Every child makes mistakes in arithmetic — but when the same mistakes keep coming back, it is a sign to stop and understand what is going on. Here are five of the most common mistakes in Years 3-6 and how to put them right at home, simply and without pressure.
Mistakes are not failure — they are part of learning
When a child comes home with an exercise book full of red crosses, every parent's first instinct is to correct and re-explain. But research in maths education teaches something different: the mistake itself is the most powerful learning tool. When a child discovers that their answer is wrong and understands why — they build a deep understanding that will stay with them for years.
The problem is not the mistake, but when the same mistake repeats itself again and again without anyone understanding its root. So we have gathered here the five most common calculation mistakes among pupils in Years 3-6, with a simple explanation of why they happen and how you can fix them at home — together with your child, without textbooks and without pressure.
Mistake 1: forgetting to carry in column addition
A very common calculation in Year 3: 47 + 38. The child works out 7 + 8 = 15, writes down the 5 and forgets to carry the 1 into the tens column. The result they get: 75 instead of 85.
Why does it happen?
Children's brains at this age are still training their working memory — the ability to hold several items at once. When the child concentrates on adding the ones, they 'forget' to keep hold of the 1 carried into the next column. It is not a problem of understanding, but of managing attention.
- Always write the carried digit above the tens column — even if it seems unnecessary. Make it a habit.
- Practise in columns: write the calculation vertically on squared paper, column by column. The visual layout helps memory.
- Check together: after the child finishes, ask them to check by subtracting — does 85 minus 38 equal 47? That is a strong reinforcement.
Mistake 2: in short and long division — muddling where the digits go
Formal division is one of the big challenges of Years 4-6. A calculation like 156 ÷ 4 requires the child to carry out several steps and place every digit in exactly the right position. A common mistake: the child divides correctly but puts the digit in the wrong column, and gets 3 instead of 39.
Why does it happen?
Long division is a complex algorithm: divide, multiply, subtract, bring down — four steps that repeat. Many children master each step separately but lose the spatial layout — exactly where to write the digit. Unlined paper, untidy handwriting, or rushing — all of them contribute to the confusion.
- Use squared paper: one digit per square. It helps keep a straight line and tidy columns.
- Write the four steps of long division in the corner: 'divide → multiply → subtract → bring down' and have the child say them out loud each time.
- Practise with a calculator afterwards: let the child solve it and then check with a calculator. The comparison between the answers is immediate and reinforcing.
Mistake 3: in fractions — adding numerators and denominators and getting a wrong answer
1/2 + 1/3 = 2/5 — this is one of the most common and most dangerous mistakes in arithmetic. The child simply added the numerators (1 + 1 = 2) and the denominators (2 + 3 = 5). Their logic is understandable, but the correct answer is 5/6.
Why does it happen?
Children learn that when adding whole numbers — you add everything together. When they meet fractions for the first time, they carry the same rule over to the fraction — and add both the numerator and the denominator. They do not understand that the denominator describes 'how many parts there are in each whole' and cannot be changed by simple addition.
- Use pizza: explain that the denominator = the number of slices in a whole pizza. If one person has 1/2 a pizza and another has 1/3 — they cannot be added directly because the slices are different sizes.
- Draw fraction bars: draw two equal rectangles, split the first into 2 and the second into 3. Shade them and show that the sizes are different — which is why you need a common denominator.
- Practise with the MathsUK fraction calculator: see the solution step by step and go over the logic together.
Mistake 4: in the order of operations — working left to right instead of by the rule
The calculation: 3 + 4 × 2. A child who works from left to right gets: 3 + 4 = 7, then 7 × 2 = 14. The correct answer is 3 + (4 × 2) = 3 + 8 = 11. The difference — three — can be the difference between a right and a wrong answer in a test.
Why does it happen?
Reading, and the maths taught in the early years, both run in one direction — from left to right, in the order things arrive. The child is used to solving as they read — from first to last. The order-of-operations rule (multiplication and division before addition and subtraction, brackets first) is a convention, not intuitive, and needs conscious practice.
