An expression uses a letter for a number we don't know. Translate the words one instruction at a time. '5 less than n' means start with n and take 5 away: n − 5. '3 times n' is written 3n. Multiplying and dividing happen before adding, so 'multiply n by 3, then add 2' is 3n + 2. If the adding must happen first, use brackets: 'add 4 to n, then multiply by 3' is 3(n + 4).
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- expression
- numbers, letters and operations with no equals sign
- variable
- a letter that stands for a number
- brackets
- show which part to work out first
Worked examples
Write an expression for: 5 less than n.
- 1.Start with n.
- 2.Take 5 away, so the 5 comes after the − sign.
= n - 5
Write an expression for: multiply n by 3, then add 2.
- 1.Multiply first: 3n.
- 2.Then add 2. No brackets are needed.
= 3n + 2
Write an expression for: add 4 to n, then multiply the result by 3.
- 1.The first step gives n + 4.
- 2.The whole of n + 4 is multiplied by 3, so it goes in brackets.
= 3(n + 4)
For parents
Method: Translate one step at a time
What to say: What happens to n first? Try n = 10: does your expression match the words?
Common mistakes:
- Joins terms together, writing n + 4 as 4n or 3n + 2 as 5n.
- Writes subtraction or division in the order the words appear, e.g. '5 less than n' as 5 − n.
- Uses adding for 'times' or subtracting for 'divided by' (additive for multiplicative).
- Uses the opposite operation to the one described (adds for 'less than', divides for 'times').
- Adds brackets that change the order of the steps, so the adding happens before the multiplying.
- Leaves out the brackets, so only part of the expression is multiplied or divided.
- Writes only the first step of a two-step description.