Activity: The Pattern Machine
The machine has a secret rule. Figure it out by looking at what goes in and what comes out!
Machine #1
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 5 |
| 2 | 6 |
| 3 | 7 |
| 4 | ? |
| 10 | ? |
Machine #2
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | ? |
| 10 | ? |
Machine #3
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 9 |
| 2 | 8 |
| 3 | 7 |
| 4 | ? |
| 10 | ? |
Challenge Machine
Rule: _________________________
| IN (n) | OUT |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | ? |
| 10 | ? |
🔑 Kaiako answer key
Machine #1 — Rule: n + 4. IN 4 → OUT 8; IN 10 → OUT 14.
Machine #2 — Rule: 3n. IN 4 → OUT 12; IN 10 → OUT 30.
Machine #3 — Rule: 10 − n. IN 4 → OUT 6; IN 10 → OUT 0.
Challenge Machine — Rule: 2n + 1. IN 4 → OUT 9; IN 10 → OUT 21.
Watch for: Machine #3 outputs zero at IN 10, and some ākonga will assume they have made a mistake. They have not — zero is a perfectly good output. It is also a good moment to ask what the machine would do with IN 11, which is the first time this unit meets a negative number as an answer.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
A Lesson 1 activity. Ākonga feed numbers through a rule and work backwards from outputs to the rule itself.
Ngā Paearu Angitū — Success Criteria
- ✅ I can work out a machine’s rule from the numbers that go in and come out.
- ✅ I can use the rule to fill in a missing output.
- ✅ I can write the rule as an expression in n.
Differentiation & Inclusion
Machines #1–#3 are one-step and the Challenge Machine is two-step; a pair that only finishes the first three has still met the learning intention. Ākonga who need support can be given the rule and asked to fill the outputs, working the machine forwards before working it backwards.