails/levy
tail/taleback end/story
taught/tautpast tense of teach/tight
tea/teemeal/golf ball holder
team/teemgroup of players/swarm
tear/tierteardrop/row
tern/turntype of bird/go round a corner
their/there/they’rebelonging to them/in that direction/they are
theirs/there’sthe one belonging to them/there is
threw/throughpast tense of throw/in and out of
thrown/thronepast participle of throw/royal chair
thyme/timetype of herb/progress of days or years
tic/tickhabit/mark (if correct)
tide/tiedflow of water/past tense of tie
to/too/twotowards/as well/2
toad/towedfrog/past tense of tow
toe/towpart of foot/pull
told/tolledpast tense of tell/rang
trussed/trustbound (with rope)/belief
vain/vane/veinproud/fin/artery
vale/veilvalley/lace face covering (for brides etc)
vial/viletest tube/evil
wade/weighedwalk in water/past tense of weigh
wail/whalehowl/type of ocean mammal
waist/wastemiddle of body/use carelessly
wait/weightdelay or stay/mass
waive/wavegive up/breaker
ware/wear/wherepottery/put on clothes/which place
way/weigh/wheymanner/measure weight/part of milk
ways/weighsmanners/measures weight
we/weepronoun/urination or little
weak/weekfeeble/seven days
weather/whetherclimatic conditions/if
we’d/weedwe would or we had/unwanted plant
we’ll/wheelwe will or we shall/round component
wet/whetliquid/sharpen
we’ve/weavewe have/make cloth
which/witchpronoun/wizard
while/wileas/ruse or cunning plan
whine/winewhimper/alcoholic grape drink
who’s/whosewho is or who has/of whom the
wood/wouldtree material/conditional marker
yoke/yolkpart of plough/yellow part of egg
yore/your/you’reformer times/belonging to you/you are
you’ll/Yuleyou will or you shall/Christmas

French regular verbs – present subjunctive tense

French verbs

“I hate French!”

The subjunctive in French is generally used in the present tense after expressions such as ‘il faut que’ and some verbs that also take the word ‘que’ after them. These are generally the ones that express feelings or doubts (eg vouloir and craindre), especially when two parts of a sentence have different subjects, eg ‘I want her to be happy’ becomes ‘Je veux qu’elle soit contente’. Verbs ending in -er or -re have one set of endings, but  -ir verbs have another (shown here in red):

Verbs ending in -er, eg donner (to give)

Je donne

Tu donnes

Il/elle donne

Nous donnions

Vous donniez

Ils/elles donnent

Verbs ending in -re, eg vendre (to sell)

Je vende

Tu vendes

Il/elle vende

Nous vendions

Vous vendiez

Ils/elles vendent

Verbs ending in -ir, eg finir (to finish)

Je finisse

Tu finisses

Il/elle finisse

Nous finissions

Vous finissiez

Ils/elles finissent

Circle theorems

This article explains circle theorems, including tangents, sectors, angles and proofs (with thanks to Revision Maths).

Isosceles Triangle

Two Radii and a chord make an isosceles triangle.

Perpendicular Chord Bisection

The perpendicular from the centre of a circle to a chord will always bisect the chord (split it into two equal lengths).

Angles Subtended on the Same Arc

Angles subtended on the same arc

Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.

Angle in a Semi-Circle

angle in a semi-circle

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a right angle.

Proof

We can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches.

Divide the triangle in two

We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles.

Two isosceles triangles

But all of these angles together must add up to 180°, since they are the angles of the original big triangle.

Therefore x + y + x + y = 180, in other words 2(x + y) = 180.
and so x + y = 90. But x + y is the size of the angle we wanted to find.

Tangents

A tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle- it just touches it).

A tangent to a circle forms a right angle with the circle’s radius, at the point of contact of the tangent.

angle with a tangent

Also, if two tangents are drawn on a circle and they cross, the lengths of the two tangents (from the point where they touch the circle to the point where they cross) will be the same.

Tangents from an external point are equal in length

Angle at the Centre

Angle at the centre

The angle formed at the centre of the circle by lines originating from two points on the circle’s circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b.

Proof

You might have to be able to prove this fact:

proof diagram 1

OA = OX since both of these are equal to the radius of the circle. The triangle AOX is therefore isosceles and so ∠OXA = a
Similarly, ∠OXB = b

proof diagram 2

Since the angles in a triangle add up to 180, we know that ∠XOA = 180 – 2a
Similarly, ∠BOX = 180 – 2b
Since the angles around a point add up to 360, we have that ∠AOB = 360 – ∠XOA – ∠BOX
= 360 – (180 – 2a) – (180 – 2b)
= 2a + 2b = 2(a + b) = 2 ∠AXB

Alternate Segment Theorem

Alternate segment theorem

This diagram shows the alternate segment theorem. In short, the red angles are equal to each other and the green angles are equal to each other.

Proof

You may have to be able to prove the alternate segment theorem:

proof of alternate segment theorem

We use facts about related angles

A tangent makes an angle of 90 degrees with the radius of a circle, so we know that ∠OAC + x = 90.
The angle in a semi-circle is 90, so ∠BCA = 90.
The angles in a triangle add up to 180, so ∠BCA + ∠OAC + y = 180
Therefore 90 + ∠OAC + y = 180 and so ∠OAC + y = 90
But OAC + x = 90, so ∠OAC + x = ∠OAC + y
Hence x = y

Cyclic Quadrilaterals

cyclic quadrilateral is a four-sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumference of the circle. The opposite angles of such a quadrilateral add up to 180 degrees.

Area of Sector and Arc Length

A sector

If the radius of the circle is r,
Area of sector = πr2 × A/360
Arc length = 2πr × A/360

In other words, area of sector = area of circle × A/360
arc length = circumference of circle × A/360

Verbal Reasoning

Verbal Reasoning (VR) tests were invented to test pupils’ logic and language skills – although they do sometimes includes questions about numbers. In order to do well in a VR test, the most important thing is to be systematic, to have a plan for what to do if the question is hard. Fortunately, there are plenty of past papers available online (including on this website!), so the types of question are well known. Here is a guide to the different kinds of problems and the best ways to approach them. I’m sorry that there are so many, but it’s best to be ready for anything…!

Insert a letter

One common type of question asks you to say which letter will start and finish two pairs of words, eg PRES( )TAND and WIND( )TAIN. Sometimes the answer is obvious (‘S’ in this case), but, if it’s not, the best thing to do is to look at all four words one after the other to see which letter might fit and then try that letter in the other words. If that doesn’t work, you should at least be able to work out if it’s a vowel or a consonant that’s missing, and it’s also useful to know the most common letters in the English language, which are (in order) E, T, A, O, N, I, R, S and H. Finally, you might just have to go through every letter of the alphabet, but there are only 26, so it shouldn’t take too long! Bear in mind that there are different ways of pronouncing letters and different places to put the emphasis, so try writing down the likely options as well as saying them in your head.

Find the odd words

In this kind of question, you’re given five words, and you have to spot the two that don’t fit with the others, eg Lorry, Helicopter, Taxi, Bus, Plane. The best way is to try and find the three words that go together – whatever is left must be the odd ones out. Don’t just try to find a pair of words that go together. If you do, you might get the answer wrong if there’s another word that goes with them. You might also get it wrong because the ‘odd ones out’ don’t have anything in common. In this case, ‘Helicopter’ and ‘Plane’ ARE related, but they don’t have to be.

Alphabet Codes/Code Words

Here, you’ll be asked either to put a word into code or to decode a word. To do that, you’ll be given a word and the coded version, and it’s up to you to work out how the code works, eg STRAW might become UVTCY. Normally, you just have move one or two spaces forwards or backwards in the alphabet (in this case, it’s +2), but look out for other combinations. They might involve changing direction or a change to the number of spaces or a combination of both, eg -1, +2, -3, +4. The good news is that you’ll usually have an alphabet printed next to the question, so you can put your pencil on a letter and ‘walk’ forwards or backwards to get the coded version, but you can also write down the code underneath the word and write down how to get each letter with a positive or negative number – just make sure you don’t get confused between coding and decoding!

Synonyms (Similar Meaning)

Synonyms are words that have similar meanings, such as cold and chilly. In synonym questions, you’re given two groups of three words, and you have to find two synonyms, one from each group, eg (FILTER MATCH BREAK) (DENY DRAIN CONTEST). The first thing to do is to have a quick look at all the words to see if the answer’s obvious (MATCH and CONTEST, in this case). If it is, write it down. If it’s not, you have to be systematic: start with the first word in the first group and compare it with the first, second and third words in the other group. If that doesn’t work, repeat for the second and third words of the first group. Just be careful to think about ALL the possible meanings of a word, eg ‘minute’ can mean 60 seconds, but it can also mean very small! If you still can’t do the question (because you don’t know one or more of the words), try to work by process of elimination. That means narrowing down the options by getting rid of any pairs of words that definitely don’t mean the same. Once you’ve done that, feel free to guess which one of the leftover pairs is the answer. Guessing is fine in Verbal Reasoning: the only thing worse than a wrong answer is no answer at all!

Hidden Words

These questions ask you to find ‘hidden’ four-letter words between two other words in a sentence, using the last few letters from one word and the first few from the next, eg ‘The bird sat on the roof’. Again, scan the sentence quickly to see if the answer’s obvious. If it is, write it down. If it’s not, check every possibility by starting with the last three letters of the first word and the first letter of the second word, moving forward one letter at a time and then checking the next pair of words. You might want to put your fingers on each pair of words with a four-letter gap in the middle so that you can see all the options as they appear just by moving your fingers along the line. In this example, the possible words are theb, hebi, ebir, irds, rdsa, dsat, sato, aton, tont, onth, nthe, ther, hero and eroo, so the answer is obviously ‘hero’, but note that ‘tont’ is spread over three words (sat, on and the), and some words are not long enough to have the usual number of possibilities.

Find the Missing Word

These questions ask you to find a missing set of three letters that make up a word, eg There is an INITE number of stars in the sky. First of all, look at the word in capitals and try to work out what it’s meant to be in the context of the rest of the sentence. If it’s not obvious, try working out where the letters might be missing – is it after the first letter or the second or the third etc? Sometimes you might not know the word (‘INFINITE’ and therefore ‘FIN’ in this case), but, again, it’s worth a guess – just make sure your made up word sounds reasonable!

Algebra (Calculating with Letters)

This is one type of question that’s easier if you’re good at Maths! Algebra uses letters to stand for numbers and is a way of creating useful general formulas for solving problems. In Verbal Reasoning tests, you’ll generally have to add, subtract, multiply and/or divide letters, eg A = 1, B = 2, C = 3, so what is A – B + C? The first step is to convert the letters to numbers, and then you can simply work out the answer as you would in Maths. Just make sure you’re aware of BIDMAS/BODMAS. This is an acronym that helps you remember the order of operations: Brackets first, then Indices/Order (in other words, powers such as x squared), then Division and Multiplication and lastly Addition and Subtraction. Note that addition doesn’t actually come before subtraction – they belong together, so those sums should be done in the order they appear in the question, eg in this case, A – B must be done first (1 – 2 = -1) and then C added on (-1 + 3 = 2).

Antonyms (Opposite Meaning)

Antonyms are words that have opposite meanings, such as hard and soft. In antonym questions, you’re given two groups of three words, and you have to find two antonyms, one from each group, eg (GROW WATER WILD) (SLICE FREE TAME). The first thing to do is to have a quick look at all the words to see if the answer’s obvious (WILD and TAME, in this case). If it is, write it down. If it’s not, you have to be systematic: start with the first word in the first group and compare it with the first, second and third words in the other group. If that doesn’t work, repeat for the second and third words of the first group. Just be careful to think about ALL the possible meanings of a word, eg ‘minute’ can mean 60 seconds, but it can also mean very small! If you still can’t do the question (because you don’t know one or more of the words), try to work by process of elimination. That means narrowing down the options by getting rid of any pairs of words that definitely don’t mean the opposite to each other. Once you’ve done that, feel free to guess which one of the leftover pairs is the answer. Guessing is fine in Verbal Reasoning: the only thing worse than a wrong answer is no answer at all!

Complete the Calculation

This is another number question, and it again means you need to know BIDMAS/BODMAS. You’ll be given an equation (or number sentence), and you just have to fill in the missing number to make sure it balances, eg 24 – 10 + 6 = 8 + 7 + ( ). First of all, work out what the complete side of the equation equals, and then add, subtract, divide or multiply by the numbers in the other side to work out the answer (in this case, 24 – 10 + 6 = 20, and 20 – 8 – 7 = 5, so 5 is the answer). Don’t forget you’re working backwards to the answer, so you have to use the opposite operators!

Rearrange to make two new words

In these questions, you’re given two words, and you have to take a letter from the first word and put it in any position in the second word to leave two new words, eg STOOP and FLAT. Again, check first to see if the answer’s obvious, but then work through systematically, picking letters from the first word one by one and trying to fit it into each position in the second word. (In this case, the answer is STOP and FLOAT.) Remember that both the new words must make sense!

Number Relationship

This is another Maths question in which you’ll be given three sets of numbers in brackets with the middle one in square brackets. The middle number in the final set is missing, though, so you have to calculate it using the two on either side, based on what happens in the first two sets, eg (3 [15] 5) (2 [8] 4) (7 [ ] 3). The calculation will only involve the four basic operations (addition, subtraction, multiplication and division), but it gets much harder when the numbers appear more than once! In this example, all you need to do is multiply the outside numbers to get the answer (3 x 5 = 15 and 2 x 4 = 8, so 7 x 3 = 21), but you might get more complicated questions like this one: (16 [40] 8) (11 [27] 5) (4 [ ] 11). Here, you have to add the first number to itself and then add the other one (16 + 16 + 8 = 40 and 11 + 11 + 5 = 27, so 4 + 4 + 11 = 19). These kinds of questions can be very difficult, so try not to spend too long on them. If it takes more than a minute or so to answer a question, it’s time to move on. You can always come back later if you have time at the end of the test.

Alphabet Series/Sequence

These questions are a variation on number sequences in Maths – except using letters – and you answer them in the same way. You’re presented with several pairs of letters, and you have to fill in the blanks by working out what the patterns are, eg AB BD CF ??. The best way to do this is to focus on the first and second letters of each pair separately as there will always be a pattern that links the first letters of each pair and a pattern that links the second letters of each pair, but there usually won’t be a pattern that links one letter to the next. There’ll be a printed alphabet next to the question, so just do the same as you would for a number sequence question in Maths, drawing loops between the letters and labelling the ‘jump’ forwards or backwards in the alphabet, eg +1 or -2. Once you know what the pattern is, you can use it to work out the missing letters.

Analogies (Complete the Sentence)

In this type of question, you’re given a sentence that includes three possibilities for two of the words. You have to use logic and common sense to work out what the two other words should be, eg Teacher is to (bus, school, kitchen) as doctor is to (office, train, hospital). This is known as an analogy: you have to work out the relationship of the first word to one of the words in the first set of brackets in order to find the same relationship in the second half of the sentence. Again, the best way to do it is to have a quick scan to see if the answer’s obvious. If it is, write it down. If it’s not, go through the possibilities one by one, making sure to put the relationship into words. In this example, a teacher ‘works in a’ school, and a doctor ‘works in a’ hospital, so ‘school’ and ‘hospital’ are the answer.

Word codes

These are complicated! You are given four words and three codes, and you have to find the code for a particular word or the word for a particular code, eg TRIP PORT PAST TEST and 2741 1462 1851. Unfortunately, there’s no set way of doing these kinds of questions, so you just have to use a bit of logic and common sense. It’s useful to remember that each letter is always represented by the same number, so you can look for patterns in the letters that match patterns in the numbers, eg a double T in one of the words might be matched by a double 3 in one of the codes, so that means T = 3, and you can also find out the numbers for all the other letters in that word. In this example, TEST starts and finishes with the same letter, and 1851 starts and finishes with the same number, so TEST = 1851, which means T = 1, E = 8 and S = 5. You can then fill in those numbers for each of the remaining words, so TRIP = 1???, PORT = ???1 and PAST = ??51. Next, you should be able to see that the letter R is the second letter in TRIP and the third in PORT, and that’s matched by the number 4, which is the second number in 1462 and the third in 2741. That means R = 4, which means TRIP = 14??, PORT = ??41 and PAST = ??51. The only code starting with 14 is 1462, so TRIP = 1462, and the only code ending with 41 is 2741, so PORT = 2741 and the only code ending with 51 is 2351, so PAST = 2351. If PAST = 2351, that also tells us that A must equal 3, so you now know what each letter stands for, and you can answer any possible question they might throw at you. Phew!

Complete Word Pairs

These questions are similar to word codes but, fortunately, much easier! You are given three pairs of words in brackets, and you have to work out the missing word at the end by what has gone before, eg (SHOUT, SHOT) (SOLDER, SOLE) (FLUTED, ). The best way to go about it is to write down the position of the letters in the second word of the first two sets of brackets as they appear in the first. In other words, the letters from SHOT appear in positions 1, 2, 3 and 5 in the first word, and the letters from SOLE also appear in positions 1, 2, 3 and 5 in the first word, so the missing word must consist of the same letters from FLUTED, which means it must be FLUE. Now, you may not know that a flue is a kind of chimney, but don’t let that put you off. Just make sure you’ve got the right letters, and the answer must be right – even if you’ve never heard of it!

Another variation on this type of question contains a string of letters that appears in both words of each pair, just with a different letter or letters to start, eg (BLOAT, COAT) (CLING, DING) (SHOUT, ). The easy bit is to find the repeated set of letters (in this case OAT) and to see that the second letter is dropped each time, but you still need to work out why the first letter changes (from B to C and then C to D). That shouldn’t be too hard to work out, though, if you just go through the alphabet to find how many positions forwards or backwards you have to go (in this case, it’s +1, so the answer is TOUT).

Number Series/Sequences

These questions provide you with a series of numbers and ask you to fill in the blanks, which might be anywhere in the sequence, eg 1, 3, 5, 7, ?, ?. As with alphabet series, the best way to find the answer is to draw a loop between each pair of numbers and write down the change in value. In this case, it’s simple (+2 each time), so the answer is 9 and 11, but look out for more complicated sequences. It’s worth knowing the most common sequences, just so you can recognise them at once and don’t have to work them out. Here are a few of the commonest ones:

Even numbers: 2, 4, 6, 8 etc… Rule: 2n
Odd numbers: 1, 3, 5, 7 etc… Rule: 2n – 1
Powers of 2: 2, 4, 8, 16 etc… Rule: 2ⁿ
Prime numbers: 2, 3, 5, 7 etc… Rule: n/a (each number is only divisible by itself and one)
Square numbers: 1, 4, 9, 16 etc… Rule: n²
Triangular numbers: 1, 3, 6, 10 etc… Rule: sum of the numbers from 1 to n
Fibonacci sequence
: 1, 1, 2, 3 etc… Rule: n₋₂ + n₋₁ (ie each successive number is produced by adding the previous two numbers together, eg 1 + 1 = 2, 1 + 2 = 3)

Things get trickier when the sequence is actually a mixture of two separate sequences, eg 1, 3, 2, 5, 3, ?, ?. Here, the integers (1, 2, 3 etc) are mixed in with odd numbers starting with 3 (3, 5 etc), so you can’t simply find the difference between one number and the next – you have to look at every other number. In this example, the first missing number is the next integer after 1, 2 and 3, which is 4, and the second one is the next odd number after 3 and 5, which is 7.

Compound Words (Form New Word)

Here, you’re given two groups of three words, and you have to make a word by adding one from the first group to one from the second, eg (sleek pain seek) (search green killer). Again, it’s important to be systematic, so you have to start with the first word in the first group and try to match it with each word in the second group. If that doesn’t work, repeat as necessary for the next two words in the first group. In this case, ‘pain’ goes with ‘killer’ to make ‘painkiller’.

Create a Word (from the Letters of Two Others)

These questions give you two groups of three words with the middle one in brackets in the first group and missing in the second, eg arise (rage) gears paste ( ) moans. What you have to do is work out what the missing word is by finding where the letters in the word in brackets in the first group come from. They are all taken from the words outside the brackets, so it’s just a case of working out which letter in the words outside the brackets matches each letter in the word inside the brackets. Your best bet is to write down the second group of words underneath the first and go through each letter one by one. Just look out for letters that either appear twice in one of the words or letters that appear in both words outside the brackets. Those will obviously give you two different possible letters for the answer word, so you should probably write both of them one above the other until you’ve worked everything out and then simply choose the one that makes a proper word. In this example, the R from ‘rage’ might come from ‘arise’ or ‘gears’, so the first letter of the answer word is going to be either the second letter of ‘paste’ (A) or the fourth letter of ‘moans’ (N). The same is true of the A and E in ‘rage’. Once you work it all out, the letters are a or n, p or a, m and e or o, and the only sensible word is ‘name’.

Similar Meaning

These questions are slightly different from the synonym questions in that you have to choose a word out of five that has some similarity to or relationship with two pairs of words in brackets, eg (alter, amend) (coins, money) repair, trial, revue, change, passage. The two pairs of words in brackets usually have different meanings, so you have to look for a word with a double meaning. Again, have a quick look at all the words to see if the answer’s obvious. If it is, write it down. If it’s not, go through the five words one by one, comparing them to the words in brackets. It’s important to be open to the possibility of different meanings, so try to think laterally. In this example, for instance, the answer is ‘change’ as it can work as a verb meaning ‘alter’ or ‘amend’ but also as a noun meaning ‘coins’ or ‘money’.

Letter Relationships

For these questions, you’re given a sentence that describes the relationship between two pairs of letters – a little bit like the sentence analogies earlier. The final pair of letters is missing, so you have to work out what they are by finding the relationship between the first two pairs, eg CG is to ED as BW is to ( ). You should see an alphabet line to help you. The first relationship to look at is between the first letter of the first two pairs. In this case, you get from C to E by moving forward two places in the alphabet. That means you need to move two places on from B to get the first letter of the missing pair, which is D. Repeat this for the second letters, and you’ll find the other half of the answer. In this case, you get from G to D by going back three places, so you have to go back the same three places from W to get T. The overall answer is therefore DT.

Comprehension

The exact format of comprehension questions differs, but you’ll usually be given a lot of information about different people, and you’ll have to find the missing data. The subject could be people’s heights or ages, or it could be a schedule of events. For example, three children – Susan, George and Ryan – all left school at 1515 and walked home. Susan arrived home first. George arrived home five minutes later at 1530. It took Ryan 10 minutes longer than Susan to walk home. What time did Ryan get home?. The way to approach any of these questions is to build a complete picture of the situation by starting with something you know and then working from there – a bit like building a jigsaw. Start with the absolute data (about heights, ages or times) and then move on to the relative data (comparing other people’s heights, ages or times). One thing that often helps is to draw a timeline or simply write down the names of the children in order (of height, age etc). In this example, a timeline is probably your best option, starting at 1515 when the children left school and including George getting home at 1530. You can then add in Susan’s arrival time of 1525 (as she arrived five minutes before George) and finally Ryan’s arrival time of 1535 (as he arrived 10 minutes after Susan.

 

Non-verbal Reasoning

Non-verbal reasoning tests are commonly found in Common Entrance exams at 11+ and 13+ level, and they’re designed to test pupils’ logical reasoning skills using series of shapes or patterns. It’s been said that they were intended to be ‘tutor-proof’, but, of course, every kind of test can be made easier through proper preparation and coaching.

Bond produces a lot of useful books of past papers, and there is also a Bond guide on How To Do Non-verbal Reasoning available from Amazon for £8.98. This article is partly a summary of that book, but it’s useful to know how Bond thinks pupils should be doing the questions as they’re the ones producing most of them!

The first thing to do is to describe the kind of questions that are involved. Here is the list taken from the back of one of the Bond papers:

  • Finding the most similar shape
  • Finding a shape within another shape
  • Finding the shape to complete the pair
  • Finding the shape to continue the series
  • Finding the code to match the shape
  • Finding the shape to complete the square
  • Finding the shape that is a reflection of a given shape
  • Finding the shape made when two shapes are combined
  • Finding the cube that cannot be made from a given net

Bond divides the questions into four different types:

  • Identifying shapes
  • Missing shapes
  • Rotating shapes
  • Coded shapes and logic

Each of these types is divided into various subtypes.

Identifying shapes

Types of question

  • Recognise shapes that are similar and different
  • Identify shapes and patterns
  • Pair up shapes

Sample questions

  • “Which is the odd one out?”
  • “Find the figure in each row that is most unlike the other figures.”
  • “Which pattern on the right belongs with the two on the left?”
  • “Which pattern on the right belongs in the group on the left?”
  • “Which shape is most similar to the shapes in the group on the left?”

Missing shapes

Types of question

  • Find shapes that complete a sequence
  • Find a given part within a shape
  • Find a missing shape from a pattern

Sample questions

  • “Which one comes next?”
  • “Which pattern completes the sequence?”
  • “Choose the shape or pattern the completes the square given.”
  • “In which larger shape or pattern is the small shape hidden?”
  • “Find the shape or pattern which completes or continues the given series.”

Rotating shapes

Types of question

  • Recognise mirror images
  • Link nets to cubes

Sample questions

  • “Work out which option would look like the figure on the left it it was reflected over the line.”
  • “Work out which of the six cubes can be made from the net.”

Coded shapes and logic

Types of question

  • Code and decode shapes
  • Apply shape logic

Sample questions

  • “Each of the patterns on the left has a two-letter code. Select the correct code for the shape on the right following the same rules.”
  • “Select the code that matches the shape given at the end of each line.”
  • “Which one comes next? A is to B as C is to ?”
    “Which pattern on the right completes the second pair in the same way as the first pair? A is to B as C is to ?”

Hints and tips

The Bond book goes into great detail about how to answer each individual type of question, but here we’ll only look at a few key things to look for:

  • Function
  • Location
  • SPANSS
  • Story
  • Symmetry
  • Process of elimination

When looking for similarities between shapes, one thing to think about is the ‘function‘ of the objects shown. In other words, what are they for? If all but one of the drawings show kitchen equipment, then the bedside lamp must be the odd one out.

Another way of looking at it is to think about is the ‘location‘ of the objects shown. Where would you usually find them? If there is a rolling pin together with a lot of tools you’d find in the garage, then the tools ‘belong’ together in the same set.

Another useful way of working through a question is to use ‘SPANSS‘, which stands for Shape, Position, Angle, Number, Shading and Size (NOT ‘sides’, as some people have written online!). This is a list of all the possible things that can change in a diagram. Non-verbal Reasoning questions demand that you’re very disciplined, logical and systematic when working through all the possibilities, so it’s useful to have a mnemonic such as SPANSS to help you tick off all the options.

If none of those works, another thing you can look for is a ‘story‘? For example, do the pictures show the steps you take to get ready for school in the morning, such as getting up, brushing your teeth, getting dressed and having breakfast?

You should also look out for ‘symmetry‘. Could the images be reflections of each other, or could they show rotational symmetry – in other words, has one pattern simply been turned upside-down or turned 90 degrees?

Finally, it’s a good idea to work by process of elimination. Just cross off all the answers that can’t be right until you’re left with only one. As Sherlock Holmes once said to Doctor Watson, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

I hope this brief outline has been useful. Beyond that, practice makes perfect, and a few lessons with a private tutor wouldn’t go amiss either…!

Creating off-the-shelf characters

Common entrance exams have a time limit. If they didn’t, they’d be a lot easier! If you want to save time and improve your story, one thing you can do is to prepare three ‘off-the-shelf’ characters that you can choose from. You can work on them beforehand, improving them and memorising them as you go. By the time the exam comes around, it’ll be easy to dash off 8-10 lines about one of your favourite characters without having to spend any time inventing or perfecting them.

Here’s what you need to do.

The first thing to say is that you need your characters to be a little out of the ordinary. Most pupils writing stories tend to write about themselves. In other words, 10-year-old boys living in London tend to write stories about 10-year-old boys living in London! Now, that’s all very well, and the story might still get a good mark, but what you want to try and do is stand out from the crowd. Why not write a story about an 18-year-old intern at a shark research institute in the Maldives?! To decide which one you’d rather write about, you just have to ask yourself which one you’d rather read about. One thing you can do to make sure your characters are special is to give them all what I call a ‘speciality’ or USP (Unique Selling Proposition). It might be a superpower such as X-ray vision or mind-reading, or it might be a special skill such as diving or surfing, or it might be a fascinating back-story such as being descended from the Russian royal family or William Shakespeare – whatever it is, it’s a great way to make your characters – and therefore your stories – just that little bit more interesting.

