Mathematics

Intermediate

50 mins

Teacher/Student led

Learning Goals

Learning Outcomes

Lesson Files

+80 XP

What you need:
IWB/Projector/Large Screen

Describing a Rule in Words

Learn to describe number-pattern rules in clear words so that anyone reading them can predict the next term. Test your wording and refine it until it works reliably.

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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
6 What Did We Notice?
7 What's Next
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.

👇 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.

👇 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.

+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).

+10 XP

Pupil practice

Module 8 · Algebra: Patterns, Expressions and Equations Algebra

Lesson 95 · Describing a Rule in Words

Download Activity Book page (PDF)

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