Mathematics

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50 mins

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+80 XP

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IWB/Projector/Large Screen

Two-step Equations: Solving One Step at a Time

Solve two-step equations by unwinding one operation at a time. Use a balance beam to see why you undo addition or subtraction first, then division, keeping both sides level.

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

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a puzzle on the board: 2x + 3 = 11. We already know how to solve x + 5 = 12 in one move. This one has two things done to the x. Have a look: what is happening to the x here, and which thing would you undo first?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~11 mins

Each beam below is already balanced. The x-block was multiplied first, then a number added or taken away on the same pan. To find x we peel those back in reverse: take off or add back that number, then split the multiplied blocks into equal shares. Watch as we work each beam, and notice which move comes first every time.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~7 mins

Key point

Let us solve 2x + 5 = 13 together on the beam. First take 5 off both pans, so 2x = 8. Now work out x by sharing 8 across the two x-blocks. Say your value for x out loud before anyone touches the slider. Then slide x to that value and watch the beam settle level to check we were right.

Level the beam

+15 XP

4 - Unwind It in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, solve each two-step equation by unwinding one operation at a time. Undo the addition or subtraction first, then the multiplication. Show every step.

Before you begin, we check one answer together so you know how. For 2x + 3 = 11, find x then put it back into the original equation and check that both sides match.

Now work these three the same way:

2x + 3 = 11
3x − 2 = 7
4x + 1 = 21

Write the original equation. Then write your working, doing the same to both sides. Then write the value of x. Check by putting your answer back into the first line, just as we did.

+10 XP

5 - Class Challenge ~10 mins

Key point

Now we work through these equations together on the board, in order. First 2x + 3 = 11. Then 4x + 2 = 14. Then 3x − 1 = 8. Then 2x − 5 = 7.

Each one adds a wrinkle. The first two are straight adds. Then comes a subtraction on the pan. The last one gives the biggest answer to work back from. Work out x each time before we slide. Then slide to check and press Check.

Find x: two moves each

+15 XP

Pupil practice

Module 8 · Algebra: Patterns, Expressions and Equations Algebra

Lesson 116 · Two-step Equations: Solving One Step at a Time

Download Activity Book page (PDF)

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