Secondly, ou should also make sure all your characters are different. Try to cover all the bases so that you have one you can use for just about any story. That means having heroes that are male and female, old and young with different looks, personalities and nationalities. For instance, Clara might be the 18-year-old intern at a shark research institute in the Maldives, Pedro might be the 35-year-old Mexican spy during the Texas Revolution of 1835-6 and Kurt might be the 60-year-old Swiss inventor who lives in a laboratory buried deep under the Matterhorn! Who knows? It’s entirely up to you.

Thirdly, creating an off-the-shelf character is a great way to force yourself to use ‘wow words’ and literary techniques such as metaphors and similes. You may have learned what a simile is, but it’s very easy to forget to use them in your stories, so why not describe one of your heroes as having ‘eyes as dark as a murderer’s soul’? If you use the same characters with similar descriptions over and over again, it’ll become second nature to ‘show off’ your knowledge, and you can do the same with your vocabulary. Again, why say that someone is ‘big’ when you can say he is ‘athletic’, ‘brawny’ or ‘muscular’?

Fourthly, try to stick to what you know. If you’ve never even ridden on a horse, it’s going to be quite tough to write a story about a jockey! Alternatively, if you’ve regularly been to a particular place on holiday or met someone you found especially interesting, then use what you know to create your characters and their backgrounds. It’s always easier to describe places if you’ve actually been there, and it’s easier to describe people if you know someone similar.

So what goes into creating off-the-shelf characters? The answer is that you have to try and paint a complete picture. It has to cover every major aspect of their lives – even if you can’t remember all the details when you come to write the story. I’d start by using the following categories:

  • Name
  • Age
  • Job or education
  • Looks
  • Home
  • Friends and family
  • Personality
  • USP (or speciality)

Names are sometimes hard to decide on, so you might want to leave this one to last, but you just need to make sure it’s appropriate to the sort of character you’re creating. It wouldn’t be very convincing to have a Japanese scientist called Emily!

Age is fairly easy to decide. Just make sure your three characters are different – and not too close to your own age!

Job or education goes a long way to pigeon-holing someone. You can tell a lot from what someone does for a living or what they are doing in school or at university. You can include as much or as little detail as you like, but the minimum is probably the name and location of the school or college and what your characters’ favourite subjects are. You never know when it might come in handy!

Looks includes hair, eye colour, build, skin colour and favourite clothes. The more you describe your heroes’ looks, the easier it’ll be for the reader to imagine them.

Home can again be as detailed as you like, but the more specific the better. It’s easier to imagine the captain of a nuclear submarine patrolling under the North Pole than someone simply ‘living in London’…

Friends and family are important to most people, and it’s no different for the heroes of your stories. We don’t need to know the names of all their aunts, uncles, cousins and grandparents, but we at least need to know who they live with and who their best friends are.

Personality covers many things, but it should show what your characters are ‘like’ and what their interests are. Again, you don’t have to go into enormous depth, but it’s good to introduce the reader to qualities that might be needed later on in the story, such as athleticism or an ability to sail a boat.

USP (or speciality) covers anything that makes a character worth reading about. One of the reasons Superman is so popular is his super powers: his ability to fly, his X-ray vision and the fact that he’s invulnerable. His greatest weakness is also important: Kryptonite. It’s the same for your characters. What can they do that most people can’t? What qualities can they show off in your stories? What will make them people we admire, respect and even love?

Once you’ve created the notes for your three characters, you can write a paragraph of 8-10 lines about each of them. This is your chance to create something that you can easily slot into any of your stories, so use the past tense and stick to what the characters are like, not what they’re doing. That will be different in each story, so you don’t want to tie yourself down.

Try using your characters for stories you’re asked to write by your English teacher (or tutor, if you have one). The more often you use them, the better they’ll get as you change things you don’t like about them, bring in new ideas and polish the wording.

Children’s reading list

Books, books, books…

I’m often asked by parents what books they should try to get their children to read, but I don’t think I’ve been much help so far, so this is my attempt to do better!

Tastes differ, obviously, so perhaps the best thing I can do is to list all the books that I loved when I was a boy. I can’t remember exactly how old I was when I read them, so you’ll have to use your common sense, but they did at least provide me with happy memories.

Ronald Welch

My favourite series of books when I was a child was the one written by Ronald Welch about the Carey family. He wrote about the men in the family over the course of around 500 years, from 1500 up to the First World War. Each novel focused on one character in one particular period – rather like Blackadder, and there was a clear formula: whatever the period, he would have to fight a duel, he would do something heroic and he would win the fair lady! The duels started with a dagger and a sword and then moved on to rapiers and then finally pistols as the years rolled on. I loved the military aspect to the books – as most boys would – and I read just about every single one I could get my hands on. Unfortunately, they’re almost impossible to find in print nowadays, but it’s always worth a look…

CS Forester

CS Forester wrote the ‘Hornblower’ novels. I was interested in both sailing and military history when I was young, and this sequence of novels about a naval officer called Horatio Hornblower in the Revolutionary and Napoleonic Wars from 1792-1815 was a perfect blend of the two.

Alexander Kent (Douglas Reeman)

Alexander Kent was the pen name of Douglas Reeman, who wrote a series of novels about Richard Bolitho. I first came across him after finishing all the CS Forester novels, and he provided a similar mix of nautical and military history during the same period. They weren’t quite as good as the Hornblower novels, but I still enjoyed them.

Enid Blyton

I didn’t read absolutely all the Enid Blyton books when I was a boy, but the one that I do remember is The Boy Next Door. Among other things, I loved the name of the character (‘Kit’), I loved the bits about climbing trees and I also loved the word ‘grin’, which I never understood but thought was somehow magical!

Roald Dahl

Again, I don’t remember reading all the Roald Dahl novels, but James and the Giant Peach left a big impression. The characters were so interesting, and the idea of escaping from home on an enormous rolling piece of fruit was very exciting to me in those days…!

Sir Arthur Conan Doyle

I read The Complete Adventures of Sherlock Holmes when I was a boy, and it’s probably still the longest book I’ve ever read. I remember vividly that the edition I read was 1,227 pages long! I listened to the whole thing again recently in a very good audiobook edition read by Stephen Fry, and it was just as good second time around. I loved the mystery of the stories, and I still read a lot of crime fiction even now. I’ve always had a very analytical mind, so Holmes’s brilliant deductions were always enjoyable to read about.

Charlie Higson

The Young Bond novels weren’t around when I was young, but I read the first few as an adult, and I enjoyed them. James Bond is a classic fictional creation that appeals to boys in particular, and I think I would’ve lapped it up as a teenager. The first one is called Silverfin. Once you’ve read it, you’ll be hooked!

Jane Austen

Jane Austen introduced me to irony with the immortal opening line from Pride and Prejudice, but the first of her novels that I read was actually Emma. I had to read it at school as part of my preparation for the Oxford entrance exam, and I didn’t like it at first. However, that was just because I didn’t understand what was going on. Once my English teacher Mr Finn had explained that the character of Emma is always wrong about everything, I found it very funny and enjoyable. They say that ‘analysing’ a book can sometimes ruin it, but in this case it was quite the opposite.

Ernest Hemingway

“If Henry James is the poodle of American literature, Ernest Hemingway is the bulldog. What do you think?” I was once asked that question in an interview at the University of East Anglia, and I had no idea how to reply! As it happens, Hemingway was one of my favourite authors. My interviewer called his style ‘macho’, but that wasn’t the appeal for me. I simply liked the stories and the settings. I particularly loved the bull-fighting scenes in The Sun Also Rises, and there was just a glamour to the characters and the period that I really enjoyed. If you don’t know where to start, try The Old Man and the Sea. It’s very simple and very short, but very, very moving.

Describing feelings

In many 11+ and 13+ exams, you have to talk about feelings. Yes, I know that’s hard for most boys that age, but I thought it might help if I wrote down a list of adjectives that describe our emotions. Here we go…

A bloke called Bob (actually Robert Plutchik) thought that people only ever felt eight different emotions:

His list is shown in this ‘wheel of emotions’. The basic eight feelings are:

  • Ecstasy
  • Admiration
  • Terror
  • Amazement
  • Grief
  • Loathing
  • Rage
  • Vigilance

If we had a think about all the adjectives that are associated with these categories (and sub-categories), we might come up with a list like this one:

  • Ecstasy
    crazy
    delirious
    ecstatic
    elated
    enthusiastic
    euphoric
    fervent
    glad
    happy
    joyful
    joyous
    mad
    overjoyed
    rapturous
    rhapsodic
    serene
    thrilled
    upbeat
  • Admiration
    accepting
    admiring
    adoring
    appreciative
    loving
    respectful
    trustful
    trusting
  • Terror
    afraid
    aghast
    alarmed
    apprehensive
    awed
    frightened
    frozen
    scared
    submissive
    terrified
  • Amazement
    amazed
    astonished
    astounded
    awe-struck
    bewildered
    dazed
    distracted
    dumbfounded
    flabbergasted
    impressed
    perplexed
    shocked
    staggered
    startled
    stunned
    surprised
    unprepared
  • Grief
    bitter
    grief-stricken
    grieving
    heart-broken
    melancholy
    mournful
    pensive
    pessimistic
    sad
    somber
    sorrowful
    sorry
    unhappy
    wistful
  • Loathing
    appalled
    bored
    disapproving
    disgusted
    outraged
    queasy
    tired
    weary
  • Rage
    angry
    aggressive
    annoyed
    contemptuous
    enraged
    exasperated
    furious
    heated
    impassioned
    indignant
    irate
    irritable
    irritated
    offended
    resentful
    sullen
    uptight
  • Vigilance
    anxious
    aware
    cautious
    circumspect
    expectant
    interested
    keen
    observant
    optimistic
    vigilant
    wary

Long division

Long division is on the syllabus for both 11+ and 13+ exams, so it’s important to know when and how to do it.

The basic idea is that it’s tricky to do short division when the number you’re dividing by (the ‘divisor’) is outside your times tables, ie more than 12. Using long division makes it easier by including a way of calculating the remainder using a proper subtraction sum. It also makes it neater because you don’t have to try and squeeze two-digit remainders in between the digits underneath the answer line (the ‘dividend’).

So how does it work? Well, the only difference involves the remainder. In normal short division, you work it out in your head and put it above and to the left of the next digit in the dividend. In long division, you work out the multiple of the divisor, write it down under the dividend and subtract one from the other to get the remainder. You then pull down the next digit of the dividend and put it on the end of the remainder, repeating as necessary.

To take the example at the top of the page, what is 522 divided by 18?

  1. How many 18s in 5?
  2. It doesn’t go
  3. How many 18s in 52?
  4. Two (write 2 on the answer line, and write 36 under the dividend with a line beneath it)
  5. What’s 52 – 36?
  6. 16 (write it on the next line)
  7. Pull down the next digit from the dividend (write it after the 16)
  8. How many 18s in 162?
  9. Nine (write it on the answer line, giving 29 as the answer, or ‘quotient’)

That’s the basic method, but here are a couple of tips to help you out.

The first is that you can make life easier for yourself by guessing round numbers. Working with numbers outside your times tables is tricky, so you can use ‘trial and error’ to come up with the right multiple of the divisor by trying ‘easy’ ones like 5 or 10. If it’s too big or too small, you can simply try again with a smaller or bigger number.

The second is that you can often divide the divisor by two to force it back into your times tables. Why divide by 18 when you can simply divide by nine and halve the result? You just have to be careful that you only deal in even multiples, eg 52 ÷ 18 is tricky, but the nearest even multiple of 9 is 4 (as 5 is an odd number and 6 x 9 = 54, which is too much), so the answer must be 4.

How to write a letter

Writing a letter is not as easy as it might seem – especially if you have to do it during a Common Entrance exam! In this post, I’d like to explain the typical format of formal and casual letters and the decisions on wording that you’ll have to make.

First of all, here’s a quick list of the main parts of a letter that the examiner will be looking at:

  • Sender’s address
  • Date
  • Greeting
  • Text
  • Sign-off
  • Signature

Sender’s address

It’s important to put the address of the sender (not the recipient!) at the top right of the letter (see above). The postman obviously doesn’t look inside the letter, so the address of the recipient needs to go on the envelope instead! The only exception is if it’s a business letter intended to be posted in a window envelope. In that case, it needs to have the recipient’s address positioned above the sender’s address at just the right height so that it shows through the window when an A4 sheet is folded in three.

The address should really be aligned right, so you must remember to leave enough space for yourself when you start writing each line. Otherwise, it’ll look a bit of a mess…

Date

The date should be placed two or three lines below the sender’s address (again aligned right) in the traditional long format rather than just in numbers, eg 7th October 2018 rather than 7/10/18 (or 10/7/18 if you’re American!).

Greeting

Which greeting you use depends on the recipient. If you know the name of the person you’re writing to, then you should use ‘Dear’ rather than ‘To’, eg ‘Dear Mr and Mrs Dursley’. ‘To’ is fine for Christmas cards, but not for letters. You should also put a comma afterwards. If you’re writing to a company or an organisation and you don’t know the name of the person, you have two options: you can either start the letter off with ‘Dear sir/madam’ or write ‘To whom it may concern’. This works better when it’s a reference for a job or a formal letter that may be circulated among several people.

Text

The text can obviously be whatever you like, but make sure you start it underneath the comma after the greeting. You should also use paragraphs if the letter is more than a few lines.

Sign-off

The sign-off is just the phrase you put at the end of the letter before your signature. If the letter is to a friend or relative, there aren’t really any rules. You can say anything from ‘Love’ to ‘Best regards’ or ‘Yours ever’. Note that they all start with a capital letter and should be followed by a comma. If the letter is to someone else, the sign-off depends on the greeting: if you’ve used someone’s name in the greeting, you should use ‘Yours sincerely’, but it’s ‘Yours faithfully’ if you haven’t.

Signature

The signature is very important in letter-writing as it’s a simple way of ‘proving’ who you are, so you should develop one that you’re happy with. It should include your first name or your initial(s) plus your surname, eg Nick Dale or N Dale or NW Dale. Your signature should be special, so it doesn’t need to be ‘neat’ or ‘clear’ like the rest of the letter. In fact, the prettier and the more stylish, the better!

And there you have it. This is only one way of writing a letter, and there are other ways of formatting the information, but these rules will at least give you the best chance of getting full marks in your Common Entrance exam!

Maths trick

maths trick

Here’s a Maths trick a friend of mine saw on QI. Who knows? It might make addition and subtraction just a little bit more fun!

  1. Find a book and write down the ninth word on p108, eg ‘becoming’.
  2. Ask someone to write down a number with three different digits in it, eg 321.
  3. Ask him to reverse it and take the smaller number away from the larger, eg 321 – 123 = 198.
  4. Ask him to write down the answer and, again, reverse it, eg 891.
  5. Ask him to add the two new numbers together, eg 198 + 891 = 1089.
  6. Ask him to find the ninth word on p108 of the book, eg ‘becoming’.
  7. Reveal the same word you wrote down earlier!

The trick is that the answer is always going to be 1089, whatever the number you first think of, so it should work every time – unless there’s a problem with the Maths!

The ones that got away

I get nervous before I go on photography trips. Part of that is just worrying about travel arrangements, visas and packing everything I need, but another part of it is worrying that I won’t get the shots I want. Here are a few examples of ‘the ones that got away’.

Taj Mahal

Before I went to the Taj Mahal, I was determined to get the classic ‘Lady Diana’ shot of the building from the end of the reflecting pools. That was the whole point of the trip, and I was really worried about it. I couldn’t face the idea of screwing up what would probably be my only opportunity to visit the world’s most famous building.

When I arrived in India on a G Adventures trip in November 2013, we went to the Taj Mahal early one morning, around 0530. We had to queue for a while and then go through security. At that point, I was about to rush off and take the shot I’d been dreaming about, but our tour leader then introduced us all to a local guide who was about to give us a 15-minute lecture about the building. What a nightmare! I knew that the whole place would be crawling with tourists if I didn’t go and take the shot immediately, but it seemed a bit rude just to rush off without hearing the talk. In the end, I was too British about the whole thing and missed the shot of a lifetime. Too bad. On the plus side, I ended up with this image of the Taj Mahal.
Taj Mahal from Agra Fort in blue haze
‘There once lived an exotic princess in a fairy tale castle…’

It’s the very opposite of the ‘Lady Diana’ shot. One is all symmetry and clarity, the other is misty and mysterious. The higgledy-piggledy minarets and the blue haze make the building seem more like a fairy tale castle. I do like this shot, but I still regret being too polite to get the one I wanted…!

Jumping impala

The one that got awayNot quite sharp enough…

This would’ve been a great shot. It could’ve been a great shot. It should’ve been a great shot. But it wasn’t. Why? Motion blur. If you look closely, you can see that the whole body is slightly out of focus, and that was simply because I didn’t think to change my shutter speed. I was parked in a jeep in Botswana when a herd of impala came chasing across the road. They were galloping fast, but there were five or six of them, so I did have time to focus on each of them, one by one, as they crossed the road in turn. Unfortunately, I was using my default camera settings that were designed to capture animals that were standing still. I was using an 80-400mm lens, so I had my camera on 1/320 and f/8 with auto ISO. That would normally have worked, but not for a jumping impala! What I really needed was a shutter speed of at least 1/1000 of a second. I just didn’t think…

Caracal

Caracal
This is what it looks like on Wikipedia.

A few years ago, I went to a talk given by Paul Goldstein somewhere in London, and one of the slides he showed was a picture of a caracal. I’d never seen one at the time, but Paul was very proud of his shot, which showed a caracal from the side running through long grass. The image stayed in my mind, and I was very excited when I went to Tanzania in January 2018 and actually saw one for myself! It was quite a way away, but I had my 800mm lens with me, and I was just about to take a shot when the driver told me to wait. He was going to drive around and get closer. Well, funnily enough, the caracal disappeared, and I never got the shot I wanted…

Polar bear

Polar bear crossing ice floe in ArcticThe best of a bad bunch

In June 2014, I went on an Exodus trip with Paul Goldstein to Spitsbergen to see the polar bear. It was a last-minute booking, so I got a good deal on the price, and I was lucky enough to share a cabin with a nice French chap called Eric, but the real prize was getting some good shots of a polar bear. We had 13 or so sightings, but, sadly, they were all too far away for my 500mm lens. That was in the days before I got into the habit of renting the Nikon 800mm monster, and I really wish I’d had it then. Amongst other sightings, a mother and her two cubs put on a great show for us on the ice, but, when I got back to my cabin to review my shots, I found they were all too soft and too distant. Ah, well, at least I have an excuse to go again now…

The kill

I’ve been to Africa several times now, visiting Kenya, Uganda, Rwanda, Zambia and Botswana, but I’ve never seen a kill. I’ve seen the chase, and I’ve seen the predator eating its prey, but I’ve never seen the crucial moment of the kill. Now, I know some people would be a little squeamish about seeing one animal kill another, but I don’t think I’d feel that way. To me, it’s the ultimate expression of ‘the survival of the fittest’, and I’d love to see a lion, leopard or cheetah kill something on the great plains of Africa.

I have many stories of ‘the one that got away’. There was the time when I climbed Mount Kenya and arrived back at the camp, only to find that everyone that morning had spent an hour watching a pride of lions kill a wildebeest 50 yards away from the gate of the national park! Or there was the time on the same trip when I booked the wrong flight home and had the chance to spend an extra day on my very own personal game drive. We saw a cheetah ‘timing’ (or hunting) an impala, and it was the most exciting thing that’s ever happened to me in Africa – but no kill. In Antarctica, I watched from a Zodiac as a leopard seal ripped apart a penguin, but I didn’t quite see the initial attack. In the Brazilian Pantanal, I was watching a jaguar on the river bank from a small boat when the call came over the radio that lunch was ready. No sooner had we met up with the other boat than we had another call, this time to say that the very same jaguar had just killed a caiman! We rushed back and watched as the young jaguar made a mess of the whole thing. To begin with, he had hold of his prey by the throat rather than the back of the neck. This is fine if you’re a lion, but jaguars prefer to kill caiman (or small crocodiles) by nipping them on the back of the neck. This jaguar was in a bit of a bind: he didn’t want to kill the caiman the ‘wrong’ way, but he couldn’t change his grip in case it got away. He spent 10 minutes humming and hawing before finally killing the caiman, but that was only the start of his problems. His next job was to find a safe place to store his prey, but the banks of the river were 8-10ft high and very steep, so he spent another 25 minutes trying to find a way up into the undergrowth, desperately trying to drag the 10ft crocodile with him. By this stage, around 20 boats had gathered to see the jaguar, and, when he eventually managed to scramble up the bank with his kill, everybody gave him a big round of applause!

NAI’d rather have seen the kill than stopped for lunch! 

Conclusion

All this goes to show exactly how close I’ve come to the elusive kill, but no luck so far. However, I’m off to the Masai Mara in a couple of weeks, so maybe, just maybe I’ll be able to bring back the shot I’ve been dying to get…

Lightroom workflow

Bear about to catch salmon in mouth

A few years ago, I started doing all my photographic post-processing in Lightroom. It’s the program used by most professional photographers and is reasonably user-friendly, I got to grips with Lightroom mostly by watching a very useful series of YouTube videos by Anthony Morganti, but this article is just a description of my basic workflow. I pay around £10 a month for access to Lightroom Classic (which I use almost all the time) and Photoshop (which I rarely use except for model releases that need thumbnail images superimposing on them).

What does ‘workflow’ mean?

Your workflow is simply the steps you go through in order to choose your best shots and make them look as good as possible. You might be on a cruise ship in the Antarctic or in a tent in Chobe National Park or back at home in Blighty, but – wherever you are – you should have a standard approach to cataloguing and post-processing your shots. This is my system, but feel free to change it or add to it according to what you prefer:

  1. Import to computer
    I like to keep up-to-date with editing my pictures, so I usually work on them every day after I get back from the game drive (or whatever the shoot happens to be). I’m usually out all day shooting, so I take the first chance I get to go through everything before lunch or dinner back at camp. To do that, I first of all connect my camera to my MacBook Pro and import all the RAW files to a new folder in Pictures using Image Capture. I have two cameras, so I usually have a shower or something while the first one’s chugging away, and then I work on the first batch of images while the second is being copied across from my other camera. I usually take over 1,000 images in a day, so this can take a while, and I get very impatient at this point! I’ve done my best to buy Compact Flash (CF) or Secure Digital (SD) cards with the fastest possible read and write speeds just to help speed up the process, and I now have an extra-fast XQD (eXperimental Quality Determination) card for my D850, but it’s never enough. I have a Mac, so Image Capture is the default program for importing files, but it will obviously be different if you have a PC. I could import my shots directly using Lightroom, but I’ve had a couple of bad experiences when Lightroom has crashed while trying to import thousands of files, so I use Image Capture just to be on the safe side.
  2. Import to Lightroom
    I then import the files to Lightroom. This doesn’t involve any actual copying of files, so it only takes a few seconds. I usually do it without any of the custom ‘Import’ settings, but you could set this up if you wanted to. It’s a trade-off between speed and convenience. If you always want a vignette, for example, then you could create a preset and import using that preset. That way, every shot has the same vignette. However, it makes the import process last that bit longer, so it’s up to you. The other thing you can do is create 1:1 previews. This again is more time-consuming, but it makes a huge difference when it comes to viewing and editing each file in full-screen mode. It’s extremely frustrating when Lightroom keeps displaying the ‘Loading…’ message for each new file, particularly when you just want to check sharpness at 1:1, but those messages disappear if you build the previews during the import process. Try it and see for yourself.
  3. Rate images
    I only end up trying to sell about 1% of the shots I take, so rating the images I like is generally much quicker than rejecting the ones I don’t! (If your hit rate is more than 50%, you can always type ‘x’ to reject images and delete them later all in one go.) To rate pictures, you simply type a number between 1 and 5, and the equivalent star rating is added to all the selected images. (You can press 0 to remove the rating or 6 to add the colour red, which I used to do for people shots.) In my system, I give 3 stars generally to shots of my friends or fellow guests worth putting on Facebook, 4 stars to shots worth selling and 5 stars to my all-time favourites. (To give you an idea, I currently have over 5,000 shots I’ve rated 4 stars or more, but only 142 5-star shots!) During the rating process, I sometimes have to crop an image or do some very basic editing to see if it’s worth keeping, but I try to keep it ‘quick and dirty’ to save time.
  4. Check ratings
    Once I’ve rated all my shots, I go over all the 4- or 5-star images again to check the rating. This crucially includes checking the sharpness at 100% because agencies are very quick to reject images that aren’t quite sharp enough. It also means checking for duplicates. It’s very easy to end up with several shots of the same subject from the same angle, especially if the shots were taken at different times so they don’t end up right next to each other. Agencies again tend to reject images that are too similar to each other, so it’s worth going through with a fine-tooth comb at this point. Otherwise, you’ll end up duplicating all your later work for a file that ends up in the trash…!
  5. Post-process images
    Digital images don’t generally look their best straight out of the box, so this is when I spend a bit of time making basic adjustments to my 4- and 5-star images. I make a couple of global changes, but the rest are local. The global changes are Dehaze and Post-crop vignetting. The Dehaze slider in the basic panel of Lightroom can remove haze, but it’s also useful for any shot that just needs a little bit more contrast, clarity, saturation and vibrance. I generally set it to +25, and I’ve created a preset that allows me to apply the change to all of my images at the same time. I do the same with Post-crop vignetting. Vignettes tend to focus the viewer’s eyes on the subject by darkening the corners of the image, so I generally set the slider to +20. As most of my pictures are wildlife portraits, that works just fine, but I generally won’t use a vignette when there’s a large expanse of sky as it just looks plain daft! The local adjustments I make to each file generally involve using the tools in the basic panel (such as cropping, changing the exposure and choosing different black and white points to avoid clipping of highlights and shadows), so I tend to click the ‘Auto’ button to begin with and then only make further changes where I have to.
  6. Add metadata
    The most time-consuming part of this whole process is adding the metadata. If you’re not a serious photographer aiming to sell your shots to stock agencies, then you obviously don’t need to do much at this point, but the more data you add, the easier it is to find files when you need to. For example, if you’ve just come back from Botswana and someone asks to see all your elephant shots, you’ll feel a bit daft if you’ve never even bothered to add any tags! I take all my 4- and 5-star images and add titles, captions and keywords. Stock agencies have rules on the type and number of characters in each metadata field, so I avoid apostrophes and give all my images seven-word titles that are no longer than 50 characters. In theory, captions should be different from titles, but I find it too time-consuming to do that for all my files, so I keep them the same except for any 5-star images. I put those on my website and tend to enter those in competitions, so it’s worth expending a little extra effort to sell the sizzle! Keywords are essential for Search Engine Optimisation, so I use at least 10 but more often 20 or 30, including tags describing the location, content and theme of the image (plus obvious synonyms). After each trip, I set up a metadata preset for Design Pics (my main stock agency) in order to add the data they require, such as city, country and copyright status. I also create a location in the Maps module and drag all my images to it in order to geotag them with GPS data. It’s worth noting that I set the time zone, date, time and copyright information on my cameras before I go on a trip so I don’t have to worry about any of that when I get home.
  7. Export images
    Lightroom is what they call a ‘non-destructive’ program, which means that the RAW files that you edit aren’t actually changed when you edit them. Instead, Lightroom keeps a list of editing instructions that it follows every time you want to view a file. As a result, it’s essential to export any files that you intend to view outside Lightroom or upload to any stock agencies. I’ve set up presets for all the folders I usually export to, but stock agencies generally want JPEG files no more than 20MB in size, so I’ve used that as my limit. Most agencies also have minimum quality thresholds, so I try not to crop so much that the image is less than 6.3 megapixels. I initially export all my 4- and 5-star images as 20MB sRGB JPEGs at the highest quality setting to three folders: ‘4*’, ‘5*’ and ‘Favourites’ – which holds both. (These files automatically show up in Lightroom as I’ve set it up that way in Preferences.) I then export the same files to my ‘To upload’ folder using a special low-resolution preset that follows the Design Pics guidelines. I have an exclusive agreement with Design Pics, and I give them first refusal on all my photographs. However, the metadata requirements for Design Pics are different from those of the other agencies, so I have to be careful to get it right. The main difference is in the Headline and Caption fields. Design Pics requires Headline to be ‘NA’, and I write a long description in the Caption field of my 5* images in order to put it on my website, but some agencies take the title of the image from the Headline and Caption fields, so I have to copy and paste the correct data several hundred times! (There is a plug-in that copies data from one field to another, but the free version only works on 10 files at a time…)
  8. Upload to agencies
    Once I’ve exported all my 4* and 5* files, I upload them to Design Pics via FTP using Filezilla. It usually takes them a few weeks to decide which ones they want. When I’ve received a list of their ‘selects’, I export high-resolution versions and upload them via FTP again. Sometimes, these files don’t pass QA due to lack of sharpness or some other issue, so I have to wait another week or so before I know exactly which files I can send to the other agencies. Once I have the definitive list, I upload them to all the other agencies using Filezilla, websites or DeepMeta (for Getty Images). Buyers tend to search among the newest images, so I’ve taken to uploading 100 files each month in order to maximise the chances of a sale. We’ll see if it works…! I keep track of the whole process on a spreadsheet. Each image has a row, and each agency has a column, and I note the current status by putting ‘u’ for ‘uploaded’, ‘s’ for ‘submitted’ and ‘y’ for accepted. I’ve also created quite a few extra columns for continent, country, type of image, exhibitions, online galleries and competitions. Managing over 5,000 images is a complicated process, so I rely on Excel to make sure I know what’s going on!
  9. Delete images
    Once all my images are copied across to my laptop and properly edited and catalogued, I can format the memory cards and delete any unrated files in Lightroom. File management should always be done in Lightroom rather than Finder in order to make sure that the changes are synchronised properly. If you do it the other way round, Lightroom will flag deleted images as ‘missing’. This also applies to any changes you make to the metadata. If you select the right settings in Lightroom, these will automatically be copied to the underlying files in Finder, and that’s a huge time-saver. For example, if you suddenly realise you’ve spelt ‘elephant’ wrong in some of your elephant pictures, you can simply search for the wrong spelling, highlight all the pictures that pop up and correct it globally in the keywords window.
  10. Back up
    Backing up all my pictures and documents is absolutely essential, so I use a cloud storage service called CrashPlan from Code42. It runs in the background and simply copies any changes or deletions to the back-up servers in real time. If I realise I’ve deleted a file by accident, I can search for it on CrashPlan and restore whichever version I want – either the latest version or the version before I made a mistake with my edits. CrashPlan works fine as long as I have a working internet connection, but it did take a few weeks to sync all my files when I first started using it, and it doesn’t help me when I’m in Africa or in the Arctic Circle without any wi-fi! My biggest fear is losing all the pictures I’ve taken while I’m on a trip, and I still haven’t worked out a solution to the problem. I guess I could take a spare hard drive or USB stick, but I’ve been too lazy so far. Let’s hope I don’t pay the ultimate price…!

