Order of operations: what children learn
When a calculation contains more than one operation, the order you do them in matters. Year 6 pupils learn to use the order of operations to carry out calculations involving all four operations. The curriculum gives the example 2 + 1 × 3 = 5, but (2 + 1) × 3 = 9.
Many schools in England teach this with the mnemonic BODMAS or BIDMAS: Brackets, Orders (or Indices), Division and Multiplication, Addition and Subtraction. In the quiz, one of the wrong choices is always the answer you would get by working strictly from left to right, which is the most common mistake.
This topic covers the Year 6 statutory requirement in the National Curriculum in England (Number – addition, subtraction, multiplication and division): pupils should be taught to “use their knowledge of the order of operations to carry out calculations involving the 4 operations”. Year 6 pupils are usually aged 10–11.
For families following US standards, the closest Common Core standard is 6.EE.A.2.c, which is taught in Grade 6.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 150-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- Brackets first. Work out anything in brackets before anything else. In (12 + 3) × 4, do 12 + 3 = 15 first.
- Then powers. Squares and cubes come next, for example 3² in 10 + 3². (The game itself doesn't include powers.)
- Then multiplication and division. These have equal priority. Work them out from left to right. In 20 + 18 ÷ 3, do 18 ÷ 3 = 6 first.
- Then addition and subtraction. These also have equal priority, worked from left to right. So 20 + 18 ÷ 3 = 20 + 6 = 26.
Worked examples
Example 1: 12 + 5 × 6 = ?
Working: Multiply first: 5 × 6 = 30. Then 12 + 30.
Answer: 42
Example 2: (20 + 9) × 6 = ?
Working: Brackets first: 20 + 9 = 29. Then 29 × 6 = 174.
Answer: 174
Example 3: 8 × (11 − 4) = ?
Working: Brackets first: 11 − 4 = 7. Then 8 × 7.
Answer: 56
Common mistakes and how to fix them
- Working left to right regardless of the operations: 12 + 5 × 6 = 17 × 6 = 102. Underline the multiplication or division before starting, and do it first.
- Thinking division always comes before multiplication because D comes before M in BODMAS. Division and multiplication have equal priority; work them left to right. The same goes for addition and subtraction.
- Ignoring brackets. Circle the brackets first. Anything inside them is one number you must find before carrying on.
Activities to try at home
- Write a calculation without brackets and challenge each other to add brackets to make different answers: 2 + 3 × 4 can be 14 or 20.
- Use the four 4s puzzle: make each number from 1 to 10 using four 4s and any operations.
- Check calculator results: does your calculator follow the order of operations? (Most scientific ones do.)
Ideas for the classroom
- Use 'target number' games where pupils combine given numbers with operations and brackets to reach a target.
- Ask pupils to find and explain the mistake in a worked example.
- Link to algebra: 3 + 2n means 3 + (2 × n), not (3 + 2) × n.
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
What does BODMAS stand for?
Brackets, Orders, Division, Multiplication, Addition, Subtraction. BIDMAS uses Indices instead of Orders. Both mean the same thing.
Does multiplication come before division?
No. Multiplication and division have the same priority, so you work them from left to right. 12 ÷ 3 × 2 = 4 × 2 = 8.
Why is there an order of operations at all?
So that everyone gets the same answer from the same calculation. Without an agreed order, 2 + 1 × 3 could mean 5 or 9.
What is the US equivalent?
Common Core 6.EE.A.2.c (Grade 6) covers the order of operations. In the US it is often taught as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). 5.OA.A.1 (Grade 5) covers using parentheses.