Concept 4 of 7
Find the Rule
Today's big idea
Compare each In with its Out to find the single × or ÷ rule the machine uses.
3→15 and 4→20 both fit × 5, so that is the rule.
How it works
👀 What's going on?
A machine takes a number in and sends a different one out, but it will not tell you what it does inside. Give it a few numbers and watch what comes back, and the secret rule reveals itself.
💡 Here's the trick
Look at the In/Out table above. Compare each in with its out: 3 turns into 15, 4 turns into 20, 5 turns into 25. Each out is five times its in, so the hidden rule is × 5. Find the rule from the pairs you are shown, then use it on the rest.
🪄 How to do it
- 1.Line up each in with its out.
- 2.Ask what single step turns every in into its out: times something, or divide by something.
- 3.Test the rule on a second pair; if it works there too, use it to fill the gaps.
✍️ Try it
In 12 → Out 3, In 20 → Out 5, In 28 → Out 7. What is the rule, and what does 40 give?
Each out is its in divided by 4, so the rule is ÷ 4. Then 40 ÷ 4 = 10.
⚠️ Watch out
Check the rule on more than one pair. '3 → 15' alone could be × 5 or + 12; only the second pair, 4 → 20, tells you it is × 5 and not + 12.
🌟 Why this matters
Finding a hidden rule from examples is the heart of patterns, algebra and code — it is spotting how the machine works before you can see inside it.
Exam tip: Try × first, then ÷; most table-machines are one clean multiply or divide.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“In → Out: 3 → 15, 4 → 20, 6 → 30. What is the rule?”
- 1
Compare in with out
Each out is 5 times its in.
- 2
Test a second pair
6 × 5 = 30 ✓, so it is not + 12.
- 3
Answer ✓
the rule is × 5
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Two pairs, not one. Then send your number through.
RULE SPOTTER · ROUND 1 OF 3
Step 1 · name the rule
Quick check
✅ VERIFICATION
In → Out: 3 → 15, 4 → 20, 6 → 30. What is the rule?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Sharing Fairly
Division is the opposite of multiplication.