Describing a Rule in Words

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

1 - Getting Started ~3 mins

Look at this sequence: 4, 7, 10, 13, …

Your task

What's the rule? Say it in plain words, so clearly that a person who has never seen the sequence could continue it just by reading what you said.

Teacher Notes

Take three or four hands-up answers. Listen for the verb pupils reach for first — add, plus, going up by. Don't lock in a winning wording yet; the lesson is about refining it.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~10 mins

Today we look at four sequences. Each one has its rule written underneath, in words.

4, 7, 10, 13 — start at 4, add 3 each time
50, 45, 40, 35 — start at 50, take 5 each time
1, 2, 4, 8, 16 — double each time
3, 5, 8, 10, 13 — alternate add-2 then add-3

Note

The first three rules tell you exactly what to do at every step. The fourth is trickier: the jump changes from one term to the next, so the rule has to mention both jumps and the order they come in.

The test for a good rule

A good rule passes one test: another person can read it, look at the first term, and predict the next term without ever seeing the rest of the sequence.

Teacher Notes

Write each sequence on the board before the rule, then add the rule in a different colour underneath. Pause between sequences for a hand or two — does this rule pass the test? Could your little sister read it and keep going?

On the fourth one, make a thing of the word alternate. Pupils will reach for "add 2, add 3, add 2, add 3" — revoice it as "alternate add-2 then add-3" so they meet the shorter wording. Both are correct; one is tighter.

Look for: pupils who say "plus 3" vs "add 3" vs "goes up by 3". They are all the same rule. Name that aloud — different words, same rule.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~10 mins

The function machine on the board has a rule showing — let's start with +3. We send a few numbers in, watch what comes out, and put the rule into words.

Key point

Then someone calls a fresh number and we predict the output from the words alone, before the machine shows it. If the prediction lands, our wording is solid. If it's off, we sharpen the words and try again.

What's the rule? Say it in words.

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Start with the visible rule +3 already in the machine. Send 4, 7, 10 through; ask the class to read the rule in words. Take two or three different wordings ("add three", "plus three", "the number goes up by three") and revoice that they all describe the same rule.

Then use the function machine's own controls on the IWB to switch the operation to × 2. Send 3, 5, 8 through. Now ask: could the same words from before still work? Why not? The verb has to change.

Watch for: pupils giving a rule that fits one pair but breaks on the next. That's the moment to ask "would your rule still work for this input?" The two-step rules are coming up in Class Challenge — leave them there.

+15 XP

4 - Write Each Rule in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, write each of the lesson's sequences on a line with its rule in words underneath.

4, 7, 10, 13 — add 3 each time
50, 45, 40, 35 — take 5 each time
1, 2, 4, 8, 16 — double each time
3, 5, 8, 10, 13 — alternate add-2 then add-3

Now underline the verb in each rule — the doing word (add, take, double, alternate).

Teacher Notes

Walk the room as pupils write — glance that the rule sits directly under its sequence and that the verb is underlined on each line. This is whole-class copybook practice, not assessment — no marking, just a quick check that pupils caught the verb of each rule.

If a pupil writes "goes up by 3" instead of "add 3", the underline goes under goes up — both are doing-words. Leave it be; the point is to notice the doing-word lives in every rule.

+10 XP

5 - Class Challenge ~16 mins

The function machine now hides each rule. A pupil at the board sends a few inputs through, the class watches the outputs, and together we say the rule in words. We predict the next input-output pair from our wording — then tap Show rule to check.

Tip

If our words don't quite match what the machine is doing, we say them again — sharper this time, with the bit that was missing.

Find each rule. Say it in words.

Teacher Notes

This round is the practice bank — 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 each challenge: a pupil sends three inputs through, then the class proposes the rule in words. Before tapping Show rule, take one more input from a different pupil and have the class predict the output from the words. That prediction is the real test — if it lands, the words pass; if it misses, the words need sharpening.

For the two-step rules (the fifth core challenge and the extensions), watch for pupils who name only one step. Push back with: "the machine does two things to the number — what's the other one?"

The extension labels nudge pupils to describe the rule in exactly six words. Don't make that the gate to passing; it's a stretch for fast finishers who already have a working wording.

Set the following rule on the machine for each challenge

Core 1 — add 3 (try inputs 5 → 8, 12 → 15)
Core 2 — subtract 4 (try inputs 20 → 16, 11 → 7)
Core 3 — multiply by 2 (try inputs 3 → 6, 7 → 14)
Core 4 — add 10 (try inputs 5 → 15, 23 → 33)
Core 5 — multiply by 2, then add 1 (try inputs 3 → 7, 5 → 11)
Extension 1 — multiply by 3, then subtract 2 (try inputs 4 → 10, 6 → 16)
Extension 2 — divide by 4 (try inputs 20 → 5, 32 → 8)
Extension 3 — multiply by 5, then add 3 (try inputs 2 → 13, 4 → 23)

+15 XP

Pupil practice

Module 8 · Algebra: Patterns, Expressions and Equations Algebra

Lesson 102 · Describing a Rule in Words

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Teacher Class Feed

1 - Getting Started ~3 mins

2 - Watch and Notice ~10 mins

3 - Try It Together ~10 mins

What's the rule? Say it in words.

4 - Write Each Rule in Your Copy ~3 mins

5 - Class Challenge ~16 mins

Find each rule. Say it in words.

Set the following rule on the machine for each challenge

Unlock the full learning experience

XP