Lightroom is a subject I’m learning all the time, but I hope this will give you a head start!

Simultaneous equations

Simultaneous equations help you work out two variables at once.

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Why do we have simultaneous equations? Well, there are two ways of looking at it.

  1. The first is that it solves a problem that seems insoluble: how do you work out two variables at once? For example, if x + y = 10, what are x and y? That’s an impossible question because x and y could literally be anything. If x was 2, then y would be 8, but if x was 100, then y would be -90, but if x was 0.5, then y would be 9.5 and so on. Simultaneous equations help us solve that problem by providing more data. Yes, we still can’t solve each equation individually, but having both of them allows us to solve for one variable and then the other.
  2. The second way of looking at simultaneous equations is to imagine that they describe two lines that meet. The x and y values are obviously different as you move along both lines, but they are identical at the point where they meet, and that is the answer to the question.

The next question is obviously ‘How do we solve simultaneous equations?’ The answer is simple in theory: you just have to add both equations together to eliminate one of the variables, at which point you can work out the second one and then put it back into one of the original equations to work out the first variable. However, it gets more and more complicated as the numbers get less and less ‘convenient’, so let’s take three examples to illustrate the three different techniques you need to know.

Simple addition and subtraction

The first step in solving simultaneous equations is to try and eliminate one of the variables by adding or subtracting them, but you can only do that if the number of the variable is the same in both. In theory, you could choose the first or the second term, but I find the one in the middle is the easiest, eg

4x + 2y = 10

16x – 2y = 10

Here, the number of the variables in the middle of the equations is the same, so adding them together will make them disappear:

20x = 20

It’s then simple to divide both sides by 20 to work out x:

x = 1

Once you have one variable, you can simply plug it back into one of the original equations to work out the other one, eg

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Multiplying one equation

If the number of variables in the middle is not the same, but one is a factor of the other, try multiplying one equation by whatever number is needed to make the number of the variables match, eg

4x + 2y = 10

7x + y = 10

Multiplying the second equation by 2 means the number of the y’s is the same:

4x + 2y = 10

14x + 2y = 20

The rest of the procedure is exactly the same, only this time we have to subtract rather than add the equations to begin with:

10x = 10

x = 1

The next part is exactly the same as the first example as we simply plug in x to find y:

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Multiplying both equations

If the number of variables in the middle is not the same, but neither is a factor of the other, find the lowest common multiple and multiply the two equations by whatever numbers are needed to reach it, eg

4x + 2y = 10

x + 3y = 10

The lowest common multiple of 2 and 3 is 6, which means we need to multiply the first equation by 3:

12x + 6y = 30

…and the second by 2:

2x + 6y = 20

As the number of variables in the middle is now the same, we can carry on as before by subtracting one from the other in order to find x:

10x = 10

x = 1

Again, the final part of the technique is exactly the same as we plug x into the first of the original equations:

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Practice questions

Job done! Now, here are a few practice questions to help you learn the rules. Find x and y in the following pairs of simultaneous equations:

  1. 2x + 4y = 16
    4x – 4y = 8
  2. 3x + 2y = 12
    5x + 2y = 16
  3. 12x – 4y = 28
    3x – 2y = 5
  4. 2x – y = 12
    3x – 2y = 17
  5. 4x + 3y = 24
    5x – 2y = 7
  6. 4x + 3y = 31
    5x + 4y = 40
  7. x + 4y = 23
    5x – 2y = 5
  8. 4x + 3y = 37
    2x – 3y = -13
  9. 2x + 4y = 16
    3x – 5y = -9
  10. 2x + 4y = 20
    3x + 3y = 21

How to become a private tutor

Adrian-Beckett_09032013_035

I’ve talked to a few people who wanted to become private tutors, so I thought I’d write down a few tips for anyone who’s interested.

How did I start out?

I started as a private tutor quite by accident. It was 2009, and I was finding it hard to get work as a freelance management consultant when I happened to read an article in the Telegraph called 10 Ways to Beat the Recession. The author mentioned a few ways of earning some extra cash, including becoming an extra on film sets – which I was already doing – and working as a private tutor. I’d never done any proper teaching before, although I was a golf coach, and I’d coached skiing a few times in the Alps, but I thought I’d sign up with a couple of agencies and see what happened. Within a week, I had two clients, and I’ve never looked back since!

What qualifications do I need?

The first and most important thing to say is that you don’t need any teaching qualifications! Yes, that’s right. You don’t need a PGCE, and you don’t need to have done any training as a teacher. As a private tutor, you are just that – private – so you don’t have to jump through all the Government hoops that a teacher in a state school would have to do. Obviously, potential clients want the best person to teach their child, so you need to show some sort of academic record, but that can be as little as a degree in English – which is what I had when I started. Admittedly, I went to Oxford, which probably counts for a lot with Russian billionaires (!), but you don’t need to have an Oxbridge degree to become a tutor. Far from it. However, what you probably will need is a criminal records check. This is just a piece of paper that certifies you haven’t been convicted of a criminal offence and was often known as a ‘CRB check’, although it’s now officially called an Enhanced Certificate from the Disclosure and Barring Service, or ‘DBS check’. You can’t apply for an ‘enhanced certificate’ yourself, but your tuition agency can help you. In fact, they may require you to have one and even to renew it every year or two. It costs around £18 and can take up to three months to arrive, so it’s worth applying as early as possible. Some agencies may charge up to £80 to make the application on your behalf, so be careful! You can find further information here.

What subjects can I teach?

You can teach whatever you like! Agencies will just ask you which subjects you offer and at what level, so you have complete freedom to choose. I focus on English and Maths, which are the most popular subjects, but that’s mostly led by demand from clients. They are the main subjects at 11+ level, so that’s what most people are looking for help with.

What age children can I teach?

Again, the choice is yours. I’ve taught students from as young as five to as old as 75, but the peak demand is at 11+ level, when the children are around 10 years old. I make it a rule that I’ll only teach a subject to a level that I’ve reached myself, such as GCSE or A-level, but clients sometimes take you by surprise. When I turned up to teach what I thought was going to be English to two boys, the nanny suddenly asked me to do Latin instead. When I said I hadn’t done any Latin since I was 15, she just said, “Oh, you’ll be fine…!”

What preparation do I need to do?

  • Research. One of the big attractions of tutoring for me is that the work is very enjoyable. I like teaching, and I like spending time with children, so it’s the perfect combination! The reason I stopped work as a management consultant was the constant stress, the persistent worry that I wasn’t up to the job, but teaching 10-year-olds never makes me feel like that. Whether it’s English or Maths, I’m confident in my ability to teach and never worry about being asked an impossible question. However, that doesn’t mean you can walk into your first lesson without doing any preparation at all. In my case, I wanted to teach English, so I needed to find out what kind of questions cropped up in 11+ and 13+ entrance exams and come up with a good method of answering them. Once I’d done that, I was ready. Maths was a bit easier, but I still looked through a few papers to make sure there was no risk of being blind-sided by something I’d forgotten how to do or had never studied. Whatever the subject you’re offering, I suggest you do the same.
  • Past papers. The other thing I needed to do was to find past papers to give to my pupils. That was a bit tricky in the early days until a kind parent gave me a collection of photocopied exams. After that, I carried a couple around with me to take to lessons, but it wasn’t a great solution, so I decided to create a website – this one. Over time, I collected dozens of past papers and wrote various articles on how to do different kinds of question in Maths, English and French. Now, I don’t have to carry around anything with me or spend time dictating notes. I can simply ask my pupils to look it up online. Setting up a website is pretty easy using WordPress or something similar, but you should feel free to use the resources on my past papers tab if you don’t want to go to the trouble yourself, and all my articles are available for free if you need them. The main ones I use for English are about doing comprehensions and writing stories, but there are plenty more. The website proved unexpectedly popular, and I had over 28,000 visitors last year! The other advantage is that it generated enough business for me not to need agencies any more. That means I can charge what I like, I don’t have to pay any commission, and I can have a direct relationship with all my clients without anybody acting as an intermediary – and often just getting in the way!
  • Business cards. I know it sounds a bit old-fashioned, but having business cards is very useful. If you’re just starting out, nobody knows your name, so paying a few quid to market your services is one of the best investments you can make. You never know when people will tell you they’re looking for a tutor, and it’s the easiest thing in the world to give them a business card. Even if you don’t have a website, it will at least tell them how to reach you, and you should get a lot more clients out of it.

How can I find work?

Tuition agencies are the best place to start, but there are different kinds. Some are online and simply require you to fill out a form for them to check and vet, but others ask you to go through an interview, either over the phone or in person. Either way, you need to put together a tailored CV that shows off your academic achievements and highlights any teaching experience you’ve had. This may not be very much at the beginning, but you simply need to show enough potential to get you through the door. Once you’ve shown enough aptitude and commitment to get accepted by a few agencies, you’ll rapidly build up your experience on the job.

Here is a list of the tuition agencies I’ve been in touch with, together with contact details where available. I’m based in London, so there is obviously a geographical bias there, but some of the agencies such as Fleet Tutors offer national coverage, and you can always search online for others in your local area.

Name

Email

Telephone

Website

A-Star Tuition astartuition@btinternet.com 01772 814739 astartuition.com
Approved Tutors approvedtutors.co.uk
Athena Tuition athenatuition.co.uk/
Beacon Tutors info@beacontutors.co.uk 020 8983 2158 beacontutors.co.uk/
Bespoke Tuition emma@bespoketuition.com 07732 371880 bespoketuition.com
Bigfoot Tutors tutors@bigfoottutors.com 020 7729 9004 bigfoottutors.com
Bright Young Things 07702 019194 brightyoungthingstuition.co.uk
Dulwich Tutors info@dulwichtutors.com 020 8653 3502 dulwichtutors.com
Enjoy Education kate@enjoyeducation.co.uk enjoyeducation.co.uk
Exam Confidence
First Tutors firsttutors.co.uk
Fleet Tutors 0845 644 5452 fleet-tutors.co.uk
Gabbitas gabbitas.com
Greater London Tutors 020 7727 5599 greaterlondontutors.com
Harrison Allen harrisonallen.co.uk
Holland Park Tuition recruitment@hollandparktuition.com 020 7034 0800 hollandparktuition.com
IPS Tutors info@ipstutors.co.uk 01509 265623 ipstutors.co.uk
Ivy Education ivyeducation.co.uk
Kensington & Chelsea Tutors tutors@kctutors.co.uk 020 7584 7987 kctutors.co.uk
Keystone Tutors enquiries@keystonetutors.com 020 7351 5908 keystonetutors.com
Kings Tutors emily@kingstutors.co.uk kingstutors.co.uk
Knightsbridge Tutors 07890 521390 knightsbridgetutors.co.uk
Laidlaw Education laidlaweducation.co.uk
Mentor & Sons andrei@mentorandsons.com 07861 680377 mentorandsons.com
Osborne Cawkwell enquiries@oc-ec.com 020 7584 5355 oc-ec.com
Personal Tutors admin@personal-tutor.co.uk personal-tutors.co.uk
Russell Education Group joe@russelleducationgroup.com n/a
Search Tutors searchtutors.co.uk
Select My Tutor info@selectmytutor.co.uk selectmytutor.co.uk
SGA Education s@sga-education.com sga-education.com
Simply Learning Tuition simplylearningtuition.co.uk
The Tutor Pages thetutorpages.com
Top Tutors 020 8349 2148 toptutors.co.uk
Tutor House info@tutorhouse.co.uk 020 7381 6253 tutorhouse.co.uk/
Tutor Hunt tutorhunt.com
Tutorfair tutorfair.com
Tutors International tutors-international.net
UK Tutors uktutors.com
Westminster Tutors exams@westminstertutors.co.uk 020 7584 1288 westminstertutors.co.uk
William Clarence Education steve@williamclarence.com 020 7412 8988 williamclarence.com
Winterwood  winterwoodtutors.co.uk

That’s obviously a long list, but, to give you an idea, I earned the most from Adrian Beckett (teacher training), Bespoke Tuition, Bonas MacFarlane, Harrison Allen, Keystone Tutors, Mentor & Sons, Personal Tutors and Shawcross Bligh.

Once you’ve been accepted by and started working for a few agencies, you’ll soon see the differences. Some offer higher rates, some the option to set your own rates, some provide a lot of work, some offer the best prospects of jobs abroad. It all depends what you’re looking for.

Where will the lessons take place?

When I first started tutoring, I had to cycle to all my clients. I put a limit of half an hour on my travel time, but it still took a lot of time and effort to get to my pupils. Fortunately, I’m now able to teach at my home, either in person or online using Skype and an electronic whiteboard, which means my effective hourly rate has gone up enormously. Travel is still a little bit of a problem for most tutors, though, and I certainly couldn’t have reached my pupils without having a bicycle. I didn’t have a car, and public transport wasn’t really an option in most cases. You just have to decide how far you’re prepared to go: the further it is, the more business you’ll get, but the longer it’ll take to get there and therefore the lower your effective hourly rate.

The other possibility, of course, is teaching abroad. I’ve been lucky enough to go on teaching assignments in Belarus, Greece, Hong Kong, Kenya, Russia, Switzerland and Turkey, and it’s a great way to see the world. The clients can sometimes be a little bit difficult, and the children can sometimes behave like spoiled brats (!), but staying with a great client in a sunny getaway overseas can be a wonderful experience. The only reason I don’t apply for more foreign postings is that I don’t want to let down my existing clients – going away for three weeks just before the 11+ exams in January would NOT go down well!

When will the lessons take place?

If you’re teaching children, lessons will usually be in the after-school slot between 1600 and 2000 or at weekends. That does limit the amount of hours you can teach, but it’s up to you how much you want to work. I used to work seven days a week, but I eventually gave myself a day off and then another, so I now work Sundays to Thursdays with Friday and Saturday off. During the holidays, you lose a lot of regular clients when they disappear to the Maldives or somewhere for six weeks (!), but others might ask for an intensive sequence of lessons to take advantage of the extra time available, and there’s obviously a greater chance of a foreign assignment. All that means that the work is very seasonal, so you should expect your earnings to go up and down a bit and plan your finances accordingly.

What should I do during the lesson?

I generally teach from past papers, so I ask pupils to do a past paper for their homework and then mark it during the following lesson. ‘Marking’ means marking the questions, obviously, but it also means ‘filling in the gaps’ in the pupil’s knowledge. If he or she is obviously struggling with something, it’s worth spending a few minutes explaining the topic and asking a few practice questions. I’ve written a few articles on common problem areas in English and Maths, such as commas and negative numbers, so I often go through one of those and ask the pupil’s parents to print it out and put it in a binder. After a few weeks, that collection of notes gradually turns into a ready-made revision guide for the exams.

If the parents want you to work on specific topics, that’s also possible. For example, one mother wanted to help her son with ratios, so she printed out dozens of past papers and circled the ratio questions for him to do. He soon got the knack!

I approach English in a slightly different way to begin with. There are two types of question in the 11+, comprehensions and creative writing, so I generally spend the first lesson teaching pupils how to do one of those. I go through my article on the subject online and then ask them to answer a practice question by following the procedure I’ve outlined. They usually finish it off for their homework. After a few weeks of stories or comprehensions, I’ll switch to the other topic and do the same with that. I also ask pupils to write down any new words or words they get wrong in a vocabulary book because building vocabulary is very important for any type of English exam (and also for Verbal Reasoning). I ask them to fold the pages over in the middle so that they can put the words on the left and the meanings on the right (if necessary). Every few weeks, I can then give them a spelling test. If they can spell the words correctly and tell me what they mean, they can tick them off in their vocab book. Once they’ve ticked off a whole page of words, they can tick that off, too! I usually try to reinforce the learning of words by asking pupils to tell me a story using as many words as possible from their spelling test. It can be a familiar fairy story or something they make up, but it just helps to move the words from the ‘passive’ memory to the ‘active memory’, meaning that they actually know how to use them themselves rather than just understand them when they see them on the page.

What homework should I set?

Most children who have private lessons have pretty busy schedules, so I don’t want to overburden them. I generally set one exercise that takes around 30-45 minutes. That might be a Maths paper or an English comprehension or story, but it obviously depends on the subject and the level. Just make sure that the student writes down what needs to be done – a lot of them forget! You should also make a note in your diary yourself, just so that you can check at the start of the next lesson if the work has been done.

What feedback should I give the parents?

I generally have a quick chat with the mother or father (or nanny) after the lesson to report on what we did during the lesson, what problems the child had and what homework I’ve set. This is also a good time to make any changes to the schedule, for instance if the family goes on holiday. If that’s not possible, I’ll email the client with a ‘lesson report’. Some agencies such as Bonas MacFarlane make this a part of their timesheet system.

How much will I get paid?

When I first started, I had absolutely no idea how much I was worth, and I ended up charging only £10 an hour, which is not much more than I pay my cleaner! Fortunately, a horrified friend pointed out that it should be ‘at least’ £35 an hour, and I upped my rates immediately. I now charge £60 an hour for private lessons, whether online or in person. Unfortunately, some agencies such as Fleet Tutors don’t allow you to set your own rates, so that’s one thing to bear in mind when deciding which agencies to work with. However, they did provide me with quite a bit of work when I first started, so it’s swings and roundabouts. The pay scale often varies depending on the age of the student and the level taught, so you’ll probably earn more for teaching older students at GCSE level or above if the agency sets the prices. If you have any private clients, you can obviously set whatever rate you like, depending on where you live, the age of your pupils, whether lessons are online or in person and so on. Personally, I only have one rate (although I used to charge an extra £5 for teaching two pupils at the same time), and I raise it by £5 every year to allow for inflation and extra demand. Tutoring is more and more popular than ever these days, and I read somewhere that over half of pupils in London have private lessons over the course of their school careers, so don’t sell yourself short! You should be able to make around £25,000 a year, which is not bad going for a couple of hours’ work a day!

Foreign jobs are a little different, and there is a ‘standard’ rate of around £800 a week including expenses. That means your flights and accommodation are all covered, and you can even earn a bit more on the side if you decide to rent out your home on Airbnb while you’re away! When it comes to day-to-day expenses such as taxis and food and drink, it’s important to negotiate that with the agency before accepting the job. It’s no good complaining about having to live in the client’s house and buy your own lunches when you’re in Moscow or Bratislava! It can be a dream job, but just make sure you look at it from every angle:

  • What subjects will I be teaching?
  • How many hours will I have to teach?
  • How many days off will I get per week?
  • Where will the lessons take place?
  • How do I get to and from my accommodation?
  • How long is the assignment? (I refuse anything more than three months.)
  • Where will I be staying? (NEVER at the client’s house!)
  • How old are the children?
  • Will I have any other responsibilities (eg ferrying the children to and from school)?
  • Do I need a visa?
  • What is the weekly rate?
  • What expenses are included (eg flights, accommodation, taxis, food, drink)?

How do I get paid?

Most agencies ask for a timesheet and pay their tutors monthly via BACS payments directly into their bank accounts. That’s a bit annoying from a cash flow point of view, but there’s not much you can do about it – other than using a different agency. When it comes to private clients, I generally ask for cash after the lesson, but it’s even more convenient if they can pay via standing order – as long as you can trust them! I once let a client rack up over £600 in fees because he tended to pay in big lump sums every few weeks, but then his business folded, and I had to use a Government website to try and chase him up. Fortunately, his wife saw the email and paid my bill, but it took months to sort out. Normally, though, the worst that happens is that a client just doesn’t have the right change and promises to pay the following week, so you just need to keep track of who owes what.

I hope all this helps. Good luck!

 

How do I make money from photography?

Adelie penguin jumping between two ice floes

The obvious question for a lot of amateur photographers is ‘How do I make money from photography?’ The answer, unfortunately, is that I don’t know. All I can do is tell you what I’ve done and give you a few ideas. I’m still learning the business after just four years, but my approach has always been to knock on as many doors as possible, whether it’s microstock, exhibitions, competitions, lessons or even talks. Every source of revenue has its part to play, and it’s just a question of working out where to focus your efforts. I make just under half my money from microstock/stock agencies and half from exhibitions, but everybody’s different.

Nick Dale Photography

I loved photography when I was a teenager. I bought (or was given) books on Henri Cartier-Bresson, Alfred Eisenstaedt, Ansel Adams and other great photographers, and I even bought myself an old Chinon CE-4 film SLR. I remember buying two 36-exposure films for it – one colour, one black and white – and using up every single frame in a couple of hours just taking pictures around the house! I took my camera on holiday to Majorca and the United States, developed pictures in a dark room at school and even talked to my mum about becoming a professional photographer. However, my mother said I could always take it up later – so that was that for 30 years! Fortunately, I was given a second chance in January 2013 when a friend of a friend invited me to climb Mount Kenya and go on safari with her and a couple of other people. I’d always wanted to go to Africa, but I’d foolishly been saving it for my honeymoon! As that didn’t seem very likely, I jumped at the chance.

My first digital camera was a Sony DSC-HX200V bridge camera, which means it had a good zoom range (both optical and digital), but not a very large sensor. As a result, it was only around £300 and therefore cheap enough for me to buy without worrying too much. Fortunately or unfortunately, a week in Kenya with people using proper Nikon SLRs gave me camera envy, and I bought a Nikon D800 SLR with a 28-300mm lens as soon as I got home!

And that was how it all started. I took hundreds of pictures in Kenya of the people, the landscape and especially the wildlife. When I got back, I bought an Apple MacBook Pro to work on them, upgraded the editing program to Aperture and then sent them off to various microstock agencies to see if they would help me sell them. It was hard at first, but getting the new camera helped, and I had a cash pile from remortgaging my flat in Notting Hill after another property purchase fell through, so I was able to go on plenty of trips to take more and more pictures.

An important breakthrough came when I sold a couple of prints for £100 each at my local tennis club’s Christmas Fair in November 2014, and another photographer told me about a cheap exhibition space called the Norman Plastow Gallery in Wimbledon Village. I’d always thought it would be very expensive to mount an exhibition, but this place was only £70 for a week, so I booked it as soon as I could! The only problem was that I didn’t have any actual prints to sell, and here I was very fortunate. I’d recently joined the Putney branch of London Independent Photography (or LIP), and there I’d met a very friendly and helpful chap called James, who’d offered to do all my printing for me at very low cost. After buying a few cheap, black, wooden frames from Amazon, I was all set. I invited all my friends to the exhibition in May 2015 – especially a group of tennis players from my club – and I ended up selling seven prints. As I was just starting out, I’d priced the small, medium and large framed prints at £80, £100 and £120 and the unframed ones at only £30, but I still managed to make £550 in total. The gallery hire charge was £200, and there were a few taxis to pay for plus incidental expenses, but the show actually turned a profit – unless you count the thousands of pounds I spent on buying camera equipment and flights to Kenya, Botswana, Antarctica and the Galápagos!

And there’s the rub. It’s relatively easy to generate revenue from photography, but actually making a profit out of it is another matter entirely. As a result, I have nothing but respect for the photographers I meet who have managed to make a career out of it. I’ve been on trips led by Paul Goldstein and Andy Skillen amongst others, and, in a way, that’s where I’d like to end up. Since that first show in Wimbledon Village, I’ve sold nearly 5,000 downloads through microstock agencies, sold 36 prints at solo exhibitions and art fairs, taught five photography students and given two or three talks to various clubs and societies. Overall, I’ve made around £12,000 from my photography – but that wouldn’t even have paid for my trip to Antarctica!

The problem is that everyone has a camera these days – even if it’s just an iPhone – and it’s almost ‘too easy’ to take pictures now that cameras are digital. The world is also a smaller place these days, with the arrival of cheap flights and a general rise in income and wealth. It takes a special talent to make it as a photographer, and part of that talent is being able to make the most of it.

What do I need to do first?

  1. Buy a camera
    If you want to make money out of photography, your first job is to get yourself a decent camera, and that means a digital SLR (or DSLR). The easiest way to earn cash is through so-called microstock agencies – which means selling pictures online in exchange for royalty payments – and they usually require shots to be taken with a camera that has at least 12 megapixels, if not more. You can obviously try to sell holiday snaps from your ‘back catalogue’, but, as I found out to my cost, it ain’t easy. Once you’ve decided to buy a DSLR, the two main brands to choose from are Nikon and Canon. There isn’t much between them these days, and the only reason I chose Nikon is that I didn’t want a camera from a company that made photocopiers! They both make good lenses, but, unfortunately, they have different mounts, so one you go with one or the other you’re locked in. I have various lenses ranging from an 18-35mm wide angle zoom to a 105mm macro lens for close-up work to an 80-400mm mid-range zoom, but I also rent an 800mm lens from Lenses for Hire whenever I go on a major wildlife photography trip.
  2. Buy a laptop
    If you don’t have one already, buying a decent laptop is great for photography. I take mine with me on all my trips, and it means that I can work on my images every evening after I get back from a shoot or a game drive. I should warn you, though, that the so-called RAW files from digital cameras are very large (in the case of my camera over 40MB each!), so I’d recommend getting as fast a processor as possible and as much memory and hard disk space as you can afford. You should also arrange a back-up system: the last thing you need is for your life’s work to disappear thanks to a software glitch! You could use an external hard drive, but I prefer backing up to the cloud just to be on the safe side. I use CrashPlan, which automatically detects any added, edited or deleted files and backs up the changes in real time, but there are other similar products out there.
  3. Subscribe to Lightroom
    Adobe Lightroom Creative Cloud is the choice of professionals and serious amateurs for organising and editing their photographs. It only costs around £8 a month (including Photoshop), and it’s a very powerful tool, as well as being relatively easy to use once you’ve mastered the basics. Digital photographs never come out of the camera looking perfect, so it’s always a good idea to try and improve the contrast, highlight and shadow areas and anything else you need to. If you’re selling through agencies, you’ll also need to add titles, captions and keywords (plus any other fields you’re asked to fill in), and all that is possible with Lightroom. It’s a pain to do for each individual photograph, but you can ‘synchronise’ any changes you make across a number of pictures, and you only need to do it once. If you’ve never used it before, I suggest you to do what I did and watch Anthony Morganti’s series of free YouTube videos on Lightroom. He takes you through all the functionality, and it’s an easy way to learn.
  4. Start taking pictures
    If you’re a wildlife photographer, this is just a euphemism for ‘spend thousands of pounds on trips to long-haul destinations’! However, you don’t have to travel far to take pictures. Whether you’re a landscape, portrait, Nature, fashion, wildlife, wedding or sports photographer, there’s always something photogenic not far from home, and you simply have to have the enthusiasm (and discipline) to be able to get out there and take more and better shots. Quality and quantity are both important. The quality of your images is ultimately what matters, but even a shot that’ll never win a competition might earn you money on a microstock site. I give my shots three stars if they’re good enough for Facebook, four if they’re good enough to be sold via agencies and five if they’re good enough to go on my website.
  5. Start marketing your work
    As a photographer, you have to learn to talk the talk as well as walk the walk. If you want to be taken seriously, you have to cover the basics, which means building a website, printing out business cards and having an active presence on social media. You can’t expect to win a bid for a photo shoot if you’re still using an old Hotmail address! Personally, I have this website powered by SquareSpace plus a Facebook ‘fan page’, a YouTube page, a LinkedIn account and a Twitter feed, all of which are printed on the back of my business cards. I post articles on my blog about photography trips, exhibitions and useful techniques (which also appear on Facebook, LinkedIn and Twitter), and I tweet and retweet a ‘Shot of the week’ (which gets fed through to my Facebook account as well).

Yes, but how can I make money?

  1. Microstock
    Microstock agencies are online intermediaries that accept work from photographers and then market those images to potential clients such as creative directors of newspapers, magazines and other buyers. The advantage of using them is that it’s ‘making money while you sleep’, in other words, it’s a passive income that you can build over time as you add more and more shots to your portfolio. Some agencies sell a lot of images but with low royalty rates, some the reverse, but here is the list of the ones I’ve used (in descending order of sales):
    Getty Images/iStock
    Shutterstock
    Adobe/fotolia
    DepositPhotos
    123RF
    Bigstock
    PIXTA
    SolidStockArt
    Dreamstime
    EyeEm
    Canstock
    photodune
    ClipDealer
    Panthermedia
    Pixoto
    featurePics
    Mostphotos
    Pond5
    500px
    Redbubble
    Alamy
    Yay Micro
    Stockfresh
    Crestock
    Zoonar
    Lobster Media

    I should mention that not all agencies will accept you, and not all your shots will be accepted by any agency that does, but you shouldn’t take it personally. I’ve had over £4,000 in microstock sales in the last four years, but my overall acceptance rate is only 41%! Even if your pictures are accepted, of course, that doesn’t mean they’ll sell. I’ve had 5,120 downloads from microstock sites, but only 1,521 individual shots have ever been sold out of a total of 4,389. The rest of them are just sitting there, waiting for a buyer. Every now and then, though, you take a picture that goes viral: I’ve sold my jumping penguin (see above) 705 times!
    The basic process is similar across all agencies. You add titles, captions and keywords to all your pictures and then export them as JPEG files to upload to each individual agency via their websites or an FTP service using a program like Filezilla. You then typically add the category, country or other data for each of them and submit them for approval. The agencies then approve the ones they like and reject the ones they don’t. After that, it’s just a question of watching the money rolling in! A useful way of doing that is by downloading an app called Microstockr. All you need to do is to set up your various agencies on the accounts page and then check the dashboard every now and then for any sales you’ve made. It’s very addictive! Sales should come quite soon after each batch is uploaded, but you may have to wait a while for payment. Most agencies have a ‘payment threshold’ of $50 or $100, which means your first payment (usually through PayPal) might take months to arrive. You’ll also need to keep adding more pictures. Buyers tend to sort images according to what’s most recent, so you definitely get diminishing returns from your shots, however good they are.
    The other thing to say is that, with dozens of agencies and hundreds or even thousands of images, it gets very confusing. As a result, I’ve created a spreadsheet to keep track of the whole thing. With filenames down the left and agency names across the top, I know if each file has been uploaded (‘u’), submitted (‘s’) or accepted (‘y’) and how many times it’s been sold. I keep a record of the dollar value of all the image downloads on a separate financial spreadsheet. I suggest you do the same.

  2. Stock agencies
    In the good old days, it was much easier to make a living out of stock photography, mainly because the royalty rates were a lot higher. The difference between ‘stock’ and ‘microstock’ is simply the average price level. Stock agencies want to differentiate themselves from microstock agencies (and everything else out there on the web) in order to charge a higher price, so they generally ask for exclusive agreements over one to five years and set a higher standard for acceptance. I use Design Pics, and you can see that they sell my images for hundreds of dollars rather than just a few dollars for the microstock agencies. My general strategy is to offer Design Pics the first pick of my pictures before sending the leftovers to all the microstock agencies. (I’ve also submitted some flower images to flowerphotos and a few marine wildlife shots to SeaPics, but I haven’t seen any sales from them so far.) Due to the long sales and reporting cycle, I didn’t see my first sale from Design Pics until more than a year after I’d signed up, but sales are starting to trickle in now, so it just takes a bit of patience. If you’re looking for a list of stock agencies, I recommend buying a copy of 2017 Photographer’s Market, which is the equivalent of the Writers’ and Artists’ Yearbook. It has comprehensive coverage of the industry, including helpful articles and a wealth of phone numbers and email addresses for magazines, book publishers, greeting card companies, stock agencies, advertising firms, competitions and more. I suggest buying the Kindle electronic version, and then you can download everything on to your laptop. I did that and then simply emailed every stock agency on the list – Design Pics was the only one to say yes!
  3. Competitions
    If you just want the ego boost of seeing yourself winning a competition, then I suggest you sign up with Pixoto and enter the contests with the lowest number of entrants. It’s a peer-to-peer site, and you can organise your own competitions, so there’s a very good chance of winning something! That’s exactly what I did, and I ended up with the Judge’s Award in four competitions. However, there isn’t much prestige to something like that, and it certainly doesn’t earn you any money. Alternatively, you can scour the 2017 Photographer’s Market for competitions, bearing in mind your chances of winning, the cost of entry, the potential prizes and the subject matter. The UK national press is a good place to start, too, and I recently won £250 in Wex Photographic vouchers in the weekly Sunday Times/Audley Travel Big Shot competition.
  4. Exhibitions
    Putting on an exhibition may seem like a big deal if you’ve never done it before, but it doesn’t have to be expensive or time-consuming. The Norman Plastow Gallery where I started out is cheap, but it’s slightly off the beaten path, and you have to man the exhibition yourself, which is obviously impossible for most full-time employees. You realise pretty soon as a freelance photographer that the most expensive item on your tab is often the opportunity cost of NOT doing what you usually do when you take time off. As a tutor, for instance, I could easily have earned £1,000 during the two weeks of my first exhibition, but them’s the breaks…
    If you’re looking for a list of galleries, www.galleries.co.uk is a useful starting point. London is obviously the best place to look, but exhibition spaces there don’t come cheap. I recently looked for galleries to use for an exhibition, and the ones in central London regularly quoted me thousands of pounds for a week! Everything is negotiable, though, so don’t give up.
    I started out with 15 prints at my first solo show, but I also printed out a few postcards and greetings cards. You might not make as much money out of them, but at least you’ll get something from punters who can’t afford a print. There are some who say that cards are just a distraction, but it’s so difficult to tell. I’ve had exhibitions with and without cards on sale, and it doesn’t seem to make much of a difference. However, the main reason for an exhibition is to sell prints, so that should be the focus.
    One of the problems you’ll almost certainly have is knowing how to price your work. Choosing your favourite shots is easy enough – although getting a second opinion from a friend is a useful exercise – but how much should you charge? I started off at £80 for an A3 print and ended up three years later at £2,000 for a 53″ x 38″ print, so you’ll just have to suck it and see. Andy Skillen suggested a mark-up of two-and-a-half times your printing and framing costs to make sure your cashflow remained positive, but that’s just a rule of thumb.
  5. Photo shoots
    Proper professional photographers make most of their money from photo shoots, but clients aren’t easy to find. If you’re a wedding photographer, I suppose you can put up flyers at various local venues such as churches and registry offices, but, for the rest of us, it’s just a question of plugging away, taking as many good shots as we can and putting them online so that as many potential clients can see them as possible. It would be a dream to be able to rely on commissions from wealthy clients who called us up whenever they wanted pictures of something. A photographer told me once about a group of directors who asked him for a picture of five hippos in a lake looking at the camera. He sent them all the hippo shots he had, but they weren’t happy. In the end, he told them if they didn’t want to compromise on the picture, then they’d have to send him on an all-expenses-paid trip to Zambia for a week. Which they did! He got the shot within a couple of days and then spent the rest of the trip taking pictures for himself! That sounds like a nice way to make a living, doesn’t it? However, until we’re well established enough with a good enough reputation to get those kinds of jobs, all we can do is keep on snapping and use the networks that we have. I’ve worked for a milliner, a local councillor, a businesswoman and others, but all my photo shoots have come from friends of friends or personal contacts. I’m not very good at networking – and it’s certainly not something I enjoy unless it happens naturally – but it’s very important in this business.
  6. Lessons
    I work as a private tutor as well as a photographer, so I guess it was an obvious fit to offer photography lessons. It’s finding the students that’s the real problem, though. One of my tuition agencies provided me with a couple of clients, while the rest came from connections I made at exhibitions and talks. You never know when you might meet just the right person, so it’s important to keep a few cards in your wallet just in case.
  7. Talks
    If you don’t mind public speaking, then giving a slideshow and talk on photography is an enjoyable way to earn some pocket money. Camera clubs and other groups won’t generally pay more than £100 (if anything at all!), but it’s also a useful chance to take along a few prints to sell and to hand out business cards. I got started after meeting a very nice woman on an Antarctic cruise, and I’ve now given talks at her branch of the WI, two camera clubs and a local library. If you want to be proactive about it, I’d simply Google camera clubs (or WI branches!) and email all of them to see what happens. As my mum used to say, you have to cast your bread upon the waters…even if it sometimes comes back a soggy mess!
  8. Photography trips
    One final way of making money is to lead photography trips. A lot of photographers do it to supplement their income, and it’s a good way to reduce your travel budget. I recently put together a list of tour operators and emailed them all one afternoon to find out if it could work, and I soon received a call from the founder of Gane & Marshall, asking me to lead a trip to Tanzania! I offered my services for free in exchange for the chance to go on an all-expenses-paid photographic safari. Now all we have to do is find at least five people to come on the trip and make it economic. Fingers crossed!

I hope all that was useful. If you have any more questions, please drop me a line at nick@nickdalephotography.com. It’s not easy becoming a professional photographer, but we can at least take pictures as a hobby while we wait for our big break.

Here’s to clicking and dreaming…

Basics of photography

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When you buy (or borrow), your first digital SLR, everything looks different, and it can be a bit worrying. What are all these buttons and dials for? Why is it so heavy? Where do I start? How do I change the shutter speed? All these are very good questions, and this is the place to find the answers!

Before we start, I should mention that I’m a Nikon user, and I have one D800 and one D810 camera body. The other major camera manufacturer is Canon, and they use slightly different terms for each function, but I’ll try and include both to make life easier.

Our first job is to cover the basics of photography: exposure and focus. Without understanding those two things, nothing else will make sense!

Exposure

Your first job as a photographer is to make sure that your images are well exposed, in other words, not too dark or too bright. Photographers talk about the ‘exposure triangle’, but that’s just a complicated way of saying that how dark or light a photograph is depends on three things: the shutter speed, the aperture and the ISO.

The level of exposure is measured in ‘stops’ or Exposure Values (EV), but what is a ‘stop’? Well, if you increase your exposure by a stop, the light is doubled (and vice versa). For example, if you lengthen your shutter speed from 1/200 of a second to 1/100 of a second, your shot will be twice as bright. They try to use round numbers, though, so the gap from 1/60 to 1/125 is obviously not quite right! The maths gets a bit more complicated when the gap is only 1/3 of a stop, but the idea is the same.

The built-in exposure meter in your camera will work out what the best exposure should be, but it has to make assumptions about the world that may not be true. To judge the ‘best’ exposure, the camera needs a starting point, and that is that the world is, by and large, 18% grey. If it assumes that to be true, then it can set the exposure accordingly. However, anyone who’s ever taken pictures of polar bears on the ice knows that that’s not always true! In order to make sure the camera is not fooled by very bright or very dark conditions, you need to use exposure compensation. If the scene is especially bright, you can dial in up to one or two stops of positive compensation. If it’s especially dark, you can do the opposite. It might take a few test shots to get it exactly right, but that’s better than coming home with lots of shots of grey bears!

Shutter speed (or Time Value if you have a Canon)

In the old days, cameras used film, and the shutter speed controlled how long it was exposed to the light in order to take the shot. These days, cameras are digital and have electronic sensors at the back, but the principle is still the same. The longer the shutter speed, the more light reaches the sensor and hence the brighter the image. The shorter the shutter speed, the less light reaches the sensor and hence the darker the image.

The shutter speed is measured in seconds and can be anything from 1/8000 of a second to 30 seconds or more. The amount of camera shake increases with the focal length, so the rule of thumb for general photography is to make sure your shutter speed is no less than the inverse of the length of your lens, eg if you’re using a 400mm lens, you should be using at least 1/400 of a second. Lens technology such as Nikon’s ‘Vibration Reduction’ or Canon’s ‘Image Stabilisation’ means that you might be able to get away with a couple of stops slower – ie 1/100 of a second – but that’s about it.

The reason why shutter speed is an important setting is that it controls how much (if any) motion blur there is in the image, and that is an artistic decision. Some people like shots of kingfishers catching a fish that look like they’re frozen in time, with every single water droplet sharp as a tack. Other people prefer shots of waterfalls shown with creamy torrents of water cascading over them. There isn’t a ‘right’ or ‘wrong’ answer. Just try both and see what you think.

Aperture

The aperture is simply the size of the hole in the lens through which light passes on its way to the sensor, and the principle is similar to that of the shutter speed. The bigger the aperture, the more light reaches the sensor and therefore the brighter the image. The smaller the aperture, the less light reaches the sensor and therefore the darker the image. The only thing difficult about it is the numbers, which often have a decimal point in them like f/5.6 or f/7.1. The reason the aperture is not always a nice round number is because it is what you get when you divide the focal length of the lens by the diameter of the hole. Neither of those numbers is necessarily going to be a nice round number, so the result of dividing one by the other certainly won’t be!

The aperture is measured in f-stops, which typically start at f/2.8, f/4 or f/5.6 and continue up to f/22 and beyond. A ‘fast’ lens is one that has a wide maximum aperture such as f/1.4. Photographers like fast lenses as they allow pictures to be taken in low light and offer great flexibility.

The reason why the aperture is such an important setting is that it controls the depth of field, which is the amount of the subject that is acceptably sharp. The human eye is drawn to things it can see clearly, so making sure the subject is sharp and the background is an ideal way to focus the viewer’s attention on an animal, say, but a landscape photographer might want his image to be sharp all the way from the boat in the foreground to the mountains on the horizon. Again, there is no right answer; the important thing is to experiment and find what works for you.

ISO (or ASA if you’re still using a film camera!)

The ISO used to measure the sensitivity of the film being used, a ‘fast’ film with a high ISO being more sensitive than a ‘slow’ film with a low ISO. Now that most cameras are digital, we get the same effect, just with an electronic sensor instead of film. You might think that extra sensitivity is a good thing – and it is – but it comes at a cost. The higher the ISO, the ‘grainier’ or ‘noisier’ the image, in other words, the less smooth it is.

ISO is measured in ISO (funnily enough!), which just stands for International Standards Organisation. The lowest value is usually ISO 100, and the highest might be 12,800 or more, although the image quality at that value wouldn’t be acceptable to most professional photographers.

Focus

Your second job as a photographer is to make sure that the subject of your images is in focus. In the old days of film cameras, there was obviously no such thing as ‘autofocus’, and focusing had to be done by manually turning a ring on the lens, but today’s digital cameras have very good systems for making sure the images are sharp. In using the autofocus system, your job is first of all to choose the correct settings and secondly to make sure the camera is focusing on the right part of the frame.

There are lots of different focus settings, but the basic choice is between single area, shown as AF-S (or one-shot AF for a Canon), and continuous, shown as AF-C (or AI Servo for a Canon). Single area looks to focus on the area of the image under the little red square in the viewfinder (which you can move around the frame manually); continuous does the same but follows the actual subject if it moves. The best version of this on Nikon cameras is called ‘3D’. The other setting you can change is which button actually does the job of focusing. The shutter button does that on most cameras, but the disadvantage of doing it that way is that the camera stops focusing when you take a picture, which is bad news if you’re tracking a cheetah running at 60mph! The alternative is to use ‘back-button focusing’, which means separating the jobs of focusing and taking pictures. The shutter button still takes the picture, but the focusing is done by pushing a button on the back of the camera. (You have to set this up yourself, but I use the AF-ON button, which I can press with my right thumb.)

Camera guide (based on the Nikon D800)

This guide won’t go through every single setting on a DSLR, but it will show how all the main buttons work, not by saying what each one does but by answering the obvious questions. I hope that’s the easier way to learn!

(All the numbers used are taken from the diagram at the top of this article.)

How do I switch it on?

That’s simple. Just turn the power switch on the top right-hand side (1) to ‘ON’ (and back to ‘OFF’ when you’ve finished). If you turn it to the light bulb symbol, that just lights up the LCD display on top of the camera.

How do I set it to Manual?

There are lots of exposure modes on a camera, such as aperture-priority, shutter-priority and program, but using anything other than manual is a bit like buying a Ferrari with an automatic gearbox – you just don’t get as much control (or satisfaction). To select manual, press the ‘Mode’ button (50) and turn the main command dial on the back right of the camera (31). This allows you to set the shutter speed, aperture and ISO yourself, although I usually set the ISO to ‘ISO-AUTO’ by pushing the ‘ISO’ button on the top left of the camera (56) and at the same time turning the sub-command dial (21).

How do I make sure I’m shooting in RAW?

Press the ‘QUAL’ button (47) and turn the main command dial until the word ‘RAW’ appears on its own. The word ‘RAW’ doesn’t actually stand for anything, but everyone writes it that way to show that it’s a file format that contains the ‘raw’ data from the sensor. The alternative is JPEG (which stands for Joint Photographic Experts Group), but that’s a compressed file format and therefore should not be used. Note that RAW files don’t end in ‘.RAW’. It’s just a generic term, so each manufacturer has its own RAW extension, such as Nikon’s .NEF.

How do I set the white balance?

Press the ‘WB’ button 57 and turn the main command dial (31) to whatever is right for the lighting conditions. The icons aren’t very easy to see, but the options are:

  • Incandescent (ie light bulbs)
  • Fluorescent
  • Direct sunlight
  • Flash
  • Cloudy
  • Shade
  • Choose colour temp
  • Preset manual

The white balance tells the camera the colour of the light you’re working with. It’s a bit like working out what colour the curtains are at the cinema. The camera can’t tell the difference between something white that’s lit by red light and something red that’s lit by white light, so the white balance setting just makes sure it makes the right call. If you can’t quite see the icons or want to set up a custom white balance or preset, you can always go through the menu system. However, if you’re shooting in RAW, you can always change the white balance later on your computer, so don’t feel bad about sticking with ‘AUTO’!

How do I set the focus mode?

First of all, make sure your lens is not set to ‘M’, or manual focus, and that the focus mode selector (18) is set to ‘AF’, or auto focus. After that, press the AF-mode button (17) and at the same time turn the main command dial (31) to choose single area or – preferably – continuous. If you want the 3D option, you press the same button but at the same time turn the sub-command dial (21) until the LCD screen shows ‘3D’.

How do I set up back button focusing?

Press the ‘MENU’ button (46), scroll to the menu item with the pencil icon, select ‘a Autofocus’ and then set ‘a4 AF activation’ to ‘AF-ON only’. Half-pressing the shutter-release button won’t work any more, so don’t forget to focus by pressing (and holding) the AF-ON button (30) with your right thumb while you shoot.

How do I set the shutter speed?

Half-press the shutter-release button (3) if the shutter speed is not illuminated in the viewfinder or on the LCD screen and then turn the main command dial (31).

How do I set the aperture?

Half-press the shutter-release button (3) if the aperture is not illuminated in the viewfinder or on the LCD screen and then turn the sub-command dial (21).

How do I set the shutter-release button to continuous shooting?

Press the release button next to the ‘D800’ symbol and turn the release mode dial (48) to ‘CH’, or Continuous High. The D800 can shoot five frames a second.

How do I move the focus point in the viewfinder?

Turn the focus selector lock switch (34) to the dot symbol (rather than ‘L’ for lock) and use the multi selector to move the focus point anywhere within the central area of the viewfinder.

How do I check the depth-of-field?

Press the depth-of-field preview button (20).

How do I set the shutter-release button to continuous shooting?

Press the release button next to the ‘D800’ symbol and turn the release mode dial (48) to ‘CH’, or Continuous High. The D800 can shoot five frames a second.

How do I add exposure compensation?

Press the exposure compensation button (52) and at the same time turn the main command dial (31) to add or subtract as many stops of compensation as you need.

How do I bracket my shots?

Press the ‘BKT’ bracketing button (55) and at the same time use the main command dial (31) to choose the number of frames (3-9) and/or the sub-command dial (21) to choose the exposure interval (from 0.3 to 1 stop).

How do I shoot video?

You have to use the monitor rather than the viewfinder for this, so first of all turn the live view selector (36) to the film camera icon, press the live view button and then, when you’re ready, press the red movie-record button to start (and stop) video recording.

How do I look at my pictures?

Just press the playback button (22) and scroll through the images using the multi selector (32). To zoom in, either use the playback zoom in/zoom out buttons (43, 44) or set up the multi selector centre button to zoom immediately to 100%. This is very useful to check that images are acceptably sharp. To do that, press the ‘MENU’ button (46), select ‘f Controls’, then ‘f2 Multi selector centre button’ and set ‘Playback mode’ to ‘Zoom on/off’ with ‘Medium magnification’.
To play videos, just press the multi selector centre button (32).

How do I delete my pictures?

Just press the delete button (23). If you want to delete all the pictures on the memory card, the best way is to format it. Press the ‘MENU’ button, select ‘Format memory card’ and then select the appropriate card, either the small, thin Secure Digital (SD) card or the thicker, bigger Compact Flash (CF) card.

Rules of composition

As everyone knows, “Those who can, do; those who can’t, teach” – but that doesn’t stop me trying to do both!

Whatever kind of photographer you are and whatever kind of pictures you take, you always need to pay attention to composition. As an introductory guide (or a reminder), here are a few principles of composition to help you take better pictures. Just make sure you break all of them once in a while!

Rule of thirds

The most common rule in photography is the rule of thirds. The aim of the game here is avoid taking pictures that are too symmetrical. For some reason, the human eye doesn’t like that, so it’s usually best to place the subject off-centre. The rule of thirds is just one way to do that. Others include the golden ratio or the Fibonacci curve, and you can find them in Lightroom if you really want to, but the rule of thirds is the best and the simplest. The idea is that you imagine that the viewfinder is divided up into thirds – both horizontally and vertically – and place the subject at the intersection of two of those invisible lines in order to give it more impact. The lines also help you to place the horizon when you’re taking a landscape shot. If the horizon is in the middle of the frame, it looks a bit static. Instead, try to establish whether most of the interest is in the land or the sky. If you want people to focus on the land, place the horizon on the lower imaginary line; if you want people to focus on the clouds in the sky, place it on the upper one. Just make sure that it’s straight!

Moth on a daisy
‘The Decisive Moment’

Henri Cartier-Bresson was a French photographer considered a master of candid photography. He pioneered the genre of street photography. The Decisive Moment was the title of a book he wrote, and his idea was that timing is the secret of a good photograph. This is obviously more important in certain types of photography (such as wildlife) than others (such as landscape), but it is still a useful guide to taking any kind of action shot.

Bear about to catch salmon in mouth


Framing

Every photograph obviously has a frame, but have you ever tried using a ‘frame-within-a-frame’? Photographic frames come in all shapes and sizes, and so do the ones you find in real life. It might be the branches of a tree or a doorway or a window – the point is that it adds depth to a picture and focuses the viewer’s attention.


Negative space

I don’t know why people call it ‘negative space’ rather than just ‘space’ (!), but the idea is that a picture with a single subject can look more balanced if there is empty space on the other side of the frame. This is particularly useful for portraits if you want to stop them looking like ‘passport photos’! It’s also a good idea to allow space for a moving subject to move into. It just looks weird if a person appears to be ‘walking out of the frame’, so try to position the subject around a third of the way across in order to draw the eye into the picture rather than out of it.


Leading lines

Leading lines are supposed to ‘lead’ the eye of the viewer into the frame – and ideally towards the main subject. They don’t have to be straight, but they tend to work best when they are. The obvious examples are railway tracks or a long, straight road stretching into the distance. S-curves can do the same job as leading lines, but they also add dynamism and visual interest to a photograph, particularly if it’s a landscape. Again, it might be a road or a railway or even a winding river. All that matters is that the line is roughly in the shape of an S, meandering left and right into the distance.


Symmetry

The rule of thirds and others are meant to stop pictures looking too symmetrical, but sometimes symmetry suits the subject matter. If you have a reflection in the water or a human face, for example, you can’t really avoid it, so it’s sometimes best to make the most of it. That might mean positioning the line where the water meets the line exactly in the centre of the frame or choosing a square aspect ratio for the picture to enhance the symmetry of a face.

Juvenile rufescent tiger heron stretching its wings


Point of view

I’m a wildlife photographer, and the most important rule of wildlife photography is to get down to eye-level with the animals. It makes a huge difference to the composition and elevates a quick snap to an intimate portrait. Taking pictures at eye level sometimes means getting wet or muddy – especially if you’re taking pictures of insects on the ground! – but it’s the best way to go. The same applies to portraits, which usually look best taken at eye-level or above. If you get down any lower than that, you take the risk of ending up with a close-up of the model’s nostrils!

Close-up of lion lying in golden light


Motion blur

A photograph is just a static image, so it’s sometimes difficult to convey a sense of motion. One way to do that is to use a slower shutter speed in order to create motion blur. Different subjects require different shutter speeds, depending on how fast they are moving, so you might need to experiment a little bit to find that sweet spot between too much sharpness and too little. You could start with 1/4 of a second for a pedestrian walking along the street, but a Formula One car would disappear if you didn’t cut that down to 1/250 or slower. If you want to go the whole hog, you might try the ‘slow pan’. Panning just means moving the camera from side-to-side to keep a moving subject in the same part of the frame. The ‘slow’ bit relates to the shutter speed. What you get with a ‘slow pan’ should be a recognisable subject with relatively sharp eyes but blurred limbs (or wings) and a blurred background. I warn you that this is a tricky business – I once took 1,500 slow pan pictures of guillemots in the Arctic and only kept four of them! – but it’s worth it when it works…

Male azure hawker dragonfly flying through undergrowth


Depth of field

Another crucial element in wildlife and other kinds of photography is depth of field. To make sure the focus is on the subject and separate it from the background, you can use a larger aperture (such as f/4 or f/2.8). That will blur anything that’s not in the same plane as the subject while keeping the focal point sharp. The eyes are always the most important part of a portrait – whether it’s of an animal or a person – and we will always see something as being ‘in focus’ as long as they look sharp. Depth of field is just as important in landscapes, but what we generally want now is sharpness all the way through the image, so it’s better to start with a smaller aperture such as f/11 or f/16.

Cobra held by snake charmer


Odd numbers

One of the funny things about the way people see the world is that we seem to like odd-numbered groups of objects more than even-numbered ones. It doesn’t really matter why, I guess, but it’s an important point to remember when planning something like a still-life shoot. Just make sure you have three or five tomatoes rather than two or four!


Fill the frame

Everyone has a camera these days because everyone has a mobile phone, but one of the problems with using your mobile to take pictures is that it’s hard to ‘fill the frame’. It’s all very well taking a selfie when you’re only a few inches from the lens, but trying to zoom in on a distant object or animal is difficult when you only have a few megapixels to play with. It’s important to remember here the difference between ‘optical zoom’ and ‘digital zoom’. The optical version is what you get naturally with a DSLR lens when you zoom in by changing the focal length; the digital version is when a phone or a bridge camera fools you into thinking you’re zooming in by focusing on a smaller and smaller portion of the sensor. It’s great when you look through the viewfinder or look at the back of the camera, but the image quality is a lot poorer. Anyway, the point is that what you really want to do is to make the subject dominate the image by making it as large as possible. If you’re taking a picture of a cheetah, you don’t want it to be a dot in the corner of the frame! You can always crop the image later using Lightroom or another editing program, but that means losing pixels, so the quality will suffer. It’s always better to get it right in camera if you can. You just need to be careful not to chop off body parts in the wrong place when you’re taking a portrait. Generally, it’s fine to crop in on someone’s face so that the top of the model’s head is not shown, but it’s not a good idea to crop people’s bodies at the joints. It just looks odd if the edge of the frame coincides with the ankles, knees, waist, elbows, wrists or neck.

Close-up of golden eagle head with catchlight


Aspect ratio

For some reason, taking a picture in landscape format just seems more ‘natural’ than turning the camera 90 degrees for a portrait, but it’s important to choose the ‘right’ aspect ratio for the image. A photographer once advised me to make sure at least a third of my pictures were in portrait format, but the point is to look at the subject and decide what’s best. If there are a lot of horizontal lines, then landscape is fair enough, but if there are more vertical lines – such as tree trunks in a forest – then you should probably choose portrait instead. If you really want to emphasise the length (or height) of a subject, why not try a panorama instead? Different cameras have different set-ups, but the average aspect ratio of a DSLR is 3:2, which doesn’t suit all subjects. I’ve set up a 3:1 template in Lightroom to use for images in which nothing much is happening at the bottom and top of the frame.

Pig peeping out from behind wall


Foreground interest

When we see a beautiful view, most people’s instant reaction is to take a picture, but what we end up with a lot of the time is an image without any focus. Placing an object in the foreground can lead the eye into the frame and give the image balance. A picture taken on the beach, for instance, might be improved by getting down low in front of a weird rock or piece of driftwood.


Balance

Speaking of balance, it can be a good idea to have the main subject on one side of the frame and a smaller subject on the other. Again, it’s just a matter of what looks most satisfying to the human eye.


Juxtaposition

Old and new, blue and orange, large and small – all these are contrasts that a photograph can pick up on and emphasise. This kind of juxtaposition can be made the point of an image. Think of an elephant beside a mouse – it’s not a picture of an elephant or a picture of a mouse, it’s a picture of the contrast between the two.


Patterns, textures and colours

Sometimes, you don’t need a traditional ‘subject’ to make an image visually interesting. There are plenty of patterns in Nature or in the man-made environment; the trick is to find them amongst all the surrounding clutter. Whether it’s the bark of a tree or paint peeling on a wall, you can sometimes get a very effective abstract image out of it. Black and white images tend to emphasise patterns and shapes, as there is no colour to distract the eye, but colours can form patterns as well – it just depends on the subject and your personal preference.


Simplicity

It’s hard to produce a visually striking image if there is no focal point, or if there are too many competing centres of attention. By creating a simple image – in terms of colour and/or composition – you can remove the distractions and focus on what’s important.


Background

To increase the focus on the subject of an image, it’s a good idea to remove any distractions in the background. It’s obviously not a good idea to take a picture of someone with a telegraph pole sticking out of his head (!), but it’s easy to pay too much attention to the subject and not enough to the background unless you consciously check the viewfinder. One useful way to reduce the chances of an embarrassing blunder is to reduce the depth of field by increasing the size of the aperture. The traditional way of taking portraits of animals or people, for instance, is to use a ‘fast’ lens, which means one that has a very wide maximum aperture, and shoot wide open. That reduces the depth of field, thus blurring the background and adding to the impact of the main subject. If you have lights in the background, you can even get a nice effect called ‘bokeh’, which works well for something like a bauble with Christmas tree lights in the background.

Malachite kingfisher on dead branch facing camera


Humour

Whatever you’re photographing, there are always odd moments of humour to be found. People and animals are usually the best sources, but it doesn’t really matter what the subject is. If there’s a visual joke to be made, why not have a go? I laughed when I saw these penguins together on South Georgia. It looked as if the female was confused by the rock. Was it an egg she was supposed to hatch, or was it just a rock? She spent about five minutes looking at it and examining it before the male came up and said something like, “Come on, darling. It’s just a rock…”

King penguin stepping over rock with another


Breaking the rules

Having said all that, it’s important to break the rules once in a while. Rules tend to set expectations, so breaking them can make an image seem fresh and original. Why should the horizon be straight? Why should we see the whole face rather than just half of it? Why should the sky start two-thirds of the way up the frame? If you can’t answer these questions, then why not take a risk? It’s a bit like being a painter: you have to be able to follow the rules before you can break them!

If you’d like to know more or want to book a photography lesson with me, then please get in touch.

Good luck…

Getting the most out of game drives

The one that got away

This would’ve been a great shot. It could’ve been a great shot. It should’ve been a great shot. But it wasn’t. Why? Motion blur. If you look closely, you can see that the whole body is slightly out of focus, and that was simply because I didn’t think to change my shutter speed. I was parked in a jeep in Botswana when a herd of impala came chasing across the road. They were galloping fast, but there were five or six of them, so I did have time to focus on each of them, one by one, as they crossed the road in turn. Unfortunately, I was using my default camera settings that were designed to capture animals that were standing still. I was using an 80-400mm lens, so I had my camera on 1/320 and f/8 with auto ISO. That would normally have worked, but not for a jumping impala! What I really needed was a shutter speed of at least 1/1000 of a second. I just didn’t think…

In order to avoid moments like that, here are my answers to a few obvious questions:

What equipment do I need?

Good question. It’s obviously too late to do anything once you’re on safari, so it pays to get your equipment sorted out beforehand. People often ask me what camera I use, and it reminds me of a story I heard about Ernest Hemingway. He went to a photography exhibition in New York and was so impressed he asked to meet the photographer.

Hemingway: These pictures are great. What camera do you use?

Photographer: Well, I use a Leica with a 50mm lens for most of my shots. I’m actually a big fan of your work, too, Mr Hemingway. I’ve read all your books. Can I just ask: what typewriter do you use…?

The point is obviously that a good camera doesn’t necessarily make a good picture, and it’s mildly insulting to photographers if you ask about their equipment without complimenting them on their talent! However, all other things being equal, a good camera can make life a lot easier for wildlife photography. I’d suggest getting a full-frame DSLR with a zoom lens with a maximum focal length of at least 300mm, preferably 400mm or more. The problem with a bridge or DX camera is that you won’t get the quality you’re after, as they don’t have large enough sensors. I started off with a bridge camera and thought the zoom was great – until I saw the Nikon DSLR one of the other guys had! I had a severe case of ‘camera envy’, so I emailed a friend of mine who was a professional photographer to ask what he would get. He recommended either Nikon or Canon, but Canon made photocopiers, so that was out of the question! Instead, I bought myself a Nikon D800 – complete with 36.3 megapixels! – and it’s served me well ever since. I now also have a D810, which is an upgraded version of the D800. Having two cameras means I don’t have to worry about changing lenses. Instead, I carry them both cameras on a SpiderPro holster that looks a bit like an old Western cowboy’s gun belt. I can take them out and put them back with just one hand, and I can lock them in place if I’m going on a boat ride or clambering over rocks and don’t want to take any chances.

As for lenses, I mainly use an 80-400mm on the D800 and rent an 800mm prime on the D810. They’re both made by Nikon, and for a very good reason. I tried a Sigma 50-500mm and then a Tamron 150-600mm lens, but the images just weren’t sharp enough. I now manually check the autofocus of all my lenses using Reikan Focal automatic lens calibration software. All you do is print out a ‘target’ and set up your camera on a tripod to take pictures of it from a certain distance away. Once you load the software, it guides you through the set-up and takes a number of exposures automatically, just asking you to change the manual focus adjustment anywhere from -20 to +20. When the routine is finished, it gives you a PDF report showing the optimal adjustment value – and that’s what persuaded me to use only Nikon lenses. I’d been on a trip to Svalbard and wasn’t happy with my shots of the polar bears, which were all just a little bit soft. One of the other guys on the trip told me he did a manual focus check, and that’s when I started doing it, too. It was only when I bought my new 80-400mm lens that I realised the huge difference in sharpness: the Sigma and Tamron were down at around 1400 on the numeric scale, and the Nikon was way up at 2200! In short, check your lenses. They’re mass-produced items, so there’s always bound to be some slight variation in focus, and you’d rather fix it yourself than have to use it as an excuse when you don’t get the sharpness you want.

I also make sure I always pack a polarising filter together with a lens cleaning kit (with sensor swabs and cleaning fluid), a beanbag (for resting the lens on the windowsill of a jeep) and my laptop (so that I can download and work on my pictures in the evening). If I’m going to be near a waterfall, like Iguazu or Victoria Falls, I’ll also take my tripod and a ‘Big Stopper’ neutral density filter to give me the chance of taking creamy pictures of the water with a  long shutter speed.

What else can I do before I leave?

Getting the right equipment (and changing the time zone on your camera!) is one thing, but you can help yourself out by booking the right holiday in the right location at the right time. Check when the ‘long rains’ are if you’re going to Africa. Check when the peak season is for wildlife viewing. Check if it’s possible to visit when there’s a full moon or – even better – a harvest moon. You can ask all these questions (and more) to make sure you get the very most out of your trip. One useful sight for African expeditions is Safari Bookings, which allows you to search for packages by location, duration and price. I also like to travel light. I hate the whole airport experience, so I avoid having to check any bags in by having a roll-aboard camera bag and packing all my clothing into a jacket that has a pocket in the lining that goes all the way round. It looks a bit funny when you walk through customs – and some people just couldn’t do it – but it saves me an awful lot of time and bother.

What should I wear?

When it comes to clothing, I tend to cover up to avoid the sun and the insects. That means I wear green cargo pants (with lots of pockets!), a brown, long-sleeved shirt, a floppy hat and trainers. If I’m going on a walking safari, I’ll put on my hiking boots, and I might bring a jacket for those cool early morning starts. There’s a reason why I don’t wear bright colours. They don’t exactly frighten the animals, but you’ll get some funny looks if you turn up in hot pants and a Day-Glo pink T-shirt…!

What should I take with me on the game drives?

If you’re a keen photographer, you won’t want to miss anything while you’re out taking pictures from the 4×4, but that doesn’t mean you need to take the entire contents of your camera bag! I would simply take your camera(s) and your longest lens(es) plus a lens cloth, a couple of spare batteries and a bottle of water. A beanbag might come in handy on certain vehicles, but that’s about it. You can apply sunscreen and/or insect repellent before you leave. When it comes to clothing, I tend to cover up to avoid the sun and the insects. That means I wear cargo pants (with lots of pockets!), a long-sleeved shirt, a floppy hat and trainers. Oh, and don’t even think about wearing a day-glo orange or pink T-shirt…!

What camera settings should I use?

There’s an old photographer’s joke:

Fan to photographer: I love your pictures. What settings did you use?

Photographer to fan: f/8 and be there!

The point is that ‘being there’ is more important than any camera settings, but that doesn’t mean they don’t matter at all – as shown by my shot of the leaping impala.

Exposure

The ‘Exposure Triangle’ consists of the aperture, shutter speed and ISO value, and these are the only three ways you can change the brightness of the image: either having a bigger hole, keeping it open for longer or increasing the sensitivity of the sensor. A lot of beginners stick to automatic as they don’t trust themselves to use manual settings, but they lose a lot of control by doing that. The camera doesn’t know how fast the animal is travelling or how much of it you want to be in focus, so how can it possibly decide the best combination of shutter speed and aperture? Why not experiment a little and decide for yourself the kind of image you’re going to take? Now, you still have to make sure you get the correct exposure somehow, and I’m not suggesting you use the exposure meter and manually change the settings for each shot! What I do is start off with a good set of general-purpose settings and set the ISO to automatic. That way, I get exactly the shutter speed and aperture I want, but the camera makes sure it’s correctly exposed. The general rule is that you need a shutter speed the inverse of your focal length, so, If I’m using my 80-400mm lens at the top end of the zoom range, that means around 1/400th of a second. (Bear in mind, though, that you have to take into account the speed of the animal as well as how steady you can hold the camera!) I generally like to take ‘portraits’ of the animals, so I want to throw the background out of focus to emphasise the eyes. That means a wide aperture such as f/5.6, but I’ve started using f/8 because my lens tests tell me that both my lenses perform at their sharpest at f/8, and I want the maximum sharpness I can get. The problem comes, obviously, when there’s not enough light to use your default settings, or the animals are moving too fast. That’s when you need to take charge and make a difficult decision: which is the most important, the shutter speed, the aperture or the ISO? If it’s a fast-moving animal, the shutter speed obviously takes priority. If the light level is dropping, then you probably want to compromise and change both aperture and shutter speed by 1/3 of a stop (or more). Most stock agencies don’t want pictures taken at high ISO values (640+), so that’s something to bear in mind if you’re trying to sell your work.

Autofocus

Manual focus has its place in macro photography and in low light conditions, but wildlife photography generally demands that we use one of the two methods of autofocus: single point (AF-S on the Nikon) or continuous (AF-C). I generally keep my D800 with the wide-angle lens on single point, as I’ll be using it to take landscape shots, but I keep my D810 with the long zoom lens on AF-C 3D, as I’ll be using it to take pictures of animals. In fact, sharpness is so important for wildlife shots that I use what’s called ‘back-button focusing’, which means setting up the camera so that I can focus by pressing the AF-ON button on the back with my right thumb. The AF-C 3D setting continuously focuses on one particular point on the animal that you select when you first press the AF button, and it magically follows that point even if the animal is moving. It’s not perfect, but what it does mean is that you don’t have to worry about losing focus when you half-press the shutter and then take a picture. By separating the focusing from releasing the shutter, you get the best chance of getting that all-important sharpness in the animal’s eye.

White balance

You can always change it in Lightroom later (or another image-processing software package), but I generally still try to update my white balance setting as the light changes. It saves time later, and it follows the general principle of trying to get everything right in camera. Messing around in Lightroom should always be a last resort.

Quality (RAW)

Shoot in RAW. There. Is. No. Alternative.

Other settings

One of the confusing and frustrating thing about the DSLR is the number of settings there are and the fact that you can’t ‘reset’ everything in one go. It would be wonderful if there were one button that would do everything, but there isn’t. There are mechanical as well as electronic settings, so it’s impossible to assign one button to change both. As it is, it’s worth having a mental checklist to go through before you go out on the game drive and even while you’re out there. The main settings to monitor are the following:

  • Mode (Manual, unless you’ve never picked up a camera before…)
  • Shutter speed (1/focal length, although Vibration Reduction means you might get away with up to four stops ‘slower’)
  • Aperture (f/5.6 or f/8, depending on where your lens’s sweet spot is)
  • ISO mode (I generally use ‘auto’)
  • Exposure compensation (0 – unless you’re photographing a very bright or dark scene)
  • Autofocus (AF-C 3D for wildlife)
  • White balance (Daylight – if it’s your typical African sunny day!)
  • Active D-lighting (Auto or off unless you’re taking a picture into the sun and want detail in the shot – it’s a kind of in-camera HDR to squeeze the histogram for images that would be too contrasty otherwise)
  • Lens lock (off, obviously – you don’t want to miss a shot because you can’t zoom in!)

What should I do while we’re driving around?

It’s all very well chatting to the guy next to you and having a laugh, but you’re there to take pictures, so you should follow these guidelines if you don’t want to be disappointed:

  • Always keep an eye out. I try to sit in the front seat so that I get a better view and can let the driver and the rest of the group know if I see something. If it’s not particularly interesting or too far away to get a good shot, I’ll just point or say, “Impala,” but I’m always ready to pat the driver on the shoulder or tell him to stop if there’s the prospect of a good sighting. One of the best sightings I had in Botswana came from the cook’s assistant sitting in the back of the jeep. As we were driving along, he suddenly said something in Setswana to our driver, who stopped and then backed up to see what was going on. After another incomprehensible conversation, I was shown a spotted eagle owl sitting on a branch not 10 yards away!
  • Don’t be shy. The guide will often be the one to spot an animal or a bird, and he or she will usually stop without having to be asked. However, if you spot something and want to take a picture, it’s important to stand up for yourself. Just tap the driver on the shoulder or ask him to stop. You always remember the shots you missed more than the shots you made, so be brave!
  • Be prepared. A lot of game drives involve looking at nothing in particular for hours on end, but that doesn’t mean you shouldn’t be ready at all times. You never know when someone will spot a white rhino or a leopard, so you need to make sure you have your camera(s) to hand with the right shutter speed, aperture and other settings dialled in. I tend to use 1/000 of a second at f/8 with auto ISO, but it depends on the light level. In the early mornings, you often have to make some awkward compromises. Just remember, though, that it’s better to get a sharp shot at a high ISO than a blurred one at ISO 100 and 1/60!
  • Keep the noise down. An animal or bird might seem quite far away, but they spook quite easily, so do make sure you don’t speak too loudly – or shout out something in your excitement! The other guests will thank you for it…
  • Keep still. You’re usually in a jeep with three or four other people, all wanting to take the best photographs they can, so you have to be sympathetic with your movements. If someone’s trying to take a picture, try to move as carefully and slowly as you can – or just wait for them to finish. You don’t want to rock the vehicle or jog an elbow and ruin the perfect shot!
  • Be polite. Tempers sometimes fray in the excitement of a game drive, when everyone wants to get the best possible view of the animals, but it’s worth keeping cool and being aware of those around you. If you take too long over a shot or you accidentally get in the way of someone else, just apologise and move on. People go on safari to enjoy themselves and have a good time, not harbour festering grudges over the guy who thought it was all about him…!
  • Take care of your kit. I always cover my lenses with dust- and waterproof covers when I’m shooting. It might not seem necessary in some countries and in some climates, but you never know when you might have a sudden shower or get a cloud of dust in your face from the jeep in front. I also take a lens cloth and/or a dust blower with me on game drives, and it’s worth checking your lens every now and then to make sure it’s not getting dusty. It’s hard to tell sometimes when you have a lens hood on, but it’s very easy for lenses to get dirty during the course of a long game drive. I found Botswana particularly dusty, and there was a lot of dust in the air in Tadoba that gradually stuck to my camera and turned my lens cloth red whenever I used it!

What makes a good photograph?

Dust, air and spume. That’s the Holy Trinity of wildlife photography, according to Paul Goldstein, who is a wildlife photographer and also a great speaker and raconteur. I’ve been on two trips he’s led to Svalbard to see the polar bear and Tadoba in India to see the tiger, and I’ve seen several of his presentations. The idea is that ‘dust’ is thrown up by the movement of the animals and gives you a sense of dynamism and energy, ‘air’ means that an animal is in the air and about to land – so we have a sense of anticipation and expectation – and ‘spume’ is the spray that is thrown up by movement in water.

That’s just Paul’s view, and there are obviously other aspects to the question. One thing that he also points out is the difference between a ‘record shot’ and a ‘photograph’. To him, a ‘record shot’ is just a snapshot, a picture that records exactly what’s in front of you, but a ‘photograph’ is something that obeys the rules of composition and has been consciously constructed by the photographer to provoke an emotional reaction. There aren’t that many rules of composition in wildlife photography, but it’s worth bearing them in mind when you’re out shooting. Here are a few of the common ones:

  • Fill the frame. Robert Capa once said: “If your pictures aren’t good enough, you aren’t close enough.” People don’t want to have to search the image for the animal, so zoom in or ask your driver to get closer so that you can make it the centre of attention!
  • Use leading lines. Where available, they can lead the eye of the viewer into the image, for instance in a picture of an impala on the horizon crossing a road leading into the distance.
  • Use the Rule of Thirds. Human eyes don’t like things that are too symmetrical – unless you can manage a perfect reflection – so try to put the focal point of your shot off-centre. That adds dynamism and a different kind of balance.
  • Focus on the eyes. People don’t care if 99% of an animal is out of focus as long as the eyes are sharp.
  • Wait for ‘the decisive moment’. A guide in the States once compared my shots to those of another guy on the trip. He said that Stefan’s were always technically perfect, very sharp and with gorgeous, saturated colours, but mine were all about the moment. I take that as a compliment. It means you have to wait for the right moment to take the shot. Don’t just keep clicking away like a Japanese tourist by Big Ben. Compose your shot and then wait for the animal to do something to make it more memorable. It could be a sneeze, a yawn – anything! – but it will mark your picture out as special. Here are a couple of examples:
    • If a lion is walking across the road in front of your jeep, don’t take the shot until it steps forward with the leg that’s furthest away from you. That means it will have to turn its body and show more of its chest in the shot, which makes a better shot.
    • Try to capture pictures of birds in flight. Portraits are all very well, but an action shot is usually better. Given how quickly birds take off, the best way to capture them with their wings spread is just before they land. Find a bird on a branch and take a few ‘portrait’ shots, but don’t give up when it flies away. A lot of birds have a ‘favourite’ branch, so it’s worth focusing on it and waiting for the bird to come back. If it does, take a series of shots in continuous mode, starting when the bird is just about to land. That’s the best way to capture the prize, which is a picture of the bird with its wings spread, showing off all its plumage. Just make sure you have reasonable depth of field (at least f/8) and a high enough shutter speed (at least 1/1000).
  • Tell a story. The tagline to this website is ‘Every picture tells a story’, and that’s a goal we should all aspire to when taking pictures. What are we trying to say? What mood are we trying to create? What’s the emotion behind the shot? It’s not always easy, but picking exactly the right composition can create humour, joy, sorrow, horror and any number of other powerful reactions – which is just what we want.
  • Break the rules – selectively! Obeying the rules will give you a nice, balanced image, but Paul for one hates ‘nice’, and I can see his point. Sometimes, the best way of creating a strongly emotional image is to break a rule or two. You have to do it sparingly – and consciously – but it sometimes gives you that much more of a chance of creating a genuinely arresting image. One of his favourite techniques is the ‘slow pan’, which means following a moving animal or bird with a slow shutter speed and taking a number of shots as it goes past. The idea is to create a sense of movement by blurring the background and the legs or wings of the animal or bird while keeping the body and especially the eyes sharp. It’s a technique that’s very difficult to master. You have to do a lot of experimentation, and it helps to have a tripod! I once went on a boat trip in Svalbard and took 1,504 pictures of guillemots using the slow pan – but I only kept four of them! It sounds like a lot of effort, but it’s worth it in the end.

A day in the life of a wildlife photographer

Spotted eagle owl in tree facing camera

My iPhone just about died yesterday, so I switched it off overnight. Miraculously, it’s now back to 24%!

We saw leopard tracks but no leopard and then a lone impala to start the day. We were out for 90 minutes before collecting the other staff and the trailer. We then drove north towards Chobe NP. At one point, the road ahead was flooded. Contrary to what you may have been told, there’s no bridge on the River Khwai, so we had to take a different route…

“Nkwe!” Makabu suddenly shouted, which I later found out meant ‘leopard’ in Setswana. He had just seen one crossing the road, and he immediately followed it. After a few yards, he stopped, got out and jumped on the roof to work out where it was, then he unhooked the trailer and drove after it off-road. You’re not supposed to do either of those things, but I like the fact Africans think rules are there to be broken! The leopard escaped, sadly, but that means Makabu now leads 2-1 in big cat sightings…

Fun fact: ‘Nkwe’ means leopard and ‘tau’ means lion in Setswana.

Having said that, our handyman chipped in with a great spot of a spotted eagle owl perched in a tree as we were driving past. It was just hidden by a branch, so I asked if I could get out and walk a bit closer. Makabu said I could, and I took a very rare picture. I’ve never seen a spotted eagle owl before…

We stopped for lunch (and to collect firewood), and I managed to get attacked by very prickly and sticky fertility grass. Not even thick socks are good enough protection against it. Then again,  you can always boil it up and drink the liquid if you’re having problems with your womb!

At around 1400, we dropped off our team to make camp, then we went back out for another game drive. The radio chatter suggested there were lions out there and maybe even a leopard, but it all seemed like a wild goose chase until we saw a pair of young lions asleep under a large fever berry tree. They like it as it has the best shade, and – lo and behold! – you can also boil its leaves in water to cure a fever. Is there any plant out here that doesn’t have medicinal properties?! We even had chance to come back later for some great close-ups.

Shockingly, I had to change my WB setting to cloudy a few times today. Very poor…

Fun fact: You can tell which termite mounds are active by the presence of wet sand deposits on the surface.

Species lists:

We saw impala, black-backed jackal, tsessebe, low veld giraffe, hippo, warthog, Burchell’s zebra, blue wildebeest, red lechwe, tree squirrel, chacma baboon, vervet monkey, elephant, waterbuck, lion, wild dog.

We ask saw birds including Burchell’s starling, African darter, blacksmith plover, Swainson’s francolin, helmeted guineafowl, red-billed hornbill, saddle-billed stork, grey hornbill, African fish eagle, spotted eagle owl, long-tailed pied shrike, African jacana, wattled crane, Cape turtle dove, little egret, Egyptian geese, Gabor goshawk.

Lightroom settings

download

In the last year, I’ve started doing all my photographic post-processing in Lightroom. It’s the program used by most professional photographers and is reasonably user-friendly, but the problem is choosing all the right settings. I shoot in RAW, which captures the maximum amount of information, but it doesn’t necessarily provide a great picture right out of the box. To do that, you need to improve the contrast, clarity, vibrance and various other settings, but what exactly should these settings be? Enigma had 150 trillion possible combinations of 10 pairs of 26 letters on the plugboard. Lightroom isn’t quite as bad as that (!), but it can be bewildering. Even the experts disagree. I got to grips with Lightroom mostly by watching a very useful series of YouTube videos by Anthony Morganti and an article on KeepSnap, but I’ve now been given conflicting advice by one of my stock agencies! What to do, what to do… In the end, I’ve used a combination of the recommended settings as a starting point, but I’ve taken on all the advice from the stock agency, as they pay the bills!

When I’ve taken a batch of pictures, this is my ‘workflow’:

  1. Connect camera to my MacBook Pro (or use my new card reader if it’s quicker!).
  2. Import all the RAW files to a new folder in Pictures using Image Capture.
  3. Import the files to Lightroom using my custom ‘Import’ settings.
  4. Rate the images (3 stars = people shots worth putting on Facebook, 4 stars = shots worth selling, 5 stars = favourite shots).
  5. Check the ratings (which includes checking the sharpness at 100%).
  6. Work on 4- and 5-star images in Lightroom (eg cropping, tagging faces, choosing custom black and white points to avoid clipping of highlights and shadows).
  7. Add metadata to 4- and 5-star images, including titles, captions, keywords, location and copyright.
  8. Export 4- and 5-star images as JPEGs to 4*, 5* and ‘To upload’ folders in Finder.
  9. Import 4- and 5-star JPEGs to 4* and 5* folders in Lightroom.
  10. Upload to stock agencies (and Facebook).
  11. Format the memory card and delete files in the ‘To upload’ folder and any unrated files in Lightroom.

I know that sounds a bit complicated, but I’ve learned from experience which steps work for me! At the end of the day, the most important thing is to keep a copy of the original RAW files. Lightroom is ‘non-destructive’, so, whatever changes you make, you can always start again.

The next thing to cover is what these mysterious ‘Import’ settings actually are. Here are my current user preset settings, shown for each panel in the Develop module:

  • Basic:
    • Contrast +25
    • Highlights -80
    • Shadows +30
    • Whites 0 (edited later for each shot to avoid pure white)
    • Blacks 0 (edited later for each shot to avoid pure black)
    • Clarity +5 (KeepSnap thinks it should be +40!)
    • Vibrance +20
  • Tone Curve
    • Highlights -5
    • Shadows +5
  • Detail:
    • Sharpening – Amount 25  (Anthony Morganti thinks is should be 70!)
    • Noise Reduction – Luminance 10 (Anthony Morganti thinks is should be 40!)
  • Lens Corrections:
    • Enable Profile Corrections ticked
    • Remove Chromatic Aberration ticked

As I say, these settings are only a starting point, and I’ll obviously change them if I think the image would benefit, but it’s important not to push things too far. That will only make the photograph look ‘over-processed’ and unnatural. The only other thing I add is a vignette to my wildlife ‘portraits’. I do this by setting the Post-Crop Vignetting Amount to -22 in the Effects module. I don’t do it when the background is a perfect blue sky, as I don’t think it looks very good.

I should say a couple of things about export settings and the use of metadata. I’ve set up presets for all the folders I usually export to, but my experience selling via stock agencies has taught me that JPEG files should be no more than 20MB each, so I’ve used that as my file size limit. Most stock agencies also have minimum quality thresholds, so I try not to crop so much that the image is less than 6.3 megapixels. The agencies also have rules on the type and number of characters in each metadata field, so I avoid apostrophes and give all my images seven-word titles that are no longer than 50 characters. Finally, keywords are essential for Search Engine Optimisation, so I use at least 10 but more often 20 or 30, including tags describing the location, content and theme of the image (plus obvious synonyms).

Lightroom is a subject I’m learning all the time, but I hope all this will give you a head start!

Red Xmas tree star with bokeh lights

Red Xmas tree star with bokeh lights

The idea

I live in an Art Deco mansion block in Putney, and every year the porters put a Christmas tree in the entrance hall. Last year, I took some pictures of some of the baubles, inspired by an email from one of the photographic magazines about how to capture bokeh lighting. This year, the tree and the baubles were different, so I decided to have another go.

