Mathematics
Advanced
50 mins
Teacher/Student led
+80 XP
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IWB/Projector/Large Screen
Counters

Equivalent Expressions

Discover how repeated addition and multiplication describe the same amount. Use a balance beam to match expressions like 4 + 4 + 4 and 3 × 4, then find missing numbers to keep both sides level.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at this: 4 + 4 + 4. That is three lots of four.

    Is there a shorter way to write three lots of four, without adding it all out one bit at a time?

    2 - Watch and Notice ~8 mins

    Two pans, and each pan holds one way of writing the same amount. When both pans hold the same value, the beam hangs level.

    Now the same idea again, with a different number of groups. Watch whether the beam still hangs level.

    3 - Try It Together ~10 mins

    Today we lay counters into equal rows and write the multiplication that matches. First we make 3 rows of 4. Then 2 rows of 6. Then 5 rows of 2. Last of all, 3 rows of 3. Each time, count the groups, count how many are in each, and say both the repeated addition and the multiplication.

    Hands-on Task

    4 - Write It Both Ways in Your Copy ~2 mins

    COPYBOOK MOMENT

    In your maths copy, write these two lines:

    • 3 + 3 + 3 + 3 written as a multiplication
    • 2 × 6 written as a repeated addition

    Underneath each line, write the total to show the two ways balance.

    5 - Class Challenge ~9 mins

    Today we balance the beam by finding the missing number. Work out how many equal groups are hiding in each puzzle.

    First, two where the group size or number of groups is missing:

    • 5 + 5 = 2 × ?
    • 2 + 2 + 2 = 3 × ?

    Then two where the missing part is inside the addition:

    • 3 × 4 = 4 + 4 + ?
    • 3 × 4 = 6 + ?  (two steps) — first work out what 3 × 4 makes, then find what you add to 6 to reach it.

    Find the missing number to balance the beam

    Pupil practice
    Module 10 · Algebra: Patterns, Rules and Number Sentences Mixed
    Lesson 117 · Equivalent Expressions
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