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ReasoningAges 10-12

Function machine rules

Apply a two-step function machine rule (multiply then add) to an input number. Review suitability for your learners before teaