Maths mistakes that cost marks

A very common mistake is to ignore a zero in the middle of a number. For example, in 3,047 some children think the 4 is in the hundreds place because they skip over the zero. But the zero is there for a reason — it is holding the hundreds place to show there are no hundreds. So the 4 is really in the tens place and is worth 40, not 400. Always count every digit, including zeros, when you work out which place a digit is in.

A very common mistake is to round the digit correctly but then leave the other digits as they are. For example, a child might round 3,472 to the nearest 100 and write 3,500 — so far so good — but then round to the nearest 1,000 and write 3,000 correctly, yet for the nearest 10 write 3,477 instead of 3,470.

This happens because it is easy to forget that the digits after the rounded place must become zeros.

Always check: after rounding, are all the digits to the right of your chosen place zeros? If not, change them to zeros before you write your answer.

A very common mistake is to carry a digit and then forget to include it when you add the next column.

For example, in 3,546 + 2,378, after adding the ones (6 + 8 = 14) you carry 1 to the tens. Some children then just work out 4 + 7 = 11 and forget the carried 1, writing 11 instead of 12.

To avoid this, always write the tiny carried digit clearly above the next column before you add, so you never lose it.

A very common mistake is to forget that 1 and the number itself are always a factor pair. Children often start looking from 2 and miss them.

1 × any number = that number, so 1 and the number are always factors.

Always write down '1 and the number' as your very first pair before you check anything else.

A very common mistake is multiplying a digit correctly and then forgetting to add the small carried number from the previous column.

For example, in 47 × 5: some children write 4 × 5 = 20, and put 20, forgetting to add the 3 they carried. The answer then becomes 205 instead of the correct 235.

How to avoid it: write the carried digit in small writing just above the next column before you do anything else. Then you will see it and remember to add it.

A very common mistake is forgetting to carry the remainder to the next digit. For example, when dividing 52 by 4, some children look at the 5, write 1 above it (because 4 goes into 5 once), and then divide 2 by 4 instead of 12 by 4. They get 13 remainder 0 instead of the correct answer 13. Wait — that one works out the same! Let us use a clearer example: 74 ÷ 3. You look at 7: 3 goes into 7 twice (2 × 3 = 6), remainder 1. If you forget to carry that 1, you divide 4 by 3 and write 1 remainder 1, giving 21 r1. But the correct answer is: carry the 1 to make 14, then 3 goes into 14 four times (4 × 3 = 12), remainder 2, giving 24 r2. Always carry the remainder before moving on.

A common mistake is thinking that −6 is bigger than −2 because 6 is bigger than 2.

Children often forget that the minus sign flips things around. The further left you go on the number line, the smaller the number — even if the digit looks big.

−6 is smaller than −2. On a thermometer, −6 °C is colder than −2 °C.

Always picture the number line. The number on the right is always the bigger one.

In a two-step problem, many children find one answer and think they have finished — but the question is asking for something else.

For example, in the sandwich problem, a common mistake is to stop after adding £2.40 + £1.15 = £3.55 and write £3.55 as the answer. But the question asked for the change, not the total cost.

How to avoid it: after every calculation, re-read the question and ask, 'Have I actually answered what it asked?' Only stop when your answer matches the question.

A very common mistake is forgetting to add the carried digit when multiplying.

For example, working out 36 × 4: - 6 × 4 = 24. Write 4 in the ones and carry the 2. - 3 × 4 = 12 — but now you must add the carried 2: 12 + 2 = 14. - Answer: 144.

If you forget the carried 2, you write 124 — which is wrong!

Always write the carried digit above the next column so you don't lose it.

A very common mistake is to multiply the amount by the denominator instead of dividing by it.

For example, for 1/4 of 20, some children write 20 × 4 = 80. That is much too big!

Always divide by the denominator first. The denominator tells you how many equal groups to split the amount into, so you share it out — and sharing means dividing.

A very common mistake is to multiply the top number but forget to multiply the bottom number (or the other way around). For example, changing 1/2 and writing 2/2 — that is wrong because 2/2 means a whole, not a half.

Always do the same thing to both the numerator and the denominator. Ask yourself: 'Did I multiply (or divide) both numbers by the same amount?' If yes, you're safe.

A very common mistake is thinking that a number with more digits must be bigger. For example, some children think 0.62 is bigger than 0.7 because it has more digits.

This is not right! Always compare the tenths digit first. 0.7 has 7 tenths but 0.62 only has 6 tenths, so 0.7 is larger.

To avoid this mistake, always line up the decimal points and compare column by column from left to right.

A very common mistake is to write 12:00 pm as 00:00 or to add 12 and get 24:00. Neither of these is right!

Here is the rule: 12:00 am (midnight) = 00:00 in 24-hour time. 12:00 pm (noon) = 12:00 in 24-hour time — it stays exactly the same.

The trick to remember: midnight is the very start of the day, so it gets the smallest number, 00:00. Noon is in the middle of the day, so it stays at 12:00. Only the hours from 1 pm to 11 pm need the +12 rule.

A very common mistake is to count the marks on a scale instead of the gaps between them. Look at a scale from 0 to 10 with marks at 0, 2, 4, 6, 8 and 10. There are 6 marks but only 5 gaps. If you divide by 6 instead of 5, you get the wrong answer.

Always count the spaces between the marks — not the marks themselves. Think of a ruler: there are spaces between the centimetre lines, not the lines themselves, that each measure 1 cm.

A very common mistake is writing 9p as £.9 instead of £0.09. The digit 9 must go in the units-of-pence column (the hundredths column), so you need a zero to hold the tens-of-pence column.

Always ask yourself: does my answer have two digits after the decimal point? If not, add a zero to fill the gap. For example, £2.5 should be written £2.50, and 9p should be written £0.09.

Many children forget to add 12 when they convert a pm time to the 24-hour clock. They write 3:00 pm as 03:00 instead of 15:00.

To avoid this, always ask yourself: 'Is it afternoon or evening?' If it is, add 12 to the hour number. Morning am times stay the same — but write midnight as 00:00, not 12:00.