Two-Step Function Machines Exploration
Year 6 Mathematics Building on Single-Step Functions Exploring Algebraic Expressions
Quick Recall: Single-Step Functions
Input → One Operation → Output Example: 4 → add 5 → 9 Algebraic form: x + 5 Let's review what we learned!
Introducing Two-Step Function Machines
Two operations in sequence Input → Operation 1 → Operation 2 → Output Order matters! Example: 5 → ×2 → +3 → 13
Think About It!
What happens if we change the order? 5 → +3 → ×2 → ? Does order matter in mathematics?
Writing Algebraic Expressions
⚙️ Two-step functions can be written algebraically 📝 Example: ×2 then +3 becomes 2x + 3 🔤 x represents our input number ➡️ The operations follow the same order
Guided Practice: Function Machine Cards
Work with a partner using function machine cards Pick any number to put in Follow each step in order Write down your answer Write the rule using letters and numbers Example card: take away 4, then multiply by 3
Problem Solving Challenge
Find the missing number Input: 4 → Output: 17 Steps: multiply by 3, then add ? What number should we add? Hint: Start with 17 and work backwards
What We've Learned Today
Machines can do two jobs at once Order is important - do things the right way We can write number patterns We can find missing numbers Next time we will learn to go backwards!