Mathematics

Advanced

50 mins

Teacher/Student led

Learning Goals

Learning Outcomes

Lesson Files

+80 XP

Teacher-led from the board. Pupils do not need a device, but can follow on one.

What you need:
IWB/Projector/Large Screen

Finding the Rule from a Table

Discover how to work out a hidden rule by looking at input-output pairs. Test your guesses on multiple pairs and use a clever test-input to tell similar rules apart.

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Work Out the Rule in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

Your turn

Your teacher is running this lesson on the board. Here is the part you can try yourself.

Your written work is on page 104

Function machine

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a machine with its rule hidden behind a question mark. It has swallowed three numbers and spat three back out:

Example

2 turned into 7. 5 turned into 16. 10 turned into 31.

What is the machine doing to every number that goes in?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Four hidden-rule machines are on the board, each showing a few pairs of what goes in and what comes out. For each one, look at how the output relates to the input and be ready to say what the machine is doing. Watch out — some machines do two things to the number.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~10 mins

Worked example

Today we crack this hidden machine together: it turns 2 → 7, 5 → 16 and 10 → 31. We'll send fresh numbers through first — try 1, then 0, then 3 — and watch what comes out before anyone names the rule. Then we'll say the rule aloud, build it on the buttons and press Check to see whether the machine agrees with us.

Crack the machine: 2 → 7, 5 → 16, 10 → 31

+15 XP

4 - Work Out the Rule in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, work out the rule for Machine A from Watch and Notice: 2 → 7, 5 → 16, 10 → 31. For each pair, write what the rule could be — 2 → 7 could be + 5 or × 3 + 1 — then test both on the next pair. Circle the rule you decide on.

+10 XP

Pupil practice

Module 8 · Algebra: Patterns, Expressions and Equations Algebra

Lesson 111 · Finding the Rule from a Table

Download Activity Book page (PDF)

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