Topics · Primary Maths · Algebra
Algebra: a letter for a number you do not know yet
A letter stands for a number. That is all it is — and it lets you write down a relationship before you know the value, which is exactly what a bar model has been doing all along with its units.
- 97 exam papers analysed
- appears in 69% of P6 Maths papers
- ~3 min read
01 A letter is just a number in disguise
If Ali has n stickers, then having 5 more is n + 5, and having three times as many is 3n.
3n means 3 × n. The multiplication sign is left out to save writing, and dropping it is a convention, not a new operation.
The letter behaves exactly like a number. It can be added, multiplied, and substituted with a value when one is finally given.
02 Writing an expression
Most P6 algebra marks are for turning a sentence into an expression, not for solving anything.
- 5 more than n → n + 5.
- 5 less than n → n − 5. Not 5 − n, which is a different number.
- 3 times n → 3n.
- n shared among 4 → n ÷ 4, usually written as a fraction.
- Twice n, then add 5 → 2n + 5. Add 5 to n, then double → 2(n + 5). Brackets are what tells the two apart.
03 Simplifying: only like terms
2n + 3n = 5n, because two lots of something plus three lots of the same thing is five lots of it.
But 2n + 3 stays as it is. You cannot add an unknown number of stickers to three stickers and write a single term, any more than you can add 2 metres to 3 kilograms.
Terms with the letter and terms without it are collected separately: 2n + 3 + 4n + 5 becomes 6n + 8.
04 Substituting a value
When the question finally gives you a value, put it in and work out the number.
If n = 4, what is 6n + 8? → 6 × 4 + 8 = 32. Order of operations still applies: multiply before adding.
Check whether the answer should be a number or an expression. “Express in terms of n” wants 6n + 8 and no more. Substituting a value there is answering a different question.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- algebrasayAL-juh-bruh
Using letters to stand for numbers you do not know yet.
- variablesayVAIR-ee-uh-buhlmore than onevariables
The letter standing for the unknown number.
- expressionsayik-SPRESH-uhnmore than oneexpressions
A piece of algebra like 2n + 5. It has no equals sign.
- termmore than oneterms
One part of an expression. 2n + 5 has two terms.
- like terms
Terms with the same letter, which can be added together. 2n and 4n are like terms; 2n and 4 are not.
- substitutesaySUB-sti-tyoot
To put a number in place of the letter and work out the value.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P6
Writing expressions from a sentence, simplifying like terms, and substituting a value to find a number.
Practise P6 Algebra — 10 questions →69% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“2n + 3 = 5n.”
Only like terms add. 2n and 3 are different things, so 2n + 3 is already as simple as it gets.
“3n means 3 and then n, like 34.”
It means 3 × n. Writing the number in front of the letter is shorthand for multiplying.
“5 less than n is 5 − n.”
n − 5. Start from n and take 5 away. 5 − n is what is left of 5 after taking n.
“2(n + 5) = 2n + 5.”
The bracket doubles everything inside it: 2n + 10.
“It asked in terms of n, so I put n = 4 and got 32.”
“In terms of n” wants the expression, 6n + 8. A number is the answer to a different question.
Now try it
10 questions across 1 levels, marked as you go with the working shown.