Undo it backwards: letters in maths
The Short Answer
Early algebra questions ask you either to substitute numbers into an expression or to find a hidden letter. Substitution works by swapping every letter for its number in brackets and then following the order of operations. Finding the letter works backwards: whatever was done last to build the equation is the first thing you undo.
Letters standing for numbers
A letter stands for a number, and 4a means four times a with the multiplication sign hidden. Most children arrive knowing that much.
Three words the paper uses precisely, so they are worth keeping straight:
An expression has no equals sign — 3n + 2. An equation has one, and can be solved — 3n + 2 = 14. A formula works one thing out from another — C = 3 + 2m.
The index only touches what it touches
This is the Year 5 mistake, and it is worth more marks than anything else here.
2a² means 2 × a × a. The little two is touching the a, and nothing else.
It does not mean 2a, all squared.
With a = 5: 2a² is 2 × 25 = 50. But (2a)² is 10² = 100.
Same symbols. Different meaning. One of them is worth a mark.
Substituting: swap in, order up, work down
Finding the letter: undo backwards
When the letter is what you are hunting for, think about how the equation was built, then take it apart in reverse. The thing that was done last is the first thing you undo.
To build 4x + 9 you start with x, multiply by four, then add nine. So to solve it: subtract nine, then divide by four.
With a bracket, the same logic. In 4(x − 3) = 28, the x had three taken away and then the whole thing was multiplied by four. So undo the times four first — divide both sides by 4, giving x − 3 = 7 — and only then add the three back. x = 10.
Answering 4 means ignoring the bracket and solving 4x − 3 = 28 instead.
And whatever you do to one side, you do to the other. That is not a rule someone invented. It is what the equals sign means.
Where do pupils lose marks?
Squaring the coefficient — 2a² read as (2a)².
Undoing in the wrong order, so 2x + 9 = 25 gives 17 instead of 8.
Ignoring a bracket, so 3(2x + 1) becomes 3 × 2x + 1.
Stopping too early — solving 5x = 45, getting 9, and writing 45. Or giving pence when the question asked for pounds. Read the last line again after you finish.
Try it yourself
Write brackets round every number you substitute, and one operation per line when you solve.
- If a = 5, what is 2a²?
- If y = 4, what is 3y²?
- Find x when 2x + 9 = 25.
- Find x when 4(x − 3) = 28.
- Find x when 7x = 4x + 21.
- 50. The index touches the a and nothing else, so five squared is 25, and 2 × 25 is 50. (2a)² would be 10², which is 100 — same symbols, different meaning.
- 48. Four squared is 16, and 3 × 16 is 48. Answering 144 means squaring the 3y — that is 12² — and it is the single most common error in Year 5 algebra.
- 8. Undo the plus nine first: 25 − 9 = 16. Then undo the times two: 16 ÷ 2 = 8. Undoing them the other way round gives 17.
- 10. The whole bracket was multiplied by four, and that happened last, so it is undone first: 28 ÷ 4 = 7, so x − 3 = 7, so x = 10. Check: 10 − 3 = 7, and 7 × 4 = 28. Answering 4 means ignoring the bracket.
- 7. There are x terms on both sides, so take 4x from both: 3x = 21, and x = 7. Check: 7 × 7 = 49, and 4 × 7 + 21 = 49 too. It balances.
How much practice does this type need at home?
Checking is the habit worth building, because it is free and it is decisive. Every solved equation can be put straight back in: 10 − 3 = 7, and 7 × 4 = 28, so x = 10 is right, and you know it is right without waiting to be told.
Children who check catch their own wrong-order and ignored-bracket errors. Children who don't, don't.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why is 2a² not the same as (2a)²?
Because an index applies only to the symbol it is touching. In 2a² the little two is touching the a, so only the a is squared and the answer is 2 × a × a. In (2a)² the bracket is touching it, so the whole of 2a is squared. With a = 5 those give 50 and 100. Substituting with brackets written in makes the difference visible immediately.
What does 'undo backwards' mean?
Think about how the equation was built, then take it apart in reverse. To build 4x + 9 you start with x, multiply by four, then add nine. So to solve it you subtract nine first and divide by four second — last thing done is first thing undone. It is the same logic as taking off a coat before a jumper.
Why must you do the same to both sides?
Because that is what the equals sign means: the two sides are worth the same, and they stay that way only if both are treated identically. It is not an arbitrary rule invented to make the working longer. Children who accept it as a rule tend to forget it; children who see why it is true rarely do.
What is the difference between an expression, an equation and a formula?
An expression has no equals sign — 3n + 2. An equation has one and can be solved — 3n + 2 = 14. A formula is an equation that works one quantity out from another, like C = 3 + 2m. The paper uses these words precisely, so it is worth being able to tell them apart even though the arithmetic does not change.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
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