Mathematics

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50 mins

Teacher/Student led

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+80 XP

What you need:
IWB/Projector/Large Screen

Solving Two-step Equations

Learn how to solve two-step equations by undoing operations in reverse order. Use balance scales to see why you remove the added or subtracted number before dividing by the multiplier.

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

1 - Getting Started ~4 mins

Key point

Here is a puzzle on the scales: 2x + 3 = 11. Two bags of the same size, plus three loose cubes, balance eleven cubes on the other side. Two things have happened to the bag: it was doubled, and three were added. Which one would you undo first to find what is in a single bag?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Three balanced puzzles on the scales, each still in its starting state. For each one, the loose cubes need to come off both pans first, and then the bags are shared out. Work out what a single bag is worth each time.

Look hard at the first puzzle before we solve it. The three loose cubes are still sitting on the pan. If we tried to share out the bags with those cubes still there, could we even tell what one bag holds? Why not?

The last one takes away instead of adds. The missing cubes need to go back on both sides first.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~7 mins

Now we solve one together on the scales: 2x + 5 = 13. First we take the loose cubes off both pans. Then we share out the bags. Say what you will do to both pans before anyone touches the slider.

Solve it together

+15 XP

4 - Solve It in Your Copy ~3 mins

COPYBOOK MOMENT

We just solved 2x + 5 = 13 on the scales. Now look at how that same work is written in two lines in your copy.

First line (peel the loose number off both sides): 2x = 8

Second line (share out the bags): x = 4

Box the final value of the letter.

In your maths copy, solve each two-step equation the same way: show both steps on separate lines, then box the final value of the letter.

2x + 7 = 15
3x − 1 = 14
4x + 2 = 18

Write the first line (what you did to both sides), the second line (dividing to find the letter), then box your answer.

+10 XP

5 - Class Challenge ~8 mins

Key point

Now we take turns solving these on the scales. First 2x + 5 = 13. Then 5x − 4 = 21. Then 3x + 2 = 20. Then 4x + 6 = 12, and that last one lands on an answer that is not a whole number. Peel off the number first, then divide. Predict where the beam will level before we check.

Balance the beam

+15 XP

Pupil practice

Module 10 · Algebra: Patterns, Expressions and Equations Algebra

Lesson 121 · Solving Two-step Equations

Download Activity Book page (PDF)

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