Order of operations — for parents

Order of operations — for parents

Order of operations — for parents

Year 5 introduces the order of operations (PEMDAS in the US, BIDMAS in the UK) as a named convention. Children have been doing single-operation arithmetic for years; now they meet expressions that combine + − × ÷ and brackets, and they need an agreed rule for which operation goes first.

What your child should master by year-end

  • Apply the order: brackets first, then × and ÷, then + and −.
  • Compute multi-operation expressions correctly (e.g. `12 + 3 × 4 − 2`).
  • Understand that brackets change the answer, and use them to override the default order.
  • Translate short word problems into expressions with the correct brackets.
  • Show working step by step, one operation per line.

Common mistakes

Going purely left to right

The single most frequent error. A child sees `2 + 3 × 4` and reads it like a sentence, computing left to right: `5 × 4 = 20`. The correct answer is 14 because × comes first.

Help: ask them to scan for × and ÷ first. Once they find them, mentally put brackets around the × or ÷ piece, then re-read.

Forgetting that + and − are at the same level

Some children think "+ comes before −" because + is the "main" operation. They aren't — they're equals, and you go left to right.

20 − 5 + 3

  • Wrong: 5 + 3 = 8, then 20 − 8 = 12. ✗
  • Right: 20 − 5 = 15, then 15 + 3 = 18. ✓
Help: same level → left to right. Repeat it aloud as a chant.

Ignoring brackets

When a child computes `(3 + 4) × 2` as `3 + 4 × 2 = 11`, they've treated the brackets as decoration. Brackets are never decoration.

Help: practise rewriting expressions step by step, with the bracket result on its own line.

Trap-style ÷ × confusion

24 ÷ 4 × 2

Some children do 4 × 2 = 8 first, then 24 ÷ 8 = 3. But ÷ and × are the same level, so it's left to right: 24 ÷ 4 = 6, then 6 × 2 = 12.

Help: emphasise that "× before ÷" is wrong — they're equal.

Show working in three steps

Encourage your child to write each step on its own line. This single habit catches almost every order-of-operations mistake:

   3 × (8 − 2) + 4
=  3 × 6 + 4         (brackets first)
=  18 + 4            (× before +)
=  22

A pencil costs nothing; rewriting saves time and marks.

Things to try at home

Make up your own puzzles

Pick three numbers, two operations, and a bracket pair. See how many different answers you can produce by moving the brackets.

`2, 3, 4` with `+` and `×`:

  • `2 + 3 × 4 = 14`
  • `(2 + 3) × 4 = 20`
  • `2 + (3 × 4) = 14`
  • `2 × (3 + 4) = 14`
  • `(2 + 3 + 4) = 9` (only + ).

"Hidden brackets" in real life

Ask: "You buy 3 packs of biscuits at €1.50 each plus a €2 drink. How much in total?" The expression is `3 × 1.50 + 2`, no brackets needed because × goes first.

Then change it: "You buy 3 packs of biscuits and a drink, then a 2-pack offer cuts the price by half. How much?" That's `(3 × 1.50 + 2) ÷ 2`.

Real situations naturally use brackets — point them out.

Calculator double-check

Most calculators apply order of operations automatically. Have your child compute on paper, then type the expression into a calculator. If the answers differ, find the step where they parted.

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