11 · Patterns & Functions
Use and discover rules that turn inputs into outputs.
What your child learns
- A function gives exactly one output for each input
- Use function machines and tables
- Find a rule like y = 2x + 3 from a table
Example
x: 1, 2, 3 → y: 5, 7, 9; rule y = 2x + 3.
Mini lesson: Patterns & Functions
Goal: Use and find rules that turn inputs into outputs.
- To find a rule from a table, see how much y changes when x goes up by 1 — that is the number in front of x.
- Then work out what to add or subtract.
Worked example
x: 1, 2, 3, 4 → y: 5, 8, 11, 14. Find the rule.
- y goes up by 3 each time → 3x.
- When x = 1, 3x = 3, but y = 5, so add 2.
- Rule: y = 3x + 2
Common mistakes
- Using only the change (y = 3x) and forgetting the “+ 2”.
- Mixing up input and output.
Practice questions
A taste of the questions in BloomTracks – the app makes fresh ones every time and adjusts the level as your child answers.
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Question 1 · Level 1
A function machine multiplies by 6. What comes out when 8 goes in?
8 → [ × 6 ] → ?Show the answer
Answer: 48
8 × 6 = 48.
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Question 2 · Level 3
The machine does × 2, then + 9. The output was 19. What was the input?
? → [ × 2 ] → [ + 9 ] → 19Show the answer
Answer: 5
(19 − 9) ÷ 2 = 5.
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Question 3 · Level 5
If f(x) = 3x² + 1, what is f(−4)?
Show the answer
Answer: 49
3 × 16 + 1 = 49.
Try it at home
Play 'guess my rule': you give inputs, your child guesses the rule.
Key takeaway
The change in y for each step in x is the number in front of x.
Practise 11 · patterns & functions with Bloomie
Bloomie reads every question aloud, listens to spoken answers and adapts the difficulty one question at a time.