Mathematics

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50 mins

Teacher/Student led

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Learning Outcomes

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+80 XP

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

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 and use Show rule to check.

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

5 - Class Challenge ~9 mins

Now we crack four hidden machines together. Each one is a little trickier than the last. Send a number through before you name the rule, build it on the buttons, and press Check.

Watch out

Watch the last machine closely. It gives 1 → 6. Someone might guess + 5, because 1 + 5 = 6 — and that fits the first pair perfectly. But send a second number through: 3 gives 14, not 8, so + 5 is wrong. One pair on its own was not enough. We only knew for sure once we tried a second number.

Crack the hidden machine

+15 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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