Algebraic expressions and simple formulae
Maths · Key Stage 2 · The School
A letter can hide inside a sentence
An algebraic expression uses a letter to stand for a number that can change. "Five more than a number" is written n add 5. "Double a number" is written 2n, with no multiplication sign needed between a number and a letter. Writing the expression is really just translating the words. Read the sentence slowly, one small piece at a time, and the expression usually follows naturally.
Substituting a number in
Take the expression 2n add 3. If n stands for 4, replace the letter with 4: 2 times 4, add 3. That gives 8 add 3, which is 11. Substituting means swapping the letter for its actual value, then working the sum out as normal. The same expression gives a different answer for a different value of n. That is the whole point of using a letter in the first place.
A formula is a useful rule
A formula is an expression with a real job to do. The area of a rectangle is given by the formula A equals length times width. Give it real numbers — a length of 5 and a width of 3 — and it tells you the area is 15. A formula saves working the same kind of problem out from scratch every time.
Using a formula for pocket money
A pocket-money rule says p equals 2a, where a is a child's age. For a child aged 9, substitute 9 for a: p equals 2 times 9. That gives 18. So a 9-year-old gets £18. Substituting one careful step at a time is what keeps a working correct all the way through.