Using a Box or a Letter for the Unknown

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Write 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 are two number sentences side by side:

□ + 3 = 9 and a + 3 = 9

One uses a box for the missing number. The other uses a letter. Is the missing number the same in both? Hands up: what do you think that missing number is?

Teacher Notes

Take three hands-up answers, not open call-outs. The point to draw out is that the box and the letter are two ways of writing the same hidden number — do not confirm the value yet, just get pupils noticing the two forms match.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Watch the balance beams. Each shows a number sentence with a letter for the unknown. Look for the value that levels the beam. The letter does the same job a box would do.

Now a fresh letter in a different sentence, b + 4 = 10.

The last one is different. Here the letter sits on its own on the left because the letter is the whole. On the right sit the two parts, 5 and 2. So d = 5 + 2. See if the same idea still works.

Teacher Notes

a + 4 = 9 — show the box version aloud first ("box plus four is nine"), then point out the letter a is doing the same job. Ask what a must be. Here a is 5.
b + 4 = 10 — a fresh letter, so pupils see the letter is just a name. This is a different sentence, so it has its own answer: b is 6. Do not link this back to the first balance; work it out fresh from four and ten.
d = 5 + 2 — hold out for this one. This is the take-away sentence d − 2 = 5 written whole-first: the letter d is the whole, and it is bigger than either part because it is the two parts joined back together. Both blocks on the beam are ordinary positive number blocks, so there is nothing negative to read. Say aloud "d is the whole, five and two are the parts".

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~9 mins

Let's work one out together on the balance. Our sentence is a + 4 = 9, written with a letter. We slide the letter until the beam hangs level. Then we say what the letter is standing in for. Remember: 9 is the whole and 4 is one part, so a has to be the other part.

Find the letter's value

Teacher Notes

Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.

Model the reasoning aloud: nine is the whole, four is one part, so a is the other part. Try a value, check the beam, adjust. Ask pupils to name the letter as a value ("a is five", not "it is five").

+15 XP

4 - Write It in Your Copy ~5 mins

COPYBOOK MOMENT

In your maths copy, copy this sentence and find a:

a + 5 = 11

Write what a equals. Then rewrite the very same sentence with a box instead of the letter. To rewrite with a box, keep every number exactly the same and just swap the letter for an empty box, like this: □ + 5 = 11. This shows the box and the letter mean the same thing.

Teacher Notes

Walk the room glancing for two things: that a is written as 6, and that the box version reads □ + 5 = 11 with the same numbers. Remind anyone who is unsure that "rewrite with a box" means copy the sentence again but draw an empty box where the letter was. No individual marking — this is whole-class copybook practice, not assessment.

+10 XP

5 - Class Challenge ~8 mins

Now your turn on the balance. First we sort out one new kind of sentence together, then you slide and Check four of your own.

Look at this sentence: 12 = a + 5. The letter is on the right this time. 12 is the whole on the left. On the right, a is one part and 5 is the other part. The missing part is what makes both sides equal, so a is 7 because 7 + 5 = 12.

Now the four challenges. Slide the letter and press Check. First a straight add: b + 7 = 15. Then the letter on the right, just like we did: 16 = c + 9. Then the letter is the whole made from the two parts on the right: e = 3 + 6. Last, the letter is the whole again, but from different parts: f = 4 + 3.

Find the missing letter

Teacher Notes

Teach the letter-on-the-right form on the board before anyone touches the interactive. Work 12 = a + 5 together (no interactive for this demo).

Point: whole is on the left (12). Letter a and 5 are the two parts on the right.
Ask: what part with 5 makes 12? a is 7. Check aloud: 7 + 5 = 12, both sides match.
Slip to watch: pupils may think the letter must always sit on the left, or may take 5 from 12 the wrong way round.

Then the practice round, pupils take turns at the board, check each answer, class confirms. Keep it brisk.

Before each reveal, ask whether the letter is a part or the whole. The 16 = c + 9 one matches the worked example (c is 7). Whole-first sentences: e is 9 and f is 7. For your eye only, e = 3 + 6 is the take-away e − 6 = 3 written whole-first, keep that framing to yourself.

+15 XP

Pupil practice

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

Lesson 113 · Using a Box or a Letter for the Unknown

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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 ~9 mins

3 - Try It Together ~9 mins

Find the letter's value

4 - Write It in Your Copy ~5 mins

5 - Class Challenge ~8 mins

Find the missing letter

Unlock the full learning experience

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