Mathematics
Advanced
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
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+80 XP
Teacher-led from the board — pupils need no device
What you need:
IWB/Projector/Large Screen

Properties of Operations: Commutative, Associative, Distributive

Explore the commutative, associative and distributive properties of addition and multiplication using balance beams, then practise breaking harder calculations into easier ones.

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    Balance scales
    Balance scales

    1 - Getting Started ~4 mins

    Key point

    Look at the two multiplications on the board. One is four sevens and the other is seven fours. Is one of them bigger than the other, or do they come to the same answer? Hands up when you think you know.

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~9 mins

    Watch the balance beam. Each time two expressions are set on the pans. Before the second pan appears, predict: will the beam stay level or tip?

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~11 mins

    Key point

    Now we test each property on the beam together. We reset the same beam for each round. Predict level or tipped before each one is set:

    • 5 × 3 against 3 × 5
    • (1 + 4) + 2 against 1 + (4 + 2)
    • 4 × (5 + 1) against 4 × 5 + 4 × 1

    Balance the two sides

    +15 XP

    4 - Test the Properties in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, use these three headings, one per section. A worked example is shown under each — write one more of your own beneath it and check that both sides give the same answer.

    • Commutative (swap the order) — worked example: 4 × 7 = 7 × 4 = 28
    • Associative (group differently) — worked example: (2 + 3) + 5 = 2 + (3 + 5) = 10
    • Distributive (split a part) — worked example: 4 × (5 + 1) = 4 × 5 + 4 × 1 = 24
    +10 XP

    5 - Class Challenge ~8 mins

    Key point

    Today we work through these together on the board. Each round shows one full pan. You build the other pan so the beam stays level, then press Check:

    • 7 × 4
    • 2 + (5 + 3)
    • 4 × 5 + 4 × 1
    • 6 × 5 + 6 × 2
    • 8 × 4

    Balance both pans

    +15 XP
    Pupil practice
    Module 8 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 118 · Properties of Operations: Commutative, Associative, Distributive
    Download Activity Book page (PDF)
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