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🧩 4th grade math · Patterns & Algebra

Function machines

A function is a rule. You put in an input and the rule gives you an output. Rule: multiply by 3, then add 2. Input 4: 4 × 3 = 12, then 12 + 2 = 14. The output is 14.

Worked example

A rule takes an input and gives an output. The rule: add 8. What is the output when the input is 9?
Answer: output = 17
Follow the rule step by step: 9 + 8 = 17; so the output is 17.

For grown-ups: Input–output rules ("function machine"). Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 4.OA.C.5
  • CCSS 5.OA.B.3
What this practises, for teachers

Practices input–output rules ("function machine") (4.OA.C.5, 5.OA.B.3). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. A rule takes an input and gives an output. The rule: subtract 3. What is the output when the input is 6?
    Show the answer and how
    Answer: output = 3
    Follow the rule step by step: 6 − 3 = 3; so the output is 3.
  2. A rule takes an input and gives an output. The rule: subtract 6, then add 6. What is the output when the input is 3?
    Show the answer and how
    Answer: output = 3
    Follow the rule step by step: 3 − 6 = −3; −3 + 6 = 3; so the output is 3.
  3. A rule takes an input and gives an output. The rule: divide by 2, then multiply by 2. What is the output when the input is 10?
    Show the answer and how
    Answer: output = 10
    Follow the rule step by step: 10 ÷ 2 = 5; 5 × 2 = 10; so the output is 10.

Before and after

Comes next: What is a function? (8th)

Name: ____________________Date: ____________Score: ____ / 12

Function machines (4th grade)

  1. A rule takes an input and gives an output. The rule: multiply by 4. What is the output when the input is 2?
  2. A rule takes an input and gives an output. The rule: add 7. What is the output when the input is 9?
  3. A rule takes an input and gives an output. The rule: subtract 1. What is the output when the input is 8?
  4. A rule takes an input and gives an output. The rule: subtract 3. What is the output when the input is 7?
  5. A rule takes an input and gives an output. The rule: add 2. What is the output when the input is 1?
  6. A rule takes an input and gives an output. The rule: multiply by 9, then add 3. What is the output when the input is 7?
  7. A rule takes an input and gives an output. The rule: divide by 4, then multiply by 8. What is the output when the input is 16?
  8. A rule takes an input and gives an output. The rule: multiply by 5, then add 8. What is the output when the input is 7?
  9. A rule takes an input and gives an output. The rule: subtract 3, then add 7. What is the output when the input is 7?
  10. A rule takes an input and gives an output. The rule: add 2, then multiply by 2. What is the output when the input is 10?
  11. A rule takes an input and gives an output. The rule: subtract 7, then add 12. What is the output when the input is 3?
  12. A rule takes an input and gives an output. The rule: add 9, then multiply by 5. What is the output when the input is 6?

Answer key

  1. output = 8
  2. output = 16
  3. output = 7
  4. output = 4
  5. output = 3
  6. output = 66
  7. output = 32
  8. output = 43
  9. output = 11
  10. output = 24
  11. output = 8
  12. output = 75

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