Stage 1 of 5: ASK

AKUUU WORKSHEETS

Mission: The Broken Machine — Level 6

Level 6 – The Analyzer General 11 min

A ASK K KNOW U UNDERSTAND U USE U UPGRADE

ASK Activate curiosity

Akuuu finds a strange machine in her attic. It has a number slot, a button, and a screen.

She tests it:

She puts in 3, presses the button → screen shows 7
She puts in 5, presses the button → screen shows 11
She puts in 2, presses the button → screen shows 5

👉 What is the machine doing? Can you figure out the secret rule?

🐥

Think: Look at the input and output. What changes? Is it adding? Multiplying? Something else?

✏️ Write your guess for the rule:

KNOW Know the concept

🔢 An input-output rule (or function) turns one number into another using a fixed pattern
🔍 To find the rule, compare: What changed? and By how much?
✅ A rule must work for every input — one example is never enough proof

1 Quick Check: Test your rule

If your rule is correct, what should the machine show for input 4?

My prediction:

My rule:

UNDERSTAND Understand the idea

Akuuu’s friend Lina finds a different machine. She tests it:

Input 2 → Output 6
Input 4 → Output 10
Input 1 → Output 4

👉 What is Lina’s machine doing? Is it the same rule as Akuuu’s?

Lina’s rule:

Same or different? Why:

👉 Draw a diagram showing how input → rule → output works:

USE Use your thinking

2 Task 1: Crack the Code

A third machine shows these results:

Input 3 → Output 9

Input 5 → Output 15

Input 2 → Output 6

👉 What is the rule? Predict the output for input 7.

Rule:

Output for 7:

3 Task 2: Spot the Broken Rule

A child says: “The rule for Akuuu’s machine is ‘add 4’ because 3 → 7 and 3 + 4 = 7. That proves it!”

👉 Is this proof enough? Test with the other inputs and explain.

💡 This proof is not enough because _______________

4 Task 3: Build Your Own Machine

Create a rule using two operations (e.g., multiply then add). Write 3 input-output pairs.

👉 Can a friend guess your rule from just one pair? Why or why not?

My rule:

Input 1 → Output:

Input 2 → Output:

Input 3 → Output:

UPGRADE Upgrade your skill

🧠 Part A — Transfer

Akuuu finds a machine with two inputs:

Input 2 and 3 → Output 5
Input 4 and 1 → Output 5
Input 3 and 3 → Output 6

👉 What could this machine be doing? Find at least two possible rules.

🐥

Think: One answer might be obvious. But can you find a different rule that also works? What does this tell you about proof?

🧠 Part B — Thinking Pause

I tested my rule with more than one example
I found the mistake in the “one example is proof” idea
I looked for more than one possible answer

⭐ Mission Reflection

Today I learned:

The hardest part was:

Next time I will:

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