Equality and the Balance

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

1 - Getting Started ~4 mins

Picture a balance beam with a pan on each side. On the left pan we have x + 3. On the right pan we have 7. We don't yet know what x is, so the beam might be tipping one way or the other.

Key point

What number would x have to be to make the two pans weigh the same and the beam sit perfectly level?

Teacher Notes

Give five seconds of quiet think-time before any hands go up. Take two or three hands-up answers, not open call-outs. Don't confirm yet — we'll test it on the beam in a moment.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~10 mins

Watch four balances on the board. In each one, x is set to the value that makes the beam sit level. Look at how the two pans match once x is right.

This next one is different: the same letter appears twice on the left. Notice how the total is shared between the two copies.

This last one is a new kind: x sits alone on the left while the 9 and a block of 4 sit on the right. Notice that x is bigger than the 9 to balance both blocks.

Teacher Notes

Point at the equation line under each beam as it settles. Take the four beams in the order they appear on screen:

x + 3 = 7 — the starter case; hold out for pupils to say the left pan comes to 7 as well, both sides the same, so the beam is level.
2x = 10 — two identical blocks; the key question is how much is one block worth?
x + x = 8 — the sharing case; the answer is 8 shared between two copies, not 8 itself. This is the one that catches people.
x − 4 = 9 — the take-away case; x sits alone on the left and both the 9 and a block of 4 sit on the right, so x must be bigger than 9. Ask the class why x can't just be 9 before you name it.

Do not proceed until the class can say why the beam is level: the two pans weigh the same.

If the board is unavailable, draw a beam on the whiteboard and use number cards or counters for the blocks. Slide a card labelled x along until the two pans match, saying each pan's total aloud.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~8 mins

Key point

For each one, slide the x block until the beam sits level, then read off the value of x.

Today we work through these together on the beam. First x + 4 = 9, then x + 6 = 15, then 3x = 12.

Level the beam to find x

Teacher Notes

Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud. Change the pans between the three problems so the beam shows each equation in turn; the prompts below walk you through the sequence.

Before anyone slides x, ask the class to predict the value. Then slide and let the beam settle. 3x = 12 is the one to slow down on — ask how many x blocks are there, and how do we share the 12 between them? Revoice a strong answer: so if three copies weigh twelve, one copy weighs four.

If the board is unavailable, run the same three problems on a drawn beam with number cards, sliding the x card until the pans match.

+15 XP

4 - Work It in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, work each find-x problem in three lines. Write the equation on the top line. On the middle line, write in words how you levelled the beam (for example, what the left pan came to, or how you shared the total between the copies of x). Write the value of x on the bottom line.

Here is one worked out in full:

x + 3 = 7
Both pans come to 7, so the beam is level
x = 4

Now work each of these the same way in your copy:

x + 3 = 7
x + 5 = 12
2x = 10

Teacher Notes

Before copies open, write the three-line model on the board and talk it through once:

x + 3 = 7 (equation)
Both pans come to 7, so the beam is level (how it levelled)
x = 4 (value)

Then set them on the three problems. Walk the room glancing at the three-line layout, this is whole-class copybook practice, not marking. Look for pupils writing the value straight away with no middle line; nudge them to write in words how they got there, the pan totals matching, or the total shared between the copies of x. For 2x = 10, listen for sharing language: two copies share 10, one copy is 5. Pupils who need the visual can use the balance beam template to sketch each beam beside their working.

+10 XP

5 - Class Challenge ~8 mins

Key point

For each one, slide the x block until the beam is level and press Check to confirm the value of x.

Today we work through these numbers together on the beam. Start with x + 3 = 7. Then try x + 5 = 12. Next comes 2x = 10. After that, x − 4 = 9. Finish with 3x = 12.

Find x so the beam levels

Teacher Notes

This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

x − 4 = 9 shows x on the left pan and both 9 and 4 on the right, so x equals 9 + 4. Ask the class to predict before sliding.
3x = 12 is the sharing case: three copies share 12, so one x is 4.

On each Check, use the ✓ as part of the narration — yes, that's it, the beam is level.

+15 XP

Pupil practice

Module 8 · Algebra: Patterns, Expressions and Equations Algebra

Lesson 104 · Equality and the Balance

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This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~10 mins

3 - Try It Together ~8 mins

Level the beam to find x

4 - Work It in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Find x so the beam levels

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