- Highlight the higher operations: before the child starts to solve, ask them to draw a circle around every multiplication or division. Those get solved first.
- Learn the acronym: BIDMAS — brackets, indices (if they have learnt them), division and multiplication, addition and subtraction. Pin it up on the wall of the homework corner.
- Build calculations together: create a calculation together where changing the order of operations gives a different answer. A child who experiences it for themselves does not forget.
Mistake 5: with negative numbers — moving the wrong way along the number line
−5 + 3: many children will work out the answer as −8 instead of −2. They saw two numbers and 'added' them — 5 + 3 = 8 — and kept the minus. The problem: adding a positive number moves right along the number line, not left.
Why does it happen?
Negative numbers are an abstract representation that does not exist in children's ordinary physical world. They cannot 'see' minus five apples. They learn a rule: 'adding = putting more on' — and when you add, they think the number goes up. They do not understand that adding a positive number to a negative one moves us right along the line — closer to zero, not further from it.
- Draw a number line: a simple hand-drawn line from −10 to +10 on paper. Ask the child to put a finger on −5 and then move three steps to the right. Where are they standing? −2.
- Use temperature: 'It is −5 °C outside. It warms up by 3 degrees. How cold is it now?' The link to real life connects the abstract to the concrete.
- Set a visual rule: 'adding = go right, subtracting = go left — always, whatever the number.'
How to build mathematical confidence over time
When you discover that a child is making one of these mistakes, the most important thing is not to react with frustration. A child who thinks they are 'no good at maths' will stop trying. A child who gets positive, precise feedback — 'you're really close, you just forgot to carry' — keeps trying and moves forward.
Together, do these simple things at home: sit for 10-15 minutes a week with focused practice sheets, get the number line out together when there is any doubt, and build a language of curiosity — 'interesting, let's work out together why that happened' — instead of a language of criticism.
Research in the UK and around the world shows that regular parental involvement in maths homework measurably improves attainment. You do not need to be a teacher — you need to be present, patient and trusting.
Frequently asked questions
Are repeated mistakes a sign of a learning difficulty?
Not necessarily. Most repeated mistakes in arithmetic come from a wrongly internalised rule — not from a difficulty. If the mistake is corrected after a focused explanation, it is an ordinary learning gap. Only if the mistake persists after repeated intervention is it worth consulting the class teacher or the school's SENCO.
How long does it take to fix a repeated mistake?
With short daily practice (10-15 minutes), most children fix a structural mistake within three to four weeks. The key is consistency — a little every day beats two hours once a week.
Should we use a calculator?
At the learning stage — no. But after solving independently, a calculator is an excellent checking tool. The child solves, checks with the calculator, and sees straight away whether they were wrong. That is immediate feedback that reinforces learning.
My daughter has been making the 1/2 + 1/3 = 2/5 mistake for six months. What do we do?
This is a deep structural mistake that needs a visual approach. Start with a real pizza or with drawing rectangles — not with a verbal rule. The moment the child understands visually that different denominators = different sizes, the correct understanding builds faster.
How do you explain to a child what a number line is?
Draw a straight line together, put zero in the middle and positive numbers to the right and negative to the left. Say that the line is 'the number road' — right = going up, left = going down. Ask the child to move a finger and not to calculate in their head at first.
Are all these mistakes covered at school?
Yes. All five mistakes we have described are part of the compulsory content of Years 3-6 in the National Curriculum. Teachers go over them, but in a class of 30 children it is not always possible to give individual attention to every child.
What do we do when the child gets cross and refuses to practise?
Reduce the amount. Only 5 questions — not 20. Present the topic as a game challenge: 'Let's see if you can do 5 without a mistake today.' A small success builds motivation for the next session.
Can MathsUK help me practise these topics?
Absolutely. On MathsUK you can practise column addition with carrying, long division, fractions and the order of operations — with questions matched by year group and instant feedback. All free, no sign-up.
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