Here is a calculation with two operations in it: 4 + 3 × 2. Work it out in your head. What answer did you get?
Hands up if you got 14. Hands up if you got 10. We have two different answers to the very same calculation. By the end of today you will know which one is right, and why mathematicians had to make a rule so this never confuses anybody.
Write 4 + 3 × 2 on the board and take three hands-up answers, not open call-outs. Both 14 and 10 will come up — write both up and leave them there. Do not resolve it yet; the whole lesson turns on this being an open question until Watch and Notice. If nobody offers 10, that is fine — the point is that a second answer is possible.
Look at each calculation. Notice which operation is worked first, and see how that decides the answer.
4 + 3 × 2: the key one. Point back at the two answers from Getting Started. × before +, so 10 was right all along; left to right wrongly gives 14.
(4 + 3) × 2: same numbers, only the brackets are new. Ask what the brackets did. Bracket first gives 7, then × 2 = 14 — the answer flips.
5 + 6 × 2 − 8 ÷ 4: pause here. Get them to predict which two run first, then point those out on the snapshot. × and ÷ first (6 × 2 = 12, 8 ÷ 4 = 2), leaving 5 + 12 − 2; then + and − left to right give 15.
Static snapshots — point at the operation being worked, don't tap or drag.
Today we work through this together on the board: (8 − 3) × 4 + 6. It has brackets, so before we tap anything we'll say out loud which part the rule makes us do first. Then we will talk through 20 − 2 × (3 + 4) the same way.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
For (8 − 3) × 4 + 6: the bracket goes first (8 − 3 = 5), then × 4 = 20, then + 6 = 26. Ask a pupil to predict the first step before tapping.
For 20 − 2 × (3 + 4): this is the tricky one — pupils want to do 20 − 2 first. Head that off. The bracket (3 + 4 = 7) goes first, then 2 × 7 = 14, then 20 − 14 = 6. Revoice a strong answer: the multiplication reaches across before the subtraction, even though the subtraction is written first.
Let a different pupil work each expression; the history strip records each step so the class can look back.
In your maths copy, work each calculation step by step in the correct order, one line at a time. Circle the operation you do first on each line, so you can check your reasoning at the end. Work these three:
Walk the room glancing at which operation each pupil circled first on each line — this is whole-class copybook practice, not marking. Watch for the classic slip of circling the leftmost operation instead of the correct one on the third calculation.
Today we work through these together, each one a step harder: 6 + 5 × 2, then (9 − 4) × 3 + 7, then 30 − 3 × (2 + 5), then 8 + 4 × 3 − 12 ÷ 6. Work each one out in BIDMAS order, then check the final answer.
These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The practice set builds and uses fresh numbers, so pupils apply the rule rather than recall demo answers. Expected answers: 6 + 5 × 2 = 16 (× before +), (9 − 4) × 3 + 7 = 22 (bracket first), 30 − 3 × (2 + 5) = 9 (bracket reaches across the subtraction), 8 + 4 × 3 − 12 ÷ 6 = 18 (all four operations). Before each Check, have the class predict the final value. Use the ✓ as part of the narration — on the last one, yes, 18, that's it. The fourth is the pause: the key one of the whole bank, where every rule they've met is in play at once.
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