The location

Ormonde Court, Upper Richmond Road, London SW15 6TW, United Kingdom, around 2100 on 12 December 2014.

The equipment

  • Nikon D800 DSLR camera
  • Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED lens
  • Nikon SB-910 Speedlight flash
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I’ve just managed to remortgage my flat in Notting Hill, so I’ve been investing in a few photographic supplies. Ever since a German called Stefan took a magnificent shot of Old Faithful at night using flash, I’ve wanted a proper flashgun. Well, now I have one. I bought the Nikon SB-910 Speedlight a couple of weeks ago, and it arrived just in time for this shoot. I didn’t know whether I’d need it or not, but I was prepared to experiment.

The settings

  • Manual ISO 100
  • f/5.6
  • 1 second
  • 105mm
  • Tungsten white balance
  • Single-point auto-focus

The technique

In the last of these posts, I mentioned how I’d got used to taking a tripod with me in almost all circumstances, and last night was no exception. Last year, I was generally pleased with my shots of the baubles, but the ISO was far too high. I was using my tripod, funnily enough, but to hold the bauble rather than my camera! This year, I decided I would definitely mount the camera on the tripod, but that left me with nothing to hold the baubles. I thought about using a light stand from my flash kit, but I needed something horizontal rather than vertical so that I could hang the decorations from it. I then had the idea of using my golf clubs. I could stand the bag in the lobby and balance one of the clubs on top, held in place by the other clubs.

As it turned out, I’d forgotten that the bag would be at an angle of 45 degrees, so my original plan didn’t work, but I simply pulled my 4-iron half-way out and hung the first bauble from that. It was a silver reindeer, but the green wire loop wasn’t very long, and I wouldn’t have been able to get the shots I wanted without the golf club getting in the frame. I needed a piece of string. I thought about going back to my flat, but leaving my golf clubs and my camera unattended in the entrance hall didn’t seem like a sensible idea! Fortunately, I was wearing trainers, so I just used one of the laces. It took a few gos to get each bauble to point in the right direction and remain still – particularly as there was a stream of curious residents opening the front door on their way home from work! – but I managed in the end. Phew!

I took lots of pictures of the silver reindeer, a red bauble with a spiral pattern on it and the red star shown above, and I played around with the flash settings to try to make the background a bit darker. Sadly my new flash was so powerful that I couldn’t manage that – even with -3.0EV of exposure compensation! There might’ve been a better way, but it was the first time I’ve ever used a flashgun, so I’m still a newbie.

The main problem I had in taking the shots was actually getting enough depth-of-field. The reindeer was fine, but the round baubles and even the star were proving a nightmare. If I focused on the front of the bauble, the metal cap and wire loop were out of focus, but, if I focused on those, the rest of the bauble was out of focus. I’m an absolute stickler for sharpness in my images, so I wasn’t sure what to do. In the end, I stopped down a little bit and hoped that f/5.6 would be a small enough aperture to keep everything acceptably sharp. I tried ‘chimping’ (or checking the shots on the LCD screen) a few times, but it was tricky to tell. My problem was a kind of Catch-22: the three variables controlling depth-of-field are normally the focal length, the aperture and the relative distances of the camera to the subject and the subject to the background. I couldn’t change to a wide-angle lens, as I needed to limit the background to just the Christmas tree; I couldn’t change to a much smaller aperture without making the bokeh circles of the blurred Christmas lights in the background too small; and I couldn’t change the relative positions of the camera, bauble and tree without changing the composition completely. Hmm… As you can see from the shot above, the two arms on the right of the red star didn’t turn out completely sharp, but it was ‘good enough for Government work’. Shutterstock obviously didn’t accept it – they’re very hot on sharpness! – but I did win an award on Pixoto for the sixth best image uploaded to the Christmas category!

The post-processing

I made three changes to this shot:

  1. I had the camera on ‘Tungsten’ white balance, as I’d just read somewhere that I should use the amber filter on the flashgun when shooting indoors in order to avoid a clash of different light sources. However, it turned out that the shot looked a lot warmer with the ‘Flash’ white balance, and that was just the look I was after at Christmastime.
  2. A lot of my images end up being quite dark, and I’m not sure whether it’s just because I’m lucky to spend a lot of time in very sunny places or whether there’s a problem with my camera! In this case, I actually had to push the exposure up by +2EV in Aperture to make it look like all the others. I have a feeling that’s because I changed from f/2.8 to f/5.6 to get more depth-of-field but forgot to lengthen the shutter speed to compensate. Silly me…
  3. I was desperately trying to frame the shot perfectly so I wouldn’t have to crop, but the balance of the bauble with the ‘negative space’ on the right wasn’t quite right, so I cropped in slightly to position the star a third of the way into the frame.

Close-up of golden eagle head with catchlight

Close-up of golden eagle head with catchlight

I’m a photographer (among other things), and this is the first of a series of posts about my favourite photographs. I’ll tell you how I took them and break down the shot into the idea, the location, the equipment, the settings, the technique and any post-processing.

The idea

When I took this shot, I was at a Battle of Hastings re-enactment at Battle Abbey in Sussex. I was there to take pictures of the battle scenes between enthusiasts dressed up as Normans and Saxons, and I had no idea there was going to be a falconry display until I bought my ticket and was given a flyer with the plan for the day.

The golden eagle is my favourite bird (isn’t it everyone’s?!), so I was very excited to be able to see one in action. The falconers from Raphael Historical Falconry put on a couple of displays with a variety of birds, including a gyrfalcon and a Harris hawk, but the golden eagle was the highlight. Afterwards, I wandered over to their tent, and I was able to get within just a few feet of all the birds. The falconer was happy to chat with the spectators with a bird on his arm (so to speak!), and later he fed and watered the birds outside. That gave me the chance to set up my tripod and get a few good close-ups, and this was the best of the lot.

The location

Battle Abbey, High Street, Hastings and Battle, East Sussex TN33 0AD, United Kingdom, around 1500 on 11 October 2014.

The equipment

  • Nikon D800 DSLR camera
  • Sigma 50-500mm F4.5-6.3 APO DG OS HSM lens
  • Manfrotto 190XProB tripod with 496RC2 universal joint head
  • Hähnel HRN 280 remote release.

I was a bit worried about using my ‘Bigma’ to take this picture, as I hadn’t been very impressed with it on my trip to Spitsbergen to see the polar bears. Admittedly, the bears were usually a few hundred yards away, and no zoom lens is at its best when it’s at its longest focal length, but I was disappointed that my shots were so soft. As a result, I did a manual focus check and discovered that the calculated auto-focus fine tune setting was a whopping -12! Armed with this new improvement to the sharpest tool in my box, I was ready for anything…

PS They call it the ‘Bigma’ as it’s made by Sigma, and it’s enormous!

The settings

  • Auto ISO 110
  • f/9
  • 1/250
  • 500mm
  • Daylight white balance
  • Single-point auto-focus

I had the camera on Manual with ISO on Auto, which I thought was appropriate for a day when lots of things would be happening, and I’d be taking candid shots without much opportunity to sit down and check my settings. However, I should probably have set the ISO to its optimum value of 100 for this shot, as I had plenty of time.

The technique

I’m generally a travel and wildlife photographer, but I normally don’t use a tripod as it gets in the way and doesn’t work too well in a Land-Rover moving at 40mph! However, I learnt a new perspective from a professional photographer called Mark Carwardine. He happened to be on a cruise to Spitsbergen that I went on a few months ago, and he was always carrying around his tripod with the legs fully extended – even on the Zodiac inflatables that we used to land on the islands. I thought to myself, If he can do it, so can I! After that, I’ve tried to use a tripod wherever possible. I love really sharp wildlife shots, and a 36.3-megapixel DSLR and a tripod make a winning combination.

Another important thing about wildlife shots is to get down to the level of the animal or bird you’re shooting. You can see from this shot that I’m right at eye-level with the eagle, and that gives the sense of power and intimacy I was looking for.

Finally, I’ve learnt from a couple of portrait shoots the value of the ‘catchlight’. This is the reflection of the light source that you see in the eye of your subject. It’s just as important with wildlife as with people, and I was lucky enough to get a break in the clouds that allowed the sun to provide the perfect catchlight. Lucky me!

The post-processing

I changed from a PC to a Mac a few years ago, so I do all my post-processing in Aperture. I suppose I should upgrade to Lightroom or Adobe Camera Raw or Photoshop, but iPhoto was the default image-processing software on the Mac, and Aperture was the cheapest upgrade!

I only had two changes to make to this shot:

  1. Even at 500mm, I still wasn’t quite close enough for the bird’s head to fill the frame, so I had to crop in later. I’ve found from experience that 6.3 megapixels is the minimum size that the major online photo libraries accept, so I never go below 6.4 MP (to avoid rounding errors), and that’s the new size of this file.
  2. In the end, the automatic ISO setting was close enough to the optimum of 100, but the shot was slightly overexposed due to the dark colours of the eagle’s feathers and the grassy background, so I had to reduce the exposure by 0.5EV.

Descriptive writing

Grand Central

Exams at 11+ and 13+ level always let you tell a story in the writing section, but they sometimes provide a picture and simply ask you to describe it or to ‘write about it in any way you like’. Writing a description is obviously different from writing a story, so it’s worthwhile pointing out the differences and the similarities.

When you write a story, the best way of doing it is probably to follow the five-step process that I outline in Story Mountains:

  1. Choose the title
  2. Brainstorm for ideas
  3. Plan your work
  4. Write it
  5. Check it

You can use a similar basic method for doing a description – except the planning stage obviously doesn’t involve creating a story mountain! – but what are the differences? Steps 1, 4 and 5 are pretty much the same, but you might want to have a look at these tips for the brainstorm and planning.

Brainstorm

When you’re brainstorming for a story, you have to think about characters, genre, period, setting and plot, and you also have to make sure there’s a ‘problem’ to solve so that your idea fits into a story mountain. However, descriptions don’t necessarily have all of those things in them, so you have to think about it in a different way.

The simplest form of description would simply involve describing what’s in a picture (or imagining what’s there if you’re just given the title). That might result in some very imaginative creative writing and open up the possibility of using some great vocabulary and all the poetic devices you can think of, including similes and metaphors. However, the very best descriptions have to have some kind of ‘hook’ to grab the reader’s attention, and that usually means a central character, situation or even a mini ‘plot’. You obviously need to describe exactly what’s in the picture, but what if you want to say more? What if the picture doesn’t have the things in it that you want. That’s a bit tricky, but you can always ask questions or just ask the narrator to imagine things.

Hal Morey’s picture of New York’s Grand Central Station is a good example. The shot has lots of elements to it, including the architecture, the people and the beams of light from the windows, so you could easily spend your whole time going over the picture in great depth, picking out each detail and thinking up the best words and metaphors to describe it. Vocabulary is important here, so you might make a list of the words that you planned to use. One good way of organising this is to think about the five senses: sight, hearing, taste, smell and touch. It’s sometimes difficult to get beyond the visual when you’re analysing a picture, so this method just forces you to think of the other aspects of a scene. Try to make separate lists for each of the senses. The visual vocabulary might include the following:

  • columns (not just walls)
  • vaulting (not just roof)
  • passengers (not just people)
  • spotlights (not just light)
  • cathedral (not just station)
  • nave (not just hall)
  • balustrade (not just railing)

It’s not enough to use words like ‘roof’ when more imaginative synonyms exist such as ‘vaulting’, so try to think of the very best words to use. After all, the examiner can’t tell that you know a word unless you use it! And the same goes for metaphors. Where did the word ‘cathedral’ come from? Well, the shape of the hall and all the windows are similar to what you’d find in a cathedral or a large church, so why not use that in a kind of ‘extended metaphor’? An extended metaphor takes a comparison and uses it more than once, so the main part of the hall might be the ‘nave’, the two large arched windows might be the ‘west windows’ and the people might be the ‘congregation’. Even better would be to link the metaphor to the purpose of the other building by saying something like this: “The congregation bustled to find their seats in the pews as they made their daily act of worship to the god of commerce.” Suddenly, you’ve gone from a bland description of what you can see for yourself to a new and imaginative way of looking at the world.

The other category of words on your checklist should be feelings. Why simply describe what people look like and not examine how they feel? As an example, use the context of Grand Central Station to imagine what’s going through the passengers’ minds? Are they bored, are they reluctant to go to work, or are they happy to be bunking off for a day at the beach?!

So what else can you do to take your writing to the next level? The answer is to introduce a main character or some kind of situation or miniature plot. You’re hardly ever ‘banned’ from using a plot in this kind of question, so there’s no problem with introducing one, but let’s stick with the idea of doing a description rather than a story. The Grand Central picture is again a good example. What would be the character or the situation or the plot here? Well, the obvious idea is to pick is a commuter who’s late for his train. You could introduce the description by focusing on one individual in the picture and explaining why he’s in a hurry. You could then have a kind of countdown clock as you described all the people and objects he sees as he rushes to make his train:

     Lionel Carey was in a hurry. He only had five minutes to make his train to get to the most important meeting of his life! He struggled along with his precious, old, leather briefcase, catching his fedora as it was blown off his head and cursing the long overcoat he had chosen to wear as it made him sweat uncomfortably and almost tripped him over. Now, what platform did he need?
     Four minutes to go…

And so on. This gives the passage a clearer focus and a sense of tension, excitement and mystery. Will Lionel catch his train? Where is he going? What is the meeting about? It just adds another layer to the description – and ideally leads to higher marks!

Alternatively, you can talk about things that are not in the picture by doing one of the following:

  • ask questions, eg if the picture was of the Colosseum in Rome, you could ask questions like Was this where the Roman gladiators stood before they made their way to their deaths in the arena?
  • create a section in which the narrator imagines objects or events, eg It was here that the emperor would stand before giving the thumbs-up or thumbs-down sign that would signal the fate of the gladiators.

Planning

It’s fairly obvious how to plan for a story because it has to have a plot, but how do you plan for a description? Do you just describe what’s in the picture, starting perhaps on the left and working  your way across? Or do you separate your work into five different paragraphs on each of the senses, with perhaps an extra one for the feelings of the travellers? Or can you introduce a timeline, charting the progress of an imaginary character – such as Lionel Carey, hurrying to catch his train? Each one might work, but you’ll probably get the best marks for something that engages the reader, and the best way of doing that is to have a central character and a carefully selected situation to place him in:

Lionel Carey in a hurry – needs to catch train for meeting, looks for platform

4 mins

Describe Lionel – importance of what’s in briefcase, mysterious ‘she’ he’s meeting
Describe station – architecture, light, people

3 mins

Describe people he sees
Bumps into coffee cart
Argues with staff
Will he ever see ‘her’?

2 mins

Describe trains – steam, smoke, whistle
Wrong platform – needs to run to Platform 16

1 min

Describe running, bumping into people, curses

Time’s up!
Too late – but wait! Train is delayed. He can give daughter Xmas present after all!

Whatever the picture or title, try giving this method a try. If you brainstorm and plan correctly, focusing on all five senses and people’s feelings and using a central character to add excitement and mystery, I’m sure you’ll do a good job.

What is a full sentence?

SVO

Teachers often tell pupils to use a ‘full sentence’ in their answers, but what is a full sentence?

Parts of a sentence

First of all, it’s important to know what all the words in the picture mean. (Note that the parts of a sentence are not always individual words, though they can be. For example, ‘she’ is the subject, but ‘a hot dog’ is the direct object even though it is three words.)

Subject

The subject of the sentence performs the action of the verb, in other words, “who’s doing the doing”. The girl in the picture is obviously the one doing the eating, not the hot dog!

Verb

The verb is often called the ‘doing word’, although some verbs like ‘being’ and ‘having’ don’t really involve much ‘doing’! Again, what’s being done is obviously shown by the word ‘ate’. There are two kinds of verb:

  • Transitive verbs need a direct object, like the word ‘ate’ in the picture
  • Intransitive verbs don’t need an object, like the word ‘swim’ in ‘They swim’.

Object

There are two kinds of object:

  • Direct objects are directly affected because they ‘suffer the action of the verb’. In other words, they have something done to them, like the hot dog in the picture.
  • Indirect objects are only indirectly affected, for example if they benefit from the verb like the teacher receiving an apple in the picture below.

Types of sentence

Now we know what the parts of a sentence are, we can talk about all the possible kinds of full sentence.

  1. Verb only
    Strictly speaking, all you really need to make a full sentence is a verb. For example, ‘Sit!’ is a full sentence, even though it only has one word in it. That only works when you’re telling a dog – or a person! – what to do. Most of the time, you need a subject as well.
  2. Subject-Verb
    ‘He swims’ is a full sentence because it has a subject and a verb, but this only works because the verb is intransitive, which means it doesn’t need an object.
  3. Subject-Verb-Object
    The picture above shows the main parts of a simple sentence, which are the subject (S), the verb (V) and the object (O). The initial letters give us a typical pattern for a sentence, which is SVO. In this case, the object is a direct object, which means it’s directly affected but it can also be an indirect object, which may benefit indirectly. Here, the hot dog is the one that has to suffer being eaten – not the girl! – but it’s slightly different in the next picture. _
  4. Subject-Verb-Indirect Object-Direct Object (or Subject-Verb-Direct Object-Indirect Object)
    Here, the apple is being ‘given’, so the apple is the direct object, but the teacher also benefits indirectly, so she is the indirect object.

Common mistakes

  1. Punctuation
    Every sentence should end with either a full-stop, a question mark or an exclamation mark, but one common mistake is to put a comma in between sentences instead, eg He loved pizza, he always chose pepperoni. This is called the ‘comma splice’.
  2. Fragments
    A sentence that doesn’t have a subject, verb or object when it needs one is called a ‘sentence fragment’, eg Gave his teacher an apple. It’s obvious that it doesn’t make sense without the word ‘He’, but it’s easily done.
  3. Starting with conjunctions
    Teachers often tell their pupils not to start a sentence with ‘because’. When asked a question like ‘Why is Jack sad?‘, it’s easy to write ‘Because his dog died‘. That’s all right when you’re speaking in class – when people don’t care as much about their grammar – but not when you’re doing your homework. It’s not always wrong to do it, though. If you use ‘because’ to link two sentences together, that’s fine, eg Because it was so sunny, I had to wear sun cream.

 

You must be crazy!

2+2=5

Why? What’s wrong with that…?

Teachers and tutors ask pupils to check their work, but how can you do that in Maths without doing the whole sum all over again? Well, you can’t! So how are you supposed to check your work?

What you have to understand first of all is that checking everything is right is very different from checking nothing is obviously wrong. To check everything is right means doing the whole paper twice, but you obviously don’t have time to do that. Checking nothing is obviously wrong is much easier because it just means doing a ‘quick and dirty’ calculation in your head. It doesn’t guarantee that the answer is right, but it’s a good compromise. I call it ‘sanity checking’, which means making sure your answers are not crazy! Unfortunately, there isn’t one method that works for every question – it depends on what type of question it is – but here are a few examples:

Algebra

If you have to ‘solve for 𝑥’ and it’s a difficult question, try putting your answer back into the original equation and seeing if one side equals the other, eg if you think 𝑥 = 5, then that works for 2𝑥 + 6 = 16, but not for 3𝑥 + 2 = 5. That would be crazy!

Multiplication

Every multiplication sum starts with multiplying the last digit of each number together, so try doing that when you’ve got your answer and checking if the last digit of the result is equal to the last digit of the answer, eg 176 x 467 is going to end in a 2 because 6 x 7 = 42, which also ends with a 2. Your answer couldn’t end in any other number. That would be crazy!

Rounding

If you have any kind of sum that involves adding, subtracting, multiplication or division, an easy way to check it is to round the numbers to one or two significant figures (eg to the nearest hundred) and work out the answer in your head. If it’s close enough, then your answer is not obviously wrong. If it’s nowhere near, then you’ll have to do it again, eg 1.7 x 3.4 is close to 2 x 3, so the answer might be 5.78, but it wouldn’t be 57.8. That would be crazy!

Units

Most answers in Maths tests need some kind of unit, such as kg, m, cm or ml. Sometimes, the units are provided, but sometimes they’re not. If they’re not, you just need to make sure that you use the right ones, eg if the scale of a map is 1:100,000, the distance represented by 9.8cm is 9.8km, not 9.8m. That would be crazy!

 

“The Incident”, by Nick Dale

Here is an example of a story I’ve written to illustrate how to use a story mountain as part of my five-step process for creative writing:

  1. Choose your title
  2. Brainstorm for ideas
  3. Create a story mountain
  4. Write the story
  5. Check your work

The title I chose was The Incident. Normally, I’d suggest drawing a triangle to represent a ‘mountain’ and putting your notes at evenly spaced intervals, but that’s a bit difficult with a blog post, so here’s my version of the story mountain:

  • Introduction (grab the reader’s attention)

A busy day in York (describe spontaneous combustion)

  • Introduction (describe the characters)

Frank and Martha driving along

  • Build-up (what the main characters are trying to do)

Christmas shopping, but have to see police at Frank’s tennis club first

  • Problem (what stops them)

Interviewed about ‘incident’ but Frank refuses to sign gagging order

  • Solution (how do they fix the problem)

Escape as Frank knows code to gate

  • Outcome (whether it’s a happy ending or not)

Go to car, but policeman follows

The Incident

xxxIt was just before Christmas, so it was a busy day in the Shambles area of York, with lots of tourists milling around, window-shopping and occasionally going into one of the olde worlde shops to find a scented candle for Aunt Doris or a packet of joss sticks for a grandson who was ‘into that kind of thing’. One man looked a little lost in all the traffic. He was tall and slim, bareheaded but wearing a grey overcoat and trousers with shiny black shoes. What made him look particularly weird was that he was walking around trying desperately to talk to passers-by and shake their hands . Most people thought he was some sort of lunatic and avoided him like the plague, tutting in that very English way before moving on hurriedly, but one man did stop to help.
xxx“Hello, are you lost or something?” said Frank.
xxx“Hello,” said the stranger, offering his hand.
xxx“Oh, er…” said Frank, awkwardly offering his hand in return. He wasn’t in the habit of shaking hands with random people in the street, but he went along with it. However, just as the two men’s hands touched, the stranger disappeared in a burst of flame, leaving only a pile of sooty ashes on the pavement. Frank jumped back in shock, looking at his hand to check he hadn’t been burned. What on Earth had just happened? It was like spontaneous combustion. Or something…
xxxA week later, Frank and his wife were driving through York on their way to their local tennis club. Progress was slow because of all the tourists, and Frank was chuntering under his breath and honking his horn occasionally – even when he didn’t need to. They were a couple in their mid-sixties. Frank was a little taller than his wife, but both were carrying a few extra pounds and had brown eyes and thinning grey hair. Frank was wearing brown trousers, a check shirt and blazer, while Martha had on a knitted dress and an overcoat with low-heeled shoes.
xxx“I thought we were going Christmas shopping?” said Martha.
xxx“We are, but the police want to interview us about that thing in the Shambles. They called it ‘the incident’.”
xxx“Yes, but why aren’t we going to the police station?”
xxx“Well, apparently, they don’t have the space…”
xxxWhen they arrived at the tennis club, there was a policeman at the gate. He checked their names on a list and pointed them towards the clubhouse. The whole place had been taken over. Frank was used to seeing the members playing tennis or lounging at the bar in their sometimes garish tennis gear, but now the courts were empty, and some of the people waiting inside were wearing leather jackets and smoking. Smoking! It was very busy, and they had to wait over an hour to be interviewed. As time went on, the atmosphere got more and more tense. Some of the people who had been seen just walked out quietly, but one man shouted, “I didn’t see a bloody thing!” in a broad Yorkshire accent on his way out of the manager’s office and was forced to sit down in the members’ lounge by one of the constables.
xxx“Mr and Mrs Marshall?”
xxxFrank and Martha got up and went into the office. The policeman at the manager’s desk looked a bit odd surrounded by tennis racquets and balls, but he gave Frank a serious look.
xxx“Hello, I’m Detective McGregor, and I’d just like to talk to you about the incident last week in the Shambles. It was you who shook the man’s hand, wasn’t it, Mr Marshall? Could you just give us an account of what happened, please?”
xxx“Well, the man just disappeared in a puff of smoke as soon as I touched his hand. That’s all there is to say, really. I don’t know anything else.”
xxxMcGregor asked a few more questions before finally giving up and pushing a form across his desk.
xxx“Well, if that’s really all you’ve got to say, I just need you to sign this form.”
xxx“What for?
xxx“Well, it’s a kind of non-disclosure agreement. Just routine. Just to make sure you don’t talk to anyone about the incident. I’m sure you understand.”
xxxFrank didn’t understand at all. If there was one thing that made him angry, it was being told what to do by pettifogging bureaucrats sitting on their fat backsides behind a desk.
xxx“We haven’t done anything wrong, and there’s no way you can force us to sign this. I have rights, you know? Freedom of speech and all that.”
xxx“Oh, Frank! Just sign the form,” sighed Martha.
xxx“No, I’m not signing this bloody form or any other. We’re leaving.”
xxx“Now, Mr Marshall. I’m afraid I can’t allow that. Everyone who comes in today as a witness must sign the form before leaving.”
xxx“So I’m going to be kept prisoner in my own bloody tennis club, am I? Not on your life, mate.”
xxxAs Frank tried to get up and leave, a constable standing beside the door put his hand on his shoulder to stop him, but, just then, there came the sound of a fierce argument from the members’ lounge. Frank could hear the sounds of a scuffle and a young man shouting, “You can’t keep me here!” McGregor and the constable ran out to see what was happening, leaving Frank and Martha alone in the room.
xxx“Come on, love. Let’s make a run for it,” whispered Frank.
xxx“But how are we going to get out?”
xxx“This is my tennis club, remember, and I know the code to the gate!”
xxxQuietly, Frank and Martha opened the door to the lounge and peeked out. Most people were still sitting down, but four or five policemen were trying to stop a couple of youths from escaping. The boys were kicking and punching anyone in uniform, and everyone was watching the fight. That allowed the Marshalls to sneak out of the door without anyone spotting them. Frank turned left instead of right and led Martha to the back gate, where he entered the numeric code on the keypad.
xxx“Here we go. 1-4-6-3. And we’re free!”
xxx“Oh, Frank! You are dreadful.”
xxx“What do you mean? I got us out of there, didn’t I? And now you can do all the Christmas shopping you want.”
xxxAs they walked back to the car, a policeman appeared at the gate and followed them down the street. And it didn’t look like he had Christmas on his mind…

Preceding Direct Objects in French

French verbs

“I hate French!”

 

Forming the perfect (or pluperfect) tense in French is sometimes made harder than necessary by what’s called a Preceding Direct Object (or PDO). The object of a sentence is whatever ‘suffers the action of the verb’, eg the nail in ‘he hit the nail on the head’. If the object is a pronoun and the perfect (or pluperfect) tense is being used, the French put it before the auxiliary rather than at the end of the sentence as in English, eg ‘il l‘a frappé’ or ‘he it has hit’!

You might think that’s bad enough, but the real problem is that the past participle has to agree in number and gender with the PDO, eg ‘il les a frappés‘ or ‘he’s hit them’.

When it comes to reflexive verbs, it gets even worse. By definition, every reflexive verb has a PDO, so that means you have to watch what you write when a female character is speaking, eg ‘Je me suis lavé’ for a boy, but ‘Je me suis lavée’ for a girl. Having said that, one of my male pupils once told me that the best way to get a good mark in his French prose was to tell a story in the first person and pretend to be a girl – that way, he’d get a tick every time he used a PDO!

Prime factors

Prime factors

Optimus Prime

Prime factors have nothing to do with Optimus Prime – sadly – but they often crop up in Maths tests and can be used to find the Lowest Common Multiple or Highest Common Factor of two numbers.

Prime factors are the lowest prime numbers that can be multiplied together to make a given number. There are two methods of finding out what they are: the ladder method and the factor tree. I prefer the ladder method.

Ladder method

  1. Write down the number for which you want to find the prime factors.
  2. Find the lowest prime number that goes into it exactly and write it down next to it on the same line.
  3. Divide one number by the other and write down the result under the original number on the next line.
  4. Repeat steps 2 and 3 until you reach the number 1.
  5. Draw a line between the two columns and lines after the first row and before the last.
  6. Write down the prime factors from the column you have just created, using powers to simplify the expression, eg the factors of 12 are 2² x 3, not 2 x 2 x 3.

Prime factors

Lowest Common Multiple (LCM)

Prime factors are useful in working out the Lowest Common Multiple (LCM) of two numbers, in other words the lowest number that is divisible by both numbers.

