Mathematics

Beginner

50 mins

Teacher/Student led

Learning Goals

Learning Outcomes

Lesson Files

+80 XP

Teacher-led from the board. Pupils do not need a device, but can follow on one.

What you need:
IWB/Projector/Large Screen

Properties of Operations, Order and Inverse Links

Explore how swapping the order of numbers in addition and multiplication keeps the answer the same, and discover how inverse operations undo each other using balanced scales.

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Write the Fact Pairs in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

Your turn

Your teacher is running this lesson on the board. Here is the part you can try yourself.

Your written work is on page 116

Balance scales

1 - Getting Started ~4 mins

Two level balance scales: 4 + 9 against 13, and 9 + 4 against 13 On one set of scales the left pan holds 4 + 9. On another the left pan holds 9 + 4. Both right pans hold 13.

Both scales stay level, even though the numbers have swapped places. Why? Would that work for any two numbers?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Look at the four scales on the board. On each one, the two pans look different but stay perfectly level. Look for the pattern in each pair, what has been swapped, and what has been taken back off.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

We'll balance these on the scales together, one at a time. Predict each missing block first, then say whether it came from swapping the order or from taking a number back off.

6 + 7 = 7 + ?
5 + 9 = 9 + ?
7 + 8 = 15, so 15 − 8 = ?
9 + 5 = 14, so 14 − 5 = ?

Balance the swap and the undo

+15 XP

4 - Write the Fact Pairs in Your Copy ~2 mins

COPYBOOK MOMENT

In your maths copy, write 7 + 8 with its matching subtraction fact, and 6 × 4 with its matching division fact. Join each pair with a "↔" arrow to show that one undoes the other.

+10 XP

5 - Class Challenge ~9 mins

Now you try these on the scales, one at a time. Predict each missing block before we check, and say which idea you used — swapping the order or taking a number back off.

Swap it or undo it

+15 XP

Pupil practice

Module 10 · Algebra: Patterns, Rules and Number Sentences Algebra

Lesson 125 · Properties of Operations, Order and Inverse Links

Download Activity Book page (PDF)

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