BODMAS tells you which operation to calculate first: brackets, powers, multiplication and division, then addition and subtraction. Work from left to right within each equal-priority pair. Practise Year 6 questions with Noah’s worked examples, a video, our game and a worksheet you can complete online or print.
Allow about 30–45 minutes for the lesson and one practice choice. Take a break or finish another day if you need to.
Progress controls need JavaScript. Saving has not been checked.
BODMAS is a memory aid for the order of operations: which part of an expression to calculate first.
Meet Noah. What does each bag need to contain?
Noah is preparing two different token orders for a school fair.
One order has loose tokens and bags. The other has three mixed bags. The arrangements are different, so their expressions need different brackets.
What you’ll learn
Choose which calculation comes first.
Use brackets, powers and equal priorities correctly.
Explain and correct a mistake.
1 · READ THE TOKEN ORDERS
Turn each picture into an expression
This is the worked model. In Order A, keep the six loose tokens separate, then show the two bags of three as 2 × 3: 6 + 2 × 3. In Order B, group the six blue and two gold tokens inside each bag: (6 + 2) × 3.
Order A
6 + 2 × 3
Order B
(6 + 2) × 3
Order A separates the six loose tokens from two bags of three. Order B keeps six blue and two gold tokens together in each bag.
Group and ungroup the tokens. The six loose tokens in A stay separate from the bags.
2 · SEE HOW THE ORDER WORKS
Follow each calculation one step at a time
Brackets: calculate inside them first.
Orders: powers such as squares; a square means multiply a number by itself. For example, 3² = 3 × 3, not 3 × 2.
Multiplication and division: they have equal priority, so work from left to right.
Addition and subtraction: they have equal priority, so work from left to right.
Multiplication and division
20 ÷ 5 × 2
20 ÷ 5 = 4, then 4 × 2 = 8.
Do not multiply 5 × 2 first. Division and multiplication share the same priority.
Addition and subtraction
16 − 7 + 3
16 − 7 = 9, then 9 + 3 = 12.
Do not add 7 + 3 first. Addition and subtraction share the same priority.
Brackets, then a power
(2 + 1)² + 4
2 + 1 = 3, so 3² + 4. Then 3² = 9, so 9 + 4 = 13.
3² means 3 × 3, not doubling 3.
Some resources use BIDMAS. Its “I” means indices, another name for powers. The order is the same.
3 · TRY IT YOURSELF
Choose the first step and finish each calculation
You have seen how the rules work. Now choose the first operation and enter the final answer. If something is wrong, use the hint and try again.
Check 1 of 5
You have practised brackets, powers and equal-priority operations. Now use the same working in your worksheet.
Need a hint?
Start with brackets, then powers. Multiplication and division share a priority, as do addition and subtraction. In either pair, work from the left.
4 · CHECK YOUR THINKING
Spot and fix the mistake
Sam works out 5 + 3 × 2 like this: (5 + 3) × 2 = 16. What did Sam change, and what is the correct answer? Try it on paper before opening the answer.
See one possible correction
The expression has no brackets, so the 3 × 2 multiplication comes first. Then add the 5: 5 + 6 = 11. Sam added 5 + 3 first, which changed the order by adding brackets that were not there.
Take the idea into your worksheet
All 14 questions continue Noah’s token orders and the rules you have just used. Their main focus is:
Token groups and brackets: questions 1, 4, 5, 12 and 13.
Choosing the next operation: questions 2, 3, 6, 7 and 8.
Powers: questions 9 and 10.
Explain, correct or create: questions 11 and 14.
Show the first step in your working. Then finish the question and check whether your answer fits the token story.