  1. Work out the prime factors of the two numbers and write them down one below the other, eg the prime factors of 30 are 2 x 3 x 5, and the prime factors of 45 are 3 x 3 x 5.
  2. Make a new list by writing down each factor the greatest number of times it appears in either list, eg there are two 3s in one list and one in the other, so the new list is 2 x 3 x 3 x 5.
  3. Multiply together the new list of factors, eg the LCM of 30 and 45 is 2 x 3 x 3 x 5 = 90.

Highest Common Factor (HCF)

Prime factors can be used to work out the Highest Common Factor (HCF) of two numbers, in other words the highest number that both numbers can be divided by exactly.

  1. Work out the prime factors of the two numbers and write them down one below the other, eg the prime factors of 30 are 2 x 3 x 5, and the prime factors of 45 are 3 x 3 x 5.
  2. Make a new list by writing down each factor that appears in both lists, eg 3 and 5 appear in both lists, so the new list is 3 x 5.
  3. Multiply together the new list of factors, eg the HCF of 30 and 45 is 3 x 5 = 15.

 

French regular verbs – conditional tense

French verbs

“I hate French!”

The conditional tense in French is used to show that someone ‘would do’ or ‘would be doing’ something. All verbs end in -er, -re or -ir, and the endings are different (as shown here in red):

Verbs ending in -er, eg donner (to give)

Je donnerais

Tu donnerais

Il/elle donnerait

Nous donnerions

Vous donneriez

Ils/elles donneraient

Verbs ending in -re, eg vendre (to sell)

Je vendrais

Tu vendrais

Il/elle vendrait

Nous vendrions

Vous vendriez

Ils/elles vendraient

Verbs ending in -ir, eg finir (to finish)

Je finirais

Tu finirais

Il/elle finirait

Nous finirions

Vous finiriez

Ils/elles finiraient

French regular verbs – future tense

French verbs

“I hate French!”

There is only one future tense in French, and it’s used to show that someone ‘will do’ or ‘will be doing’ something. Verbs end in -er, -re or -ir, but the endings are the same (as shown here in red):

Verbs ending in -er, eg donner (to give)

Je donnerai

Tu donneras

Il/elle donnera

Nous donnerons

Vous donnerez

Ils/elles donneront

Verbs ending in -re, eg vendre (to sell)

Je vendrai

Tu vendras

Il/elle vendra

Nous vendrons

Vous vendrez

Ils/elles vendront

Verbs ending in -ir, eg finir (to finish)

Je finirai

Tu finiras

Il/elle finira

Nous finirons

Vous finirez

Ils/elles finiront

French regular verbs – past tense

French verbs

“I hate French!”

Here are the basic forms of French regular verbs in the past tense, which include the perfect (or passé composé), pluperfect, imperfect and past historic (or passé simple). All verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red.

Perfect (or passé composé)

The perfect tense is used in formal written French to say someone ‘has done’ something, but they sometimes use it in conversation and casual writing in the same way we use the simple past tense (or ‘preterite’), eg ‘j’ai donné’ might mean ‘I gave’ rather than ‘I have given’ – you just need to look at the context to help you decide which is the right translation.

Verbs ending in -er, eg donner (to give)

J’ai donné
Tu as donné
Il/elle a donné
Nous avons donné
Vous avez donné
Ils/elles ont donné

Verbs ending in -re, eg vendre (to sell)

J’ai vendu
Tu as vendu
Il/elle a vendu
Nous avons vendu
Vous avez vendu
Ils/elles ont vendu

Verbs ending in -ir, eg finir (to finish)

J’ai fini
Tu as fini
Il/elle a fini
Nous avons fini
Vous avez fini
Ils/elles ont fini

Pluperfect

The pluperfect tense is used to say someone ‘had done’ something. This is common in story-writing when an event is described that happened before that particular moment in the story, eg ‘j’avais donné’ means ‘I had given’.

Verbs ending in -er, eg donner (to give)

J’avais donné
Tu avais donné
Il/elle avait donné
Nous avions donné
Vous aviez donné
Ils/elles avaient donné

Verbs ending in -re, eg vendre (to sell)

J’avais vendu
Tu avais vendu
Il/elle avait vendu
Nous avions vendu
Vous aviez vendu
Ils/elles avaient vendu

Verbs ending in -ir, eg finir (to finish)

J’avais fini
Tu avais fini
Il/elle avait fini
Nous avions fini
Vous aviez fini
Ils/elles avaient fini

Imperfect

The imperfect tense is used to say someone ‘was doing’ or ‘used to do’ something, eg ‘je donnais’ means ‘I was giving’ or ‘I used to give’.

Verbs ending in -er, eg donner (to give)

Je donnais
Tu donnais
Il/elle donnait
Nous donnions
Vous donniez
Ils/elles donnaient

Verbs ending in -re, eg vendre (to sell)

Je vendais
Tu vendais
Il/elle vendait
Nous vendions
Vous vendiez
Ils/elles vendaient

Verbs ending in -ir, eg finir (to finish)

Je finissais
Tu finissais
Il/elle finissait
Nous finissions
Vous finissiez
Ils/elles finissaient

Past historic (or passé simple)

The past historic is the equivalent of the simple past tense (or preterite) in English and is used in novels and other formal writing to say someone ‘did’ something, eg ‘je donnai’ means ‘I gave’ or ‘I used to give’. It is never used in conversation, where it is replaced by the perfect tense.

Verbs ending in -er, eg donner (to give)

Je donnais
Tu donnas
Il/elle donna
Nous donnâmes
Vous donnâtes
Ils/elles donnèrent

Verbs ending in -re, eg vendre (to sell)

Je vendis
Tu vendis
Il/elle vendit
Nous vendîmes
Vous vendîtes
Ils/elles vendirent

Verbs ending in -ir, eg finir (to finish)

Je finis
Tu finis
Il/elle finit
Nous finîmes
Vous finîtes
Ils/elles finirent

 

Common French verbs – present tense

French verbs

“I hate French!”

Language changes over time because people are lazy. They’d rather say something that’s easy than something that’s correct. That means the most common words change the most, and the verbs become ‘irregular’. In French, the ten most common verbs are ‘être’, ‘avoir’, ‘pouvoir’, ‘faire’, ‘mettre’, ‘dire’, ‘devoir’, ‘prendre’, ‘donner’ and ‘aller’, and they’re all irregular apart from ‘donner’. Here are their forms in the present tense.

Note: the irregular forms are shown in red.

Etre (to be)

Je suis
Tu es
Il/elle est
Nous sommes
Vous êtes
Ils/elles sont

Avoir (to have)

J’ai
Tu as
Il/elle as
Nous avons
Vous avez
Ils/elles ont

Pouvoir (to be able to, ‘can’)

Je peux
Tu peux
Il/elle peut
Nous pouvons
Vous pouvez
Ils/elles peuvent

Faire (to do, to make)

Je fais
Tu fais
Il/elle fait
Nous faisons
Vous faites
Ils/elles font

Mettre (to put)

Je mets
Tu mets
Il/elle met
Nous mettons
Vous mettez
Ils/elles mettent

Dire (to say, to tell)

Je dis
Tu dis
Il/elle dit
Nous disons
Vous disez
Ils/elles disent

Devoir (to have to, ‘must’)

Je dois
Tu dois
Il/elle doit
Nous devons
Vous devez
Ils/elles doivent

Prendre (to take)

Je prends
Tu prends
Il/elle prend
Nous prenons
Vous prenez
Ils/elles prennent

Aller (to go)

Je vais
Tu vas
Il/elle va
Nous allons
Vous allez
Ils/elles vont

French regular verbs – present tense

French verbs

“I hate French!”

Nobody likes French verbs – not even the French! – but I thought I’d start by listing the most basic forms of the regular verbs in the present tense. All French verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red:

Verbs ending in -er, eg donner (to give)

Je donne
Tu donnes
Il/elle donne
Nous donnons
Vous donnez
Ils/elles donnent

Verbs ending in -re, eg vendre (to sell)

Je vends
Tu vends
Il/elle vend
Nous vendons
Vous vendez
Ils/elles vendent

Verbs ending in -ir, eg finir (to finish)

Je finis
Tu finis
Il/elle finit
Nous finissons
Vous finissez
Ils/elles finissent

If you’re learning French and have to memorise the present tense, it helps if you can spot the patterns:

  • The je, tu, il/elle and ils/elles forms all sound the same for -er and -re verbs (and the same is true of the je, tu and il/elle forms of -ir verbs)
  • The nous and vous forms always end in -ons and -ez (although -ir verbs have an extra -ss- in the middle)

People learn things in different ways, but the best way I’ve found is to make a recording on my phone and try to repeat the words at the same time as I listened to them on my headphones. I did a lot of acting at Oxford and in the Edinburgh Fringe, and that was the way I learned my lines. If I made a mistake or forgot something, the recording prompted me with the right words, and I could carry on repeating the exercise until I was word-perfect. It meant I could learn my lines any time, anywhere – whether I was watching sport, making dinner or cycling around town!

Good luck…

Negative numbers

negative-numbers

Working with negative numbers can be confusing, but a few simple rules can help you add, subtract, multiply and divide successfully:

Adding and subtracting

If the operator and the sign are the same, then you must add the number, eg 4 – -3 = 4 + 3 = 7 or 4 + +3 = 7.

If the operator and the sign are different, then you must subtract the number, eg 4 + -3 = 4 – 3 = 1 or 4 – +3 = 1.

Here are a few practice questions:

  1. 14 – -3
  2. -4 + -7
  3. 21 – +8
  4. -8 + -7
  5. 6 – -4

Multiplication and division

If the signs of the two numbers are the same, then you must make the answer positive, eg -4 x -3 = 4 x 3 = 12 or +4 x +3 = 4 x 3 = 12.

If the signs of the two numbers are different, then you must make the answer negative, eg -4 x +3 = -12 or +4 x -3 = -12.

Here are a few practice questions:

  1. 1 × -3
  2. -8 ÷ -4
  3. 2 × -7
  4. -14 ÷ -7
  5. 6 × -4

Useful terms in Maths

maths

Maths is complicated, but a good first step on the road to understanding it is to get to know the most useful terms. There are lists in the front of the Bond books, but here’s my own contribution. I hope it helps!

Algebra: expressions using letters to represent unknown values, eg 2(x + 3) = 16.

Angles: there are three types of angle, depending on the number of degrees.

  • acute angles are between 0 and 90 degrees.
  • obtuse angles are between 90 and 180 degrees.
  • reflex angles are between 180 and 360 degrees.

Arc: part of the circumference of a circle.

Averages: there are three types of average, and they are all useful in different ways.

  • The mean is found by adding up all the values and dividing the total by how many there are, eg the mean of the numbers 1-10 is 5.5, as 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55, and 55 ÷ 10 = 5.5.
  • The mode is the most common value (or values), eg the mode of 1, 2, 2, 3, 4, 5 is 2.
  • The median of an odd number of values sorted by size is the one in the middle, eg the median of the numbers 1-5 is 3. The median of an even number of values is the mean of the two numbers in the middle, eg the median of the numbers 1-10 is 5.5, as 5 and 6 are the numbers in the middle, and 11 ÷ 2 = 5.5.

Chord: a straight line drawn between two points on the circumference of a circle.

Circumference: the distance all the way round the edge of a circle.

Congruent: triangles are congruent if they are the same shape and size, eg two right-angled triangles with sides of 3cm, 4cm and 5cm would be ‘congruent’, even if one is the mirror image of the other. You can prove that two triangles are congruent by using any of the following methods: SAS (Side-Angle-Side), SSS (Side-Side-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side) and RHS or HL (Right-angle-Hypotenuse-Side or Hypotenuse-Leg). If all three measurements of the angles and/or sides are equal, the triangles are congruent. You can only create a congruent copy of a triangle by translation, reflection or rotation. (Note: congruence is the same as similarity, except that the triangles have to be the same size.)

Cube: the result of multiplying any number by itself twice, eg 8 is the cube of 2, as 2 x 2 x 2 = 8.

Cube root: the number that has to be multiplied by itself twice to make another number, eg 2 is the cube root of 8, as 2 x 2 x 2 = 8.

Cuboid: a solid with a rectangle for each of the six sides, eg a shoe box.

Denominator: the number on the bottom of a fraction, eg 2 is the denominator of ½.

Diameter: the length of a line drawn across a circle passing through the centre.

Equation: any line of numbers and operators with an equals sign in the middle, showing that the two sides balance, eg 4x + 12 = 34.

Factor: a number that goes into another number evenly, eg 6 is a factor or 12.

Fibonacci series: a sequence of numbers created by adding the previous two numbers together to get the next one, eg 1, 1, 2, 3, 5, 8, 13…

Formula: a way of calculating the answer to a common problem using letters or words, eg the formula for distance is speed x time (or D = S x T).

Highest common factor (or HCF): the highest number that goes into two other numbers evenly, eg the HCF of 12 and 18 is 6.

Improper fraction: a fraction that is greater than one (in other words, the numerator is greater than the denominator), eg 9/5.

Lowest common multiple (or LCM) / Lowest common denominator (or LCD): the lowest number that is divisible by two other numbers, eg the LCM of 6 and 8 is 24.

Multiple: a number that can be divided evenly by another number, eg 12 is a multiple of 6.

Numerator: the number on the top of a fraction, eg 3 is the numerator of ¾.

Order of operations: the sequence of doing basic mathematical sums when you have a mixture of, say, addition and multiplication. BIDMAS (or BODMAS) is a good way of remembering it, as it stands for:

  • Brackets
  • Indices/Order (in other words, squares, cubes and so on)
  • Division
  • Multiplication
  • Addition
  • Subtraction

Note that addition doesn’t come ‘before’ subtraction – these operations have to be done in the order in which they occur in the sum, and it makes a difference to the answer, eg 4 – 3 + 2 = 3 if you do the operations in order, which is correct, but you’d get the wrong answer of -1 if you did 3 + 2 first.

Operator: the sign telling you which mathematical operation to do. The most common ones are +, -, x and ÷.

Parallel: two lines are parallel if they will never meet, eg the rails on a railway line.

Perimeter: the distance all the way round the outside of a shape.

Perpendicular: at 90 degrees to each other.

Pi (or π): a constant used to work out the circumference and area of circles, often shown as 22/7 or 3.14 although it’s actually an ‘irrational’ number, which means it goes on for ever.

Prime factors: the lowest prime numbers that can be multiplied together to make a given number, eg the prime factors of 12 are 2² x 3.

Prime numbers: a number that can only be divided by itself and one, eg 2, 3, 5, 7, 11, 13…

Probability: the chance of something happening, calculated as the number of ways of getting what you want divided by the total number of possible outcomes, eg the chance of a coin toss being heads is ½ as there is one ‘heads’ side but two sides in total. To work out the probability of a sequence of events, you have to multiply the individual probabilities together, eg the chance of a coin toss being heads twice in a row is ½ x ½ = ¼

Product: the result of multiplying two numbers together, eg 35 is the product of 5 and 7.

Quadrilateral: a four-sided shape such as the following:

  • Kite: a quadrilateral with two pairs of equal sides next to each other (or ‘adjacent’ to each other).
  • Parallelogram: a quadrilateral with opposite sides parallel to each other.
  • Rectangle: a quadrilateral with two opposite pairs of equal sides and four right angles.
  • Rhombus: a quadrilateral with equal sides.
  • Square: a quadrilateral with equal sides and four right angles.
  • Trapezium: a quadrilateral with one pair of parallel sides. (Note: an isosceles trapezium is symmetrical.)

Radius: the distance from the centre of a circle to the circumference.

Range: the highest minus the lowest value in a list, eg the range of the numbers 1-10 is 9.

Regular: a shape is regular if all its sides and angles are equal, eg a 50p piece is a regular (-ish!) heptagon.

Right angle: an angle of 90 degrees.

Sector: a ‘slice’ of a circle in between two radii.

Segment: a part of a circle separated from the rest by a chord.

Shapes: the name of each shape depends on the number of sides. Here are the first 12.

  • Quadrilaterals have four sides.
  • Pentagons have five sides.
  • Hexagons have six sides.
  • Heptagons have seven sides.
  • Octagons have eight sides.
  • Nonagons have nine sides.
  • Decagons have 10 sides.
  • Hendecagons have 11 sides.
  • Dodecagons have 12 sides.

Similar: triangles are similar if they are the same shape, but not necessarily the same size, eg a right-angled triangle with sides of 3cm, 4cm and 5cm is ‘similar’ to a right-angled triangle with sides of 6cm, 8cm and 10cm. (Note: similarity is the same as congruence, except that the triangles don’t have to be the same size.)

Square number: the result of multiplying any number by itself, eg 49 is a square number, as 7 x 7 = 49.

Square root: the number that has to be multiplied by itself to make another number, eg 6 is the square root of 36, as 6 x 6 = 36.

Sum: the result of adding two numbers together, eg 17 is the sum of 8 and 9.

Tangent: either a straight line that touches the circumference of a circle OR the length of the opposite side of a triangle divided by the length of the adjacent side

Triangles: there are four main types, each with different properties.

  • equilateral triangles have all three sides the same length and all three angles the same.
  • isosceles triangles have two sides the same length and two angles the same.
  • scalene triangles have three sides of different lengths with three different angles.
  • right-angled triangles have one 90-degree angle.

Variable: an unknown in algebra, eg x or y.

Algebra

Nothing makes the heart of a reluctant mathematician sink like an algebra question.algebra

Algebra is supposed to make life easier. By learning a formula or an equation, you can solve any similar type of problem whatever the numbers involved. However, an awful lot of students find it difficult, because letters just don’t seem to ‘mean’ as much as numbers. Here, we’ll try to make life a bit easier…

Gathering terms

X’s and y’s look a bit meaningless, but that’s the point. They can stand for anything. The simplest form of question you’ll have to answer is one that involves gathering your terms. That just means counting how many variables or unknowns you have (like x and y). I like to think of them as pieces of fruit, so an expression like…

2x + 3y – x + y

…just means ‘take away one apple from two apples and add one banana to three more bananas’. That leaves you with one apple and four bananas, or…

x + 4y

Here are a few practice questions:

  1. 3x + 4y – 2x + y
  2. 2m + 3n – m + 3n
  3. p + 2q + 3p – 3q
  4. 2a – 4b + a + 4b
  5. x + y – 2x + 2y

Multiplying out brackets

This is one of the commonest types of question. All you need to do is write down the same expression without the brackets. To take a simple example:

2(x + 3)

In this case, all you need to do is multiply everything inside the brackets by the number outside, which is 2, but what do we do about the ‘+’ sign? We could just multiply 2 by x, write down ‘+’ and then multiply 2 by 3:

2x + 6

However, that gets us into trouble if we have to subtract one expression in brackets from another (see below for explanation) – so it’s better to think of the ‘+’ sign as belonging to the 3. In other words, you multiply 2 by x and then 2 by +3. Once you’ve done that, you just convert the ‘+’ sign back to an operator. It gives exactly the same result, but it will work ALL the time rather than just with simple sums!

Here are a few practice questions:

  1. 2(a + 5)
  2. 3(y + 2)
  3. 6(3 + b)
  4. 3(a – 3)
  5. 4(3 – p)

Solving for x

Another common type of question involves finding out what x stands for (or y or z or any other letter). The easiest way to look at this kind of equation is using fruit again. In the old days, scales in a grocery shop sometimes had a bowl on one side and a place to put weights on the other. To weigh fruit, you just needed to make sure that the weights and the fruit balanced and then add up all the weights. The point is that every equation always has to balance – the very word ‘equation’ comes from ‘equal’ – so you have to make sure that anything you do to one side you also have to do to the other.

There are three main types of operation you need to do in the following order:

  1. Multiplying out any brackets
  2. Adding or subtracting
  3. Multiplying or dividing

Once you’ve multiplied out any brackets (see above), what you want to do is to simplify the equation by removing one expression at a time until you end up with something that says x = The Answer. It’s easier to start with adding and subtracting and then multiply or divide afterwards (followed by any square roots). To take the same example as before:

2(x + 3) = 8

Multiplying out the brackets gives us:

2x + 6 = 8

Subtracting 6 from both sides gives us:

2x = 2

Dividing both sides by 2 gives us the final answer:

x = 1

Simple!

Here are a few practice questions:

  1. b + 5 = 9
  2. 3y = 9
  3. 6(4 + c) = 36
  4. 3(a – 2) = 24
  5. 4(3 – p) = -8

Multiplying two expressions in brackets (‘FOIL’ method)

When you have to multiply something in brackets by something else in brackets, you should use what’s called the ‘FOIL’ method. FOIL is an acronym that stands for:

First
Outside
Inside
Last

This is simply a good way to remember the order in which to multiply the terms, so we start with the first terms in each bracket, then move on to the outside terms in the whole expression, then the terms in the middle and finally the last terms in each bracket. Just make sure that you use the same trick we saw earlier, combining the operators with the numbers and letters before multiplying them together. For example:

(a + 1)(a + 2)

First we multiply the first terms in each bracket:

a x a

…then the outside terms:

a x +2

…then the inside terms:

+1 x a

…and finally the last terms in each bracket:

+1 x +2

Put it all together and simplify:

(a + 1)(a + 2)

= a² + 2a + a + 2

=a² + 3a + 2

Here are a few practice questions:

  1. (a + 1)(b + 2)
  2. (a – 1)(a + 2)
  3. (b + 1)(a – 2)
  4. (p – 1)(q + 2)
  5. (y + 1)(y – 3)

Factorising quadratics (‘product and sum’ method)

This is just the opposite of multiplying two expressions in brackets. Normally, factorisation involves finding the Highest Common Factor (or HCF) and putting that outside a set of brackets containing the rest of the terms, but some expressions can’t be solved that way, eg a² + 3a + 2 (from the previous example). There is no combination of numbers and/or letters that goes evenly into a², 3a and 2, so we have to factorise using two sets of brackets. To do this, we use the ‘product and sum’ method. This simply means that we need to find a pair of numbers whose product equals the last number and whose sum equals the multiple of a. In this case, it’s 1 and 2 as +1 x +2 = +2 and +1 + +2 = +3. The first term in each bracket is just going to be a as a x a = a². Hence, factorising a² + 3a + 2 gives (a + 1)(a + 2). You can check it by using the FOIL method (see above) to multiply out the brackets:

(a + 1)(a + 2)

= a² + 2a + a + 2

=a² + 3a + 2

Subtracting one expression from another*

Here’s the reason why we don’t just write down operators as we come across them. Here’s a simple expression we need to simplify:

20 – 4(x – 3) = 16

If we use the ‘wrong’ method, then we get the following answer:

20 – 4(x – 3) = 16

20 – 4x – 12 = 16

8 – 4x = 16

4x = -8

x = -2

Now, if we plug our answer for x back into the original equation, it doesn’t balance:

20 – 4(-2 – 3) = 16

20 – 4 x -5 = 16

20 – -20 = 16

40 = 16!!

That’s why we have to use the other method, treating the operator as a negative or positive sign to be added to the number before we multiply it by whatever’s outside the brackets:

20 – 4(x – 3) = 16

20 – 4x + 12 = 16

32 – 4x = 16

4x = 16

x = 4

That makes much more sense, as we can see:

20 – 4(4 – 3) = 16

20 – 4 x 1 = 16

20 – 4 = 16

16 = 16

Thank Goodness for that!

Here are a few practice questions:

  1. 30 – 3(p – 1) = 0
  2. 20 – 3(a – 3) = 5
  3. 12 – 4(x – 2) = 4
  4. 24 – 6(x – 3) = 6
  5. 0 – 6(x – 2) = -12

Other tips to remember

  • If you have just one variable, leave out the number 1, eg 1x is just written as x.
  • When you have to multiply a number by a letter, leave out the times sign, eg 2 x p is written as 2p.
  • The squared symbol only relates to the number or letter immediately before it, eg 3m² means 3 x m x m, NOT (3 x m) x (3 x m).

It’s all about the apostrophe

Apostrophes. The difference between feeling you’re nuts and feeling your nuts.Apostrophe

The apostrophe is tricky. It means different things at different times. This article is meant to clear up any confusion and help you use apostrophes, which might mean you get straight As in your exams – or should that be A’s?!

  1. The main reason for using apostrophes is to show a contraction, which is a word made up of two other words shunted together – the apostrophe just stands for the missing letter(s), eg didn’t = did not, could’ve = could have and won’t = will not.
  2. The second most common usage is in showing the possessive, in other words showing that something belongs to someone (or something). This is where it gets tricky, because where you put the apostrophe depends on how many things you’re talking about. If the noun is plural and ends with -s, you just need to put an apostrophe on the end of the word. In all other cases,  you should put ‘s, eg two horses’ hooves, BUT a horse’s hooves or the children’s books or St James’s Palace.
  3. The other occasion when you might find an apostrophe is in the plural of individual letters or numbers. Somehow, it just looks better, eg he got three A’s at O-level back in the 1980’s.

If you think you’ve mastered the rules, try taking this quiz!

Spelling rules

The problem with the English is that we’ve invaded (and been invaded by) so many countries that our language has ended up with a mish-mash of spelling rules.

Keep calm and check your spelling

 

 

 

 

 

 

English is among the easiest languages to learn but among the most difficult to master. One of the problems is spelling. We have so many loan words from so many different languages that we’ve been left with a huge number of spelling rules – and all of them have exceptions! Contrast that with Spanish, for example, where what you see is generally what you get. The problem for students of English, then, is that it’s very difficult to find shortcuts to improve your spelling, and an awful lot of words just have to be learned off-by-heart. Considering that there are over a million words in English, that’s a big ask!

There are lists of spelling rules out there (including a good one at www.dyslexia.org), but I thought I’d put down what I think are the most useful ones.

  1. I before E except after C when the sound is /ee/.
    This is the most famous rule of English spelling, but there are still exceptions! Hence, we write achieve with -ie- in the middle but also ceiling, with -ei- in the middle, as the /ee/ sound comes after the letter c. The most common exceptions are weird and seize.
  2. If you want to know whether to double the consonant, ask yourself if the word is like dinner or diner.
    One of the most common problems in spelling is knowing when to double a consonant. A simple rule that helps with a lot of words is to ask yourself whether the word is more like dinner or diner. Diner has a long vowel sound before a consonant and then another vowel (ie vowel-consonant-vowel, or VCV). Words with this long vowel sound only need one consonant before the second vowel, eg  shinerfiver and whiner. However, dinner has a short first vowel and needs two consonants to ‘protect’ it (ie vowel-consonant-consonant-vowel, or VCCV). If the word is like dinner, you need to double the consonant, eg winnerbitter or glimmer. Just bear in mind that this rule doesn’t work with words that start with a prefix (or a group of letters added to the front of a word), so it’s disappoint and not dissapoint.
  3. If the word has more than one syllable and has the stress on the first syllable, don’t double any final consonant.
    This rule sounds a bit complicated, but it’s still very useful – particularly if it helps you spot your teacher making a mistake! We generally double the final consonant when we add a suffix starting with a vowel, such as -ing, but this rule means we shouldn’t do that as long as a) the word has more than one syllable and b) the stress is on the first syllable, eg focusing and targeted, but progressing and regretting. The main exceptions to this are words ending in -l and -y, hence barrelling and disobeying.
  4. When adding a suffix starting with a consonant, you don’t need to change the root word unless it ends in -y. This is among the easiest and most useful rules. There are loads of words ending in suffixes like -less-ment or -ness, but spelling them should be easy as long as you know how to spell the root word, eg shoe becomes shoelesscontain becomes containment and green becomes greenness. However, words ending in -y need the y changing to an i, so happy becomes happiness.
  5. When adding a suffix starting with a vowel to a word ending in a silent -e, the must be dropped unless it softens a or a g.
    An at the end of a word is often called a ‘Magic E’, as it lengthens the vowel before the final consonant, eg fat becomes fate. However, that job is done by the vowel at the start of the suffix when it is added to the word, so it needs to be dropped, eg race becomes racing and code becomes coded. The main exceptions come when the word ends with a soft or g, which need to be followed by an -e, an -i or a -y to sound like /j/ and /s/ rather than /g/ and /k/. If the suffix doesn’t begin with an e- or an i-, we still need the to make sure the word sounds right, eg managing  is fine without the -e, as the in -ing keeps the soft, but manageable needs to keep the -e to avoid a hard /g/ sound that wouldn’t sound right.
  6. The only word ending in -full is full!
    There are lots of words ending in what sounds like -full, but the only one that has two ls at the end is full. All the other words – and there are thankfully no exceptions! – end in -ful, eg skilfulbeautiful and wonderful.

 

Parts of speech

When is a verb not a verb? When it’s a part of speech.

Parts of speech

English exams often ask questions about the ‘parts of speech’. This is just a fancy term for all the different kinds of words, but they’re worth knowing just in case. Just watch out for words such as ‘jump’, which can be more than one part of speech!

