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How to spot errors in calculations

Part of Mathematics and NumeracyPractise and revise KS2 maths

Introduction to errors in calculations

A girl studying errors in calculations for the SEAG transfer test

This page has been put together to help you practise and revisit some of the brilliant skills you’ve learned all through primary school.

It’s a great way to boost your confidence in Maths and get you ready for the exciting next step into Year 8!

Finding mistakes in a maths problem is a top skill to have and it's a great way to get better at checking your own work.

In this guide, you'll learn how to spot common errors in calculations, like mistakes with place value or decimal points.

We'll also look at how to explain what went wrong and how to correct it!

A girl studying errors in calculations for the SEAG transfer test
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Finding the mistake: column subtraction

A very common question in a maths test is the error spotting question.

You will be shown a calculation or a word problem that has a mistake.

Your job is to be a detective: find the mistake, explain what the pupil did wrong using clear mathematical terms, and show the correct working.

Let's look at a classic example in column subtraction.

The Problem: Anna was asked to solve £500 - £135.

Here is her working:

Sum £500 minus £135 equals £435 in order to show how to spot mistakes.

Her final answer was £435. Can you spot the mistake?

The Explanation: Anna's mistake happened in the units column. She tried to calculate 0 - 5 and wrote 5. She forgot to exchange (or 'borrow') from the tens and hundreds columns. Because the tens column was also a zero, she needed to exchange from the 5 in the hundreds column, all the way across.

By exchanging, the calculation becomes:

Units: 10 - 5 = 5

Tens: 9 - 3 = 6

Hundreds: 4 - 1 = 3

The correct answer is £365.

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Finding the mistake: decimals and place value

Another very common error is with place value, especially when decimal points are involved. This is a key part of the KS2 Number curriculum.

The golden rule is: line up the decimal points!

The Problem: Éamonn tried to add 14.5 + 3.95. Here's his setup:

A sum showing 14.5 plus 3.95 but no placeholder zero has been used to make sure the decimal points line up, useful skills for those preparing for the SEAG transfer test.

The Explanation: Éamonn's mistake was in the set-up. He lined up the numbers on the right-hand side, instead of lining up the decimal points. This means he added the 5 tenths (50p) from 14.5 to the 5 hundredths (5p) from 3.95, which is incorrect.

The Correction: To fix this, you must line up the decimal points. It helps to add a placeholder zero to 14.5 to make it 14.50.

sum showing 14.50 plus 3.95 equals 18.45, a placeholder zero has been added 14.50 to ensure the decimal points line up.

This shows the correct answer is 18.45. Always check the set-up!

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Finding the mistake: the method

Sometimes, a calculation is done correctly, but the method itself is wrong.

The Problem: A question asks: 'Find 25% of 80'. Charlie writes: 'To find 25%, I divided 80 by 25. The answer is 3.2.'

The Explanation: Charlie's calculation (80 ÷ 25 = 3.2) is correct, but his method is wrong. He has confused '25%' with 'divide by 25'.

The Correction: To find 25% of a number, you are finding a quarter (1/4). The correct method is to divide the number by 4.

Correct Working: 80 ÷ 4 = 20.

So, 25% of 80 is 20.

This type of error shows why you must read the question carefully and understand what it is asking you to do

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The builder's plank problem-solving journey

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Summary

A girl studying errors in calculations for the SEAG transfer test

Well done, error spotter! You now know how to check calculations for common mistakes.

You can spot errors in exchanging (subtraction), place value (decimals), and method (percentages).

A girl studying errors in calculations for the SEAG transfer test
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Brain boost

Think about these questions to stretch your thinking and sharpen your skills!

  • What is the most common mistake pupils make when calculating £1000 - £253? (Hint: Think about all the zeros!)

  • A pupil says, 'To find 50% of 90, I divide by 50.' Explain their mistake and describe the correct method.

  • Look at this sum: 7.2 x 100 = 7,200. Is this correct? Explain the mistake in terms of place value or 'moving the decimal point'.

Have a chat about your answers with a parent, teacher or your class.

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