Mathematics

Advanced

50 mins

Teacher/Student led

Learning Goals

Learning Outcomes

Lesson Files

+65 XP

What you need:
IWB/Projector/Large Screen

Using a Letter or Word for the Unknown

You'll learn to use a letter to stand for a missing number in a number sentence, then find its value by keeping both sides of the balance equal. You'll check your answer by putting the number back in and reading the sentence.

Warning: Your screen size is quite small for viewing this. Rotate your device into landscape mode if you can.

1 Getting Started
2 Watch and Notice
3 Try It Together
4 Find the Letters in Your Copy
5 Class Challenge
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started

Key point

Here is a puzzle on a balance: a + 3 = 10. The letter a is hiding a number. Both pans have to weigh the same, so the beam stays level. What number do you think a is hiding?

Teacher Notes

Write the equation a + 3 = 10 on the board as pupils settle. Give five seconds of quiet think-time, then take three hands-up answers, not open call-outs. Do not confirm yet — hold the answer for the next step. Listen for whether pupils treat the letter as a real hidden number, not as decoration.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Watch these balanced sentences on the scales. In each one a letter is standing in for a missing number. See how the letter is just a name for the number that keeps both pans level.

In the next one the total is on the left — the balancing job is still the same.

In the last one the same letter appears twice. That means two of the same hidden number added together.

Teacher Notes

a + 3 = 10, the beam is level with the letter a as 7. Read it back: seven and three make ten.
b − 2 = 5 — the letter is 7; head off the slip of doing 5 − 2. Ask what number, take away 2, leaves 5. Confirm pupils read the −2 as take away two, not as a negative number.
4 + c = 11 — the letter sits in the middle now; the balance still decides it is 7.
15 = d + 6 — the total is on the left this time; the letter is 9. Point out the equals sign does not care which side the total is on.
a + a = 12 — the same letter twice, so both blocks are the same hidden number; each a is 6 because 6 + 6 = 12. This builds the repeated-letter idea before the challenge round.

Say verbatim after each: the letter is only a name for the missing number.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~9 mins

Key point

Each time we say the value of the letter aloud. Then we read the whole sentence back with the number in place of the letter to check both sides match.

Let us find the value of the letter together. First we work e + 4 = 9 on the balance, sliding the letter block until the beam is level. Then we work three more the same way at the board: g − 3 = 8, then 7 + h = 16, then 13 = k + 5.

Find the value of the letter

Teacher Notes

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

Work e + 4 = 9 on the balance tool first, sliding the letter block until the beam levels. Then work the other three at the board with the same balancing move. Say the value each time. Hold out for pupils to read the whole sentence back with the number in place of the letter — that is the check. For g − 3 = 8, watch for the pupil who slides to 5 (8 − 3); ask what number, take away 3, leaves 8? For 13 = k + 5, name that the total is on the left — the balancing job is unchanged. Values in order: 5, 11, 9, 8.

+15 XP

4 - Find the Letters in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, find the value of the letter in each of these, then write the full sentence with the number in place of the letter:

a + 5 = 12
n − 4 = 6
9 = m + 2

Read each finished sentence back to yourself to check both sides match.

Teacher Notes

Walk the room glancing for whether pupils rewrite the sentence with the number swapped in — that rewrite is the check. No individual marking — this is whole-class copybook practice, not assessment. Answers: a = 7, n = 10, m = 7.

+10 XP

5 - Class Challenge ~8 mins

Now we work through these together at the board, sliding the letter block until both pans balance. First is a + 4 = 13. Then b + 4 = 18. Then c + 7 = 6 + 8. Last is d + d = 14.

Tip

The last two are the ones to slow down for. For c + 7 = 6 + 8, work out the right pan first — 6 + 8 = 14 — then find c to match it. For d + d = 14, the same letter appears twice, so it means two of the same hidden number added together — each d must be the same.

Find the value of the letter

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.

For c + 7 = 6 + 8, work out the right pan (14) first, then find c. For d + d = 14, both blocks are the same letter, so both must be 7. Values in order: a = 9, b = 14, c = 7, d = 7. Read each finished sentence back as the check.

+15 XP

Pupil practice

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

Lesson 122 · Using a Letter or Word for the Unknown

Download Activity Book page (PDF)

123learn · Online learning platform

Unlock the full learning experience

You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.

Hundreds of curriculum-aligned lessons

Interactive activities in every lesson

Printable resources & progress tracking

Get started

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

Using a Letter or Word for the Unknown

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

3 - Try It Together ~9 mins

Find the value of the letter

4 - Find the Letters in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Find the value of the letter

Unlock the full learning experience

XP