Noun: a word for a person, place or thing

  • abstract noun: a word to describe an idea, eg peace
  • common (or concrete) noun: a word for a thing or object, eg table
  • proper noun: the name of a person, place etc, eg Nick, London
  • collective noun: the name of a group of animals, eg herd or flock

Tip: Make up a phrase or a sentence with ‘the’ in front of the word. If it makes sense, it’s probably a noun, eg He looked at the ______.

Pronoun: a word that stands in for a noun

  • personal pronoun: a word that shows a person or thing, eg he, she, them
  • possessive pronoun: a word that shows the owner of an object, eg his, their
  • relative pronoun: a word that ‘relates’ to the subject just mentioned, eg who, that, which

Tip: Make up a phrase or a sentence with a verb after the word (but without ‘the’ or ‘a’ in front of it). If it makes sense, it’s probably a pronoun, eg ______ looked at the wall.

Verb: a doing word, eg jumped, was, pays

Tip: Make up a phrase or a sentence putting the word after a pronoun such as ‘he’. If it makes sense, it’s probably a verb, eg He ______ it or He ______ in the garden.

Adjective: a word that describes a noun or pronoun, eg green or young

Tip: Make up a phrase or a sentence putting the word between ‘the’ and a noun. If it makes sense, it’s probably an adjective, eg The ______ book lay on the table.

Article: a word that introduces a noun

  • definite article: the
  • indefinite article: a or an

Tip: Make up a phrase or a sentence with the word in front of a noun. If it makes sense, it’s probably an article, eg ______ book lay on the table.

Adverb: a word that describes an adjective, adverb or verb, usually ending in -ly, eg really or quickly

Tip: Make up a phrase or a sentence with the word after a verb. If it makes sense, it’s probably an adverb, eg He ran ______ around the garden.

Preposition: a word that shows the position in time or space, eg in, at or after

Tip: Make up a phrase or a sentence about placing something somewhere, putting the word before the location. If it makes sense, it’s probably a preposition, eg She put the book ______ the table.

Conjunction: a word that connects two sentences together (sometimes called a connective), eg and, but or because

Tip: Make up a phrase or a sentence with two clauses joined by the word. If it makes sense, it’s probably a conjunction, eg He looked at the problem ______ decided to do something about it.

Interjection: an outburst or word people say when they’re playing for time, eg hey, well, now or so

Tip: Make up a phrase or a sentence that someone might say, putting the word at the start, followed by a comma. If it makes sense, it’s probably an interjection, eg ______, can we go to the mall?

You can test yourself by reading any passage in English and going through it word by word, asking yourself what parts of speech they all are. Why not start with this article? See how fast you can go. If you’re not sure, ask yourself the questions in each of the tips shown above, eg if you think it’s a noun, can you put it into a sentence with ‘the’ in front of it?

Capital!

I always sign Christmas and birthday cards with a capital ‘N’. It makes me feel like Napoleon…

Letter N

The three main things to check after writing anything are spelling, punctuation and capital letters, so when do you use capitals?

  1. For the important words in titles, either of individuals or pieces of writing, eg Chief Inspector of Schools or This Blog Post is Great!
  2. For proper nouns, eg Peter, Tuesday and Chelsea.
  3. For abbreviations, eg BBC (although acronyms you can actually pronounce only need one at the start, eg Nato, not NATO).
  4. For the first word in a sentence, eg This is a sentence.
  5. For the first word in direct speech, eg he said, “Hello.”
  6. The word “I”.

Speech marks

Speech marks, inverted commas, quotation marks, quote marks, quotes, 66 and 99 – does any other punctuation mark have so many names or cause so much confusion…?!

speech marks

Writing a story means striking a balance between what I call The Three Ds: Drama, Description and Dialogue. I’ve read quite a few stories from my pupils in which nobody talks to anyone – which is a bit odd! – but you need to know the rules of punctuation before you start.

  • Start a new paragraph whenever the speaker changes or someone stops talking.
  • Put speech marks before and after the actual words spoken, eg Hello, he said, NOT “Hello, he said.”
  • Start the first spoken word with a capital letter, eg she said, “This needs a capital letter,” NOT she said, “this needs a capital letter.”
  • Put either a comma, question mark, exclamation mark or colon between the speech and the ‘he said/she said’, eg “Don’t forget the comma,” he said, NOT “Don’t forget the comma” he said.
  • Put punctuation that belongs to the speech inside the speech marks, eg “The exclamation mark belongs inside!“, NOT “The exclamation mark belongs inside”! (The only exception comes with inverted commas, which look the same but are used with quotations rather than speech.)
  • Put a full-stop after the ‘he said/she said’ if it comes in the middle of the speech and the first part is a full sentence; otherwise, just put a comma, eg “This is a full sentence,” she said. “This is, too.” BUT “This is not a full sentence,” she said, “and nor is this.”
  • Don’t start the ‘he said/she said’ with a capital letter, even if it comes after a question mark or exclamation mark, eg “Don’t use a capital letter!” he shouted, NOT “Don’t use a capital letter!” He shouted.
  • If a speech lasts more than one paragraph, put speech marks before each paragraph and after the last one but NOT after the ones before.
  • Finally, don’t put ‘he said/she said’ after every single line of dialogue in a long conversation if it’s obvious who is speaking.

Sample questions

Format and put the correct punctuation and capital letters into the following lines of speech:

  1. I say john what time is it she asked
  2. hello she said my name is tara
  3. what are you talking about he cried I never said that
  4. hello he said whats your name Sarah she said Im Alan Nice to meet you you too
  5. I hate chocolate she said I only really eat chocolate ice-cream

Divisibility rules OK!

Divisibility rules OK

And, no, this is nothing to do with Harry Potter’s invisibility cloak…

Times tables can be tricky, and there’s no substitute for learning them by heart. However, the divisibility rules can at least tell you whether an answer is definitely wrong. I’m a great believer in ‘sanity checking’ your work. Just ask yourself, “Is this crazy?” If it is, you’ll have to do the question again!

The divisibility rules are quite simple (except for the ones for 7 and 8). They tell you whether a number can be divided by any number from 1 to 10. They’re most useful when simplifying fractions…or when you’re struggling to remember your times tables!

  1. Must be a whole number, eg 2, but not 2.5.
  2. Must be an even number ending in 0, 2, 4, 6 or 8, eg 22, but not 23.
  3. The sum of the digits must be divisible by 3, eg 66, but not 67.
  4. The number formed by the last two digits must be ’00’ or divisible by 4, eg 500 or 504, but not 503.
  5. Must end in 5 or 0, eg 60, but not 61.
  6. Must be divisible by both 2 and 3, eg 18, but not 23.
  7. If you double the last digit and take this away from the number formed by the rest of the digits, the result must be 0 or divisible by 7, eg 672 (2 x 2 = 4, and 67 – 4 = 63, which is divisible by 7), but not 674.
  8. The number formed by the last three digits must be ’00’ or divisible by 8, eg 5,000 or 5,008, but not 5,003.
  9. The sum of the digits must be divisible by 9, eg 666, but not 667.
  10. Must end in 0, eg 110, but not 111.

Tips for the QTS numeracy test

“If I’d known I’d have to go back to school, I’d never have become a teacher!” Back-to-school-blackboard-chalk

The QTS numeracy and literacy tests are not very popular, but trainee teachers still have to pass them before they can start teaching in the state sector, so I thought I’d try and help out. There is always more than one way of doing a Maths question, but I hope I’ll demonstrate a few useful short cuts and describe when and how they should be used. The point of short cuts is that, even though you may have to do more sums, they’ll be easier sums that can be done faster and more accurately. The numeracy test consists of two sections – mental Maths and interpreting charts – and I’m going to focus on the first of these.

Fractions to percentages – type 1

There are a number of typical types of questions in the numeracy test, and a lot of them involve multiplication – so knowing your times tables is an absolute must! One of the most common kinds of question involves converting fractions to percentages. These are just two ways of showing the same thing, but to answer these questions you’ll need to try different approaches. First of all, have a look to see if the denominator (or the number on the bottom of the fraction) is a factor or a multiple of 100. If it is, you can simply multiply or divide the numerator (the number on the top) and the denominator by whatever it takes to leave 100 on the bottom. Any fraction over 100 is just a percentage in disguise, so you just need to put the percentage sign after the numerator, eg what is the percentage mark if:

  1. a pupil scores 7 out of a possible 20?
    Answer: 20 x 5 = 100, so 7 x 5 = 35%.
  2. a pupil scores 18 out of a possible 25?
  3. a pupil scores 7 out of a possible 10?
  4. a pupil scores 9 out of a possible 20?
  5. a pupil scores 130 out of a possible 200?

Fractions to percentages – type 2

If the denominator is not a factor of 100, check if it’s a multiple of 10. If it is, you can convert the fraction into tenths and then multiply the top and bottom by 10 to get a fraction over 100, which, again, is just a percentage in disguise, eg what is the percentage mark if:

  1. A pupil scores 24 marks out of a possible 40?
    Answer: 40 ÷ 4 = 10, so 24 ÷ 4 = 6 and 6 x 10 = 60%.
  2. A pupil scores 12 marks out of a possible 30?
  3. A pupil scores 32 marks out of a possible 80?
  4. A pupil scores 49 marks out of a possible 70?
  5. A pupil scores 24 marks out of a possible 60?

Fractions to percentages – type 3

If neither of the first two methods works, that means you have to simplify the fraction. Once you’ve done that, you should be able to convert any common fraction into a percentage in your head. The most commonly used fractions are halves, quarters, fifths and eighths, so it’s worth learning the decimal and percentage equivalents off-by-heart, ie

  • ½ = 0.5 = 50%
  • ¼ = 0.25 = 25%
  • ¾ = 0.75 = 75%
  • ⅕ = 0.2 = 20%
  • ⅖ = 0.4 = 40%
  • ⅗ = 0.6 = 60%
  • ⅘ = 0.8 = 80%
  • ⅛ = 0.125 = 12.5%
  • ⅜ = 0.375 = 37.5%
  • ⅝ = 0.625 = 62.5%
  • ⅞ = 0.875 = 87.5%

To simplify the fractions, check first to see if the numerator goes into the denominator. If it does, you can simply divide both numbers by the numerator to get what’s called a ‘unit fraction’, in other words a fraction with a one on top. By definition, a unit fraction can’t be simplified, so then you just have to convert it into a percentage. If the numerator doesn’t go exactly, try the first few prime numbers, ie 2, 3, 5, 7 and perhaps 11. Keep dividing both numbers in the fraction by the lowest possible prime number, and you’ll eventually show the fraction in its lowest terms. (If you happen to find a bigger number you can use, that’s great, as it means you won’t need to do as many sums.) When you’re left with one of the common fractions in the list above, you just have to convert it into the correct percentage, eg what is the percentage mark if:

  1. a pupil scores 7 out of a possible 28?
    Answer: 7 goes into 28 four times, so the fraction is 1/4, which is 25%.
  2. a pupil scores 27 out of a possible 36?
    Answer: 27 doesn’t go into 36, but 3 does, so 27/36 = 9/12, but 9 and 12 are also divisible by 3, so that makes 3/4, which is 75%.
  3. a pupil scores 24 out of a possible 48?
  4. a pupil scores 8 out of possible 32?
  5. a pupil scores 9 out of a possible 24?

Multiplying three numbers involving money

There is often a ‘real world’ money problem in the QTS numeracy test. That usually means multiplying three numbers together. The first thing to say is that it doesn’t matter in which order you do it, eg 1 x 2 x 3 is the same as 3 x 2 x 1. The next thing to bear in mind is that you will usually have to convert from pence to pounds. You could do this at the end by simply dividing the answer by 100, but a better way is to divide one of the numbers by 100 (or two of the numbers by 10) at the beginning and then multiply the remaining three numbers together, eg a number of pupils in a class took part in a sponsored spell to raise money for charity. The pupils were expected to get a certain number of correct spellings, and the average amount of sponsorship is shown for each. How many pounds would the class expect to raise for charity if the basic sum is:

  1. 20 x 30 x 5p?
    Answer: 2 x 3 x 5 = 6 x 5 = £30.
  2. 40 x 500 x 7p?
  3. 30 x 400 x 6p?
  4. 50 x 40 x 8p?
  5. 60 x 20 x 9p?

Division by single-digit numbers

This is what I call the ‘wedding planner problem’. There are three ways of doing this type of question:

  • Method A: Use the ‘bus stop’ method to divide the total number of guests by the number of seats per table – remembering to add one if there is a remainder.
  • Method B: Go straight to the end of your times tables by multiplying the number of seats by 12, then calculating the remainder and dividing by the number of seats per table, again remembering to add one if there is another remainder.
  • Method C: Use trial and error by estimating the number of tables needed using a nice, round number such as 5, 10 or 20 and working out the remainder as before.
  1. Dining tables seat 7 children. How many tables are needed to seat 100 children?
    Answer:
    Method A) 100 ÷ 7 = 14 r 2, so 14 + 1 = 15 tables are needed.

    Method B) 7 x 12 = 84, 100 – 84 = 16, 16 ÷ 7 = 2 remainder 2, 12 + 2 + 1 = 15 tables.
    Method C) 10 x 7 = 70, which is too small, 20 x 7 = 140, which is too big, 15 x 7 = 70 + 35 = 105, which is just right as there are only 5 seats to spare.
  2. Dining tables seat 6 children. How many tables are needed to seat 92 children?
  3. Dining tables seat 5 children. How many tables are need to seat 78 children?
  4. Dining tables seat 9 children. How many tables are needed to seat 120 children?
  5. Dining tables seat 6 children. How many tables are needed to seat 75 children?

Division by two-digit numbers

If the number of seats is outside your times tables, the best option is just to use trial and error, starting with 5, 10 or 20, eg

  1. It is possible to seat 40 people in a row across the hall. How many rows are needed to seat 432 people?
    Answer: 40 x 10 = 400, 432 – 400 = 32, so one more row is needed, making a total of 10 + 1 = 11 rows.
  2. It is possible to seat 32 people in a row across the hall. How many rows are needed to seat 340 people?
  3. It is possible to seat 64 people in a row across the hall. How many rows are needed to 663 people?
  4. It is possible to seat 28 people in a row across the hall. How many rows are needed to seat 438 people?
  5. It is possible to seat 42 people in a row across the hall. How many rows are needed to seat 379 people?

Percentages to fractions

This is a type of question that looks hard at first but becomes dead easy with the right short cut. All you need to do is to work out 10% first and then multiply by the number of tens in the percentage. Another way of saying that is just to knock one zero off each number and multiply them together, eg a test has a certain number of questions, each worth one mark. For the stated pass mark, how many questions had to be answered correctly to pass the test?

  1. ?/30 = 40%
    Answer: 3 x 4 = 12 questions (ie 10% of 30 is 3 questions, but we need 40%, which is 4 x 10%, so we need four lots of three, which is the same as 3 x 4).
  2. ?/40 = 70%
  3. ?/50 = 90%
  4. ?/80 = 70%
  5. ?/300 = 60%

Ratio – distance

There are two ways of converting between different units of distance from the metric and imperial systems:

  • Method A: Make the ratio into a fraction and multiply the distance you need to find out by that same fraction, ie multiply it by the numerator and divide it by the denominator. (Start with multiplication if doing the division first wouldn’t give you a whole number.)
  • Method B: Draw the numbers in a little 2 x 2 table, with the figures in the ratio in the top row and the distance you need to find out in the column with the appropriate units, then find out what you need to multiply by to get from the top row to the bottom row and multiply the distance you have to find out by that number to fill in the final box.
  1. 8km is about 5 miles. How many kilometres is 40 miles?
    Answer:
    Method A) 8:5 becomes 8/5, and 40 x 8/5 = 40 ÷ 5 x 8 = 8 x 8 = 64km.
    Method B)
    Miles                 km
    5                          8
    x 8
    40               8 x 8 = 64km
  2. 6km is about 4 miles. How many kilometres is 36 miles?
  3. 4km is about 3 miles. How many kilometres is 27 miles?
  4. 9km is about 7 miles. How many miles is 63 kilometres?
  5. 7km is about 4 miles. How many kilometres is 32 miles?

Ratio – money

You can use the same methods when converting money, except that the exchange rate is now a decimal rather than a fraction. Just remember that the pound is stronger than any other major currency, so there will always be fewer of them. It’s easy to get things the wrong way round, so it’s worth spending a couple of seconds checking, eg

  1. £1 = €1.70. How much is £100 in euros?
    Method A) 100 x 1.70 = €170.
    Method B)
    £                                      €
    1.00                              1.70
    x 100
    100                    1.70 x 100 = €170
  2. £1 = €1.60. How much is £200 in euros?
  3. £1 = €1.50. How much is €150 in pounds?
  4. £1 = €1.80. How much is €90 in pounds?
  5. £2 = €3.20. How much is £400 in euros?

Time – find the end time

The most useful trick to use here is rounding. If the length of a lesson is 45 minutes or more, then just round up to the full hour and take the extra minutes off at the end. This avoids having to add or subtract ‘through the hour’, which is more difficult. If the lessons are less than 45 minutes long, just work out the total number of minutes, then convert into hours and minutes and add to the start time, eg

  1. A class starts at 9:35. The class lasts 45 minutes. What time does the class finish?
    Answer: 9:35 + 1 hour – 15 minutes = 10:35 – 15 minutes = 10:20.
  2. A class starts at 11:45. There are three consecutive classes each lasting 25 minutes and then half an hour for lunch. What time does lunch finish?
    Answer: 11:45 + 3 x 25 + 30 = 11:45 + 75 + 30 = 11:45 + 1 hour and 15 minutes + 30 minutes = 13:30.
  3. Lessons start at 11:15. There are two classes each lasting 40 minutes and then lunch. What time does lunch start?
  4. Lessons start at 2:00 in the afternoon. There are four 50-minute classes with a 15-minute break in the middle. What time does the day finish?
  5. Lessons start at 9:40. There are two classes of 50 minutes each with a break of 15 minutes in between. What time do the classes finish?

Time – find the start time

It’s even more important to use rounding when working backwards from the end of an event, as subtraction is that bit more difficult, eg

  1. A school day finishes at 3:15. There are two classes of 50 minutes each after lunch with a break of 15 minutes in the middle. What time does lunch end?
    Answer: 3:15 – 2 hours + 2 x 10 minutes – 15 minutes = 1:15 + 20 minutes -15 minutes = 1:20.
  2. A school day finishes at 4:30. There are two classes of 40 minutes each after lunch. What time does lunch finish?
    Answer: 4:30 – 2 x 40 = 4:30 – 80 minutes = 4:30 – 1 hour and 20 minutes = 3:10.
  3. Lunch starts at 1:05. There are two classes before lunch of 55 minutes each. What time do the classes start?
  4. Lunch starts at 1:15. There are three classes before lunch of 45 minutes each. What time do the classes start?
  5. A school bus arrives at school at 8:45. It picks up 20 children, and it takes an average of four minutes to pick up each child. What time is the first child picked up?

Percentage to decimal

A decimal is a fraction of one unit, but a percentage is a fraction of 100 units, so, to convert from a percentage to a decimal, you just need to divide by 100, eg

  1. What is 20% as a decimal?
    Answer: 20 ÷ 100 = 0.2.
  2. What is 30% as a decimal?
  3. What is 17% as a decimal?
  4. What is 6% as a decimal?
  5. What is 48% as a decimal?

Multiplying decimals

Decimal points can be confusing, so the best way to do these sums is to take out the decimal point and put it back at the end. You just need to remember to make sure there are the same number of decimal places in the answer as in both numbers in the question, eg

  1. 1.5 x 1.5
    Answer: 15 x 15 = 10 x 15 + 5 x 15 = 150 + 75 = 225, but there are two decimal places in the numbers you’re multiplying together, so the answer must be 2.25.
  2. 3 x 4.5
  3. 4.7 x 8
  4. 7.5 x 7.5
  5. 2.5 x 6.5

Multiplying decimals by a power of 10

Because we have 10 fingers, we’ve ended up with a ‘decimal’ number system based on the number 10. That makes it really easy to multiply by powers of 10, because all you have to do is to move the decimal point to the right by a suitable number of places, eg one place when multiplying by 10, two when multiplying by 100 etc. (You can also think of it as moving the digits in the opposite direction.) This type of question is therefore one of the easiest, eg

  1. 4.5 x 10
    Answer: 45.
  2. 3.8 x 100
  3. 7.6 x 1000
  4. 4.6 x 100
  5. 3.5 x 10

Percentage of quantity

Finding a percentage is easy if it ends with a zero, as you can start by finding 10% (Method A). If you happen to know what the fraction is, you can also divide by the numerator of that fraction (Method B), so 20% is 1/5, so you just need to divide by five, eg

  1. Find 20% of 360
    Answer:
    Method A) 360/10 x 2 = 36 x 2 = 72.
    Method B) 360 ÷ 5 = 72 (or 360 x 2 ÷ 10 = 720 ÷ 10 = 72).
  2. Find 20% of 45
  3. Find 30% of 320
  4. Find 60% of 60
  5. Find 80% of 120

Multiplication

Just because this is the ‘mental Maths’ section of the test doesn’t mean that you can’t work things out on paper, and these simple multiplication sums can be done like that. Alternatively, you can use ‘chunking’, which means multiplying the tens and units separately and adding the results together, and the short cut for multiplying by five is to multiply by 10 and then divide by two, eg

  1. 23 x 7
    Answer: 20 x 7 + 3 x 7 = 140 + 21 = 161.
  2. 42 x 5
    Answer: 42 x 10 ÷ 2 = 420 ÷ 2 = 210
  3. 34 x 6
  4. 56 x 8
  5. 34 x 8

Short division

Again, working these sums out on paper is probably quicker (and more reliable), although the easiest way to divide by four is probably to halve the number twice, and the short cut for dividing by five is to multiply by two and then divide by 10.

  1. 292 ÷ 4
    Answer: 292 ÷ 2 ÷ 2 = 146 ÷ 2 = 73.
  2. 345 ÷ 5
    Answer: 345 x 2 ÷ 10 = 690 ÷ 10 = 69.
  3. 282 ÷ 3
  4. 565 ÷ 5
  5. 432 ÷ 4

Ratios

Hundreds of years ago, it was traditional to put dragons on maps in places that were unknown, dangerous or poorly mapped. Ratios are one of those places…

Here be ratios...!

Here be ratios…!

A ratio is just a model of the real world, shown in the lowest terms, but answering ratio questions can be just as scary as meeting dragons if you don’t know what you’re doing. The key to understanding ratios is to work out the scale factor. This is just like the scale on a map. If a map is drawn to a scale of 1:100,000, for instance, you know that 1cm on the map is the same as 100,000cm (or 1km) in the real world. To convert distances on the map into distances in the real world, you just need to multiply by the scale factor, which is 100,000 in this case. (You can also go the other way – from the real world to the map – by dividing by the scale factor instead.)

To work out the scale factor in a Maths question, you need to know the matching quantities in the real world and in the model (or ratio). Once you know those two numbers, you can simply divide the one in the real world by the one in the ratio to get the scale factor. For example:

If Tom and Katie have 32 marbles between them in the ratio 3:1, how many marbles does Tom have?

To answer this question, here are the steps to take:

  1. Work out the scale factor. The total number of marbles in the real world is 32, and the total in the ratio can be found by adding the amounts for both Tom and Katie, which means 3 + 1 = 4. Dividing the real world total by the ratio total gives 32 ÷ 4 = 8, so the scale factor is 8.
  2. Multiply the number you want in the ratio by the scale factor. If Tom’s share of the marbles in the ratio is 3, then he has 3 x 8 = 24 marbles.

The matching numbers in the real world and the ratio are sometimes the totals and sometimes the individual shares, but it doesn’t matter what they are. All you need to do is find the same quantity in both places and divide the real world version by the ratio version to get the scale factor. Once you’ve done that, you can multiply any of the ratio numbers to get to the real world number (or divide any real world number to get to the ratio number). Different questions might put the problem in different ways, but the principle is the same.

One complication might be having two ratios that overlap. In that case you need to turn them into just one ratio that includes all three quantities and answer the question as you normally would. For example:

If there are 30 black sheep, and the ratio of black to brown sheep is 3:2, and the ratio of brown to white sheep is 5:4, how many white sheep are there?

This is a bit more complicated, but the basic steps are the same once you’ve found out the ratio for all three kinds of sheep. To do this, we need to link the two ratios together somehow, but all the numbers are different, so how do we do it? The answer is the same as for adding fractions with different denominators (or for solving the harder types of simultaneous equations, for that matter): we just need to multiply them together. If we were adding fifths and halves, we would multiply the denominators together to convert them both into tenths. Here, the type of sheep that is in both ratios is the brown one, so we simply have to make sure the numbers of brown sheep in each ratio (2 and 5) are the same by multiplying them together (to give 10). Once we’ve done that, we can combine the two ratios into one and answer the question. Here goes:

  • Ratio of black sheep to brown sheep = 3:2

Multiply by 5

  • Ratio of black sheep to brown sheep = 15:10
  • Ratio of brown to white sheep = 5:4

Multiply by 2

  • Ratio of brown to white sheep = 10:8
  • Therefore, ratio of black sheep to brown sheep to white sheep = 15:10:8

Now that we have just one ratio, we can answer the question by following exactly the same steps as before:

  1. Work out the scale factor. The total number of black sheep in the real world is 30, and the total in the ratio is 15. Dividing the real world total by the ratio total gives 30 ÷ 15 = 2, so the scale factor is 2.
  2. Multiply the number you want in the ratio by the scale factor. If the number of white sheep in the ratio is 8, then there are 8 x 2 = 16 white sheep.

Simple!

Here are a few practice questions:

  1. One hundred paintings have to be selected for an art exhibition. If the ratio of amateur paintings to professional paintings has to be 2:3, how many amateur paintings and professional paintings have to be selected?
  2. The ratio of brown rats to black rats is 3:2. If there are 16 black rats, how many brown rats are there?
  3. Peter has 20 blue pens. How many red pens must he buy if the ratio of blue to red pens has to be 2:3?
  4. There are 35 children in a class and 15 are boys. What is the ratio of boys to girls?
  5. There are 15 girls and 12 boys in a class. What is the ratio of girls to boys? Give your answer in its simplest form.
  6. A newspaper includes 12 pages of sport and 8 pages of TV. What is the ratio of sport to TV? Give your answer in its simplest form.
  7. Anna has 75p, and Fiona has £1.20. What is the ratio of Anna’s money to Fiona’s money in its simplest form?
  8. Sam does a scale drawing of his kitchen. He uses a scale of 1:100. He measures the length of the kitchen as 5.9m. How long is the kitchen on the scale drawing? Give your answer in mm.
  9. A recipe to make lasagne for 6 people uses 300 grams of minced beef. How much minced beef would be needed to serve 8 people?
  10. A recipe for flapjacks requires 240g of oats. This makes 18 flapjacks. What quantity of oats is needed to make 24 flapjacks?
  11. Amit is 12 years old. His brother, Arun, is 9. Their grandfather gives them £140, which is to be divided between them in the ratio of their ages. How much does each of them get?
  12. The angles in a triangle are in the ratio 1:2:9. Find the size of the largest angle.
  13. In a certain town, the ratio of left-handed people to right-handed people is 2:9. How many right-handed people would you expect to find in a group of 132 people?
  14. Twelve pencils cost 72p. Find the cost of 30 pencils.
  15. Jenny buys 15 felt-tip pens. It costs her £2.85. How much would 20 pens have cost?
  16. If three apples cost 45p, how much would five apples cost?
  17. Sam is 16 years old. His sister is 24 years old. What’s the ratio of Sam’s age to his sister’s age? Give your answer in its simplest form.
  18. A map scale is 1:20000. A distance on the map is measured to be 5.6cm. What’s the actual distance in real life? Give your answer in metres.
  19. A recipe for vegetable curry needs 300 grams of rice, and it feeds 4 people. How much rice would be needed for 7 people?
  20. £60 is to be divided between Brian and Kate in the ratio 2:3. How much does Kate get?

Athens

Teaching Greek children is like watching France play rugby: you never know what you’re going to get…

The Stoa of Attalos marble colonnade and ceiling

Stoa of Attalos: the Athenian version of the local mall

 

I just spent two weeks in Greece preparing a Greek boy and his twin sisters for 10+ and 12+ entrance examinations at a school in England. Highlights included spending a long, sunny weekend at a holiday home in Lagonissi, spending another long, sunny weekend skiing near Delphi – I wonder if the oracle saw that one coming! – and seeing the Parthenon every day from my hotel balcony.

Political refugees take many forms, but, personally, I prefer shipping magnates fleeing with their adorable (if strong-willed) families from Communist governments in the Mediterranean…