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Introducing Letter-symbols as Variables

Learn to use letters like x and n to stand for numbers we don't know yet. Explore balances where a bag of hidden counters sits on one side, and discover what value makes each balance level.

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

1 - Getting Started ~5 mins

Illustration for Getting Started Here is a closed lunch bag. Nobody can see inside, but we know it holds some counters. We do not know how many yet, so let us call that hidden number n.

If we drop three more counters into the bag, how many counters would be inside now?

Teacher Notes

Take three hands-up answers, not open call-outs. The answer you are steering toward is written as the letter n plus 3, not a number.

Hold out for the idea that we cannot give a number yet — the whole point is that n stands in for the unknown. If a pupil offers a specific number, ask how do you know how many are in the bag?

👇 Mark your steps as done as you complete them.

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2 - Watch and Notice ~9 mins

In the opening we called the hidden number n. We can use any letter to stand for an unknown, so for the balances we will use x. It is doing exactly the same job that n did.

Watch three balances on the board. On each one, a bag holding x counters (and sometimes some loose counters) sits on the left pan, and loose counters sit on the right. The beam is level, so the two pans weigh exactly the same.

Look at the next one. The bag on its own balances five loose counters, so what must the bag be holding?

Now two identical bags balance ten counters. Both bags hold the same amount, so what must be inside each one?

Teacher Notes

Point to each balance in turn. On the first, ask what the bag alone must weigh, then confirm 6 + 2 = 8.

First balance: the bag plus loose counters — draw attention to the added 2 and let a pupil reason back to 6.
Second balance: the bag alone — the simplest case, x is exactly what the counters show.
Third balance: two bags — this is the one that catches people. Ask are both bags the same? before revealing that each holds five, so 2x means x doubled.

Say the word variable plainly: a letter standing in for a number we have not found yet. When you make the switch from n to x, say it out loud too — any letter can hold the unknown.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Write the Variable in Your Copy ~4 mins

COPYBOOK MOMENT

In your maths copy, write three short statements that use a letter for an unknown number, then say what adding to it would mean. For example:

Let b = the number of books on the shelf. Then b + 2 means two more books.
Let c = the number of coins in the jar. Then c + 5 means five more coins.
Let p = the number of players on the team. Then p + 1 means one extra player.

Underline the letter in each statement so you can see your variable clearly.

Teacher Notes

Walk the room and glance for one thing: is the letter underlined and used consistently. This is whole-class copybook practice, not marking.

Nudge anyone who writes a number instead of a letter back toward the unknown.

+10 XP

4 - Try It Together ~9 mins

Now we work through these balances together on the board. One pupil comes up to the board while the rest of the class predicts and checks aloud. Slide the bag value until the beam sits level. Say the value of x aloud before you check it.

x + 3 balances 9
x + 4 balances 6
3x balances 9
2x + 1 balances 11

Find x to level the beam

Teacher Notes

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

Before each slide, ask the class to predict where the beam levels. Hold out for the reasoning: how much has to be in the bag so both pans match?

x + 3 = 9 → x = 6.
x + 4 = 6 → x = 2 (a smaller answer catches over-guessers).
3x = 9 → x = 3 (three bags now — revoice each bag holds the same, so share the nine across three bags; this is the case that prepares them for 3x + 1 in the challenge).
2x + 1 = 11 → x = 5, the first with a bag and a loose counter, the bridge to the challenge.

+15 XP

5 - Class Challenge ~8 mins

Now we solve these balances one after another. Each one has a bit more to think about than the last. Predict the value of x, level the beam, and check with the class.

x + 3 = 7
2x = 12
3x + 1 = 10
x + 5 = 5
2x + 3 = 15

Level every beam

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 + 3 = 7 → x = 4.
2x = 12 → x = 6 (two bags, halve the counters).
3x + 1 = 10 → x = 3 (three bags now, as in Try It Together — the leap).
x + 5 = 5 → x = 0, the one that surprises them: an empty bag still balances.
2x + 3 = 15 → x = 6, the stretch that combines two bags and a loose set.

Watch for the x + 5 = 5 case — hold out for someone spotting that the bag must be empty. That is the answer the sequence was building toward.

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Pupil practice

Module 10 · Algebra: Patterns, Expressions and Equations Mixed

Lesson 107 · Introducing Letter-symbols as Variables

Download Activity Book page (PDF)

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

Introducing Letter-symbols as Variables

Teacher Class Feed

1 - Getting Started ~5 mins

2 - Watch and Notice ~9 mins

3 - Write the Variable in Your Copy ~4 mins

4 - Try It Together ~9 mins

Find x to level the beam

5 - Class Challenge ~8 mins

Level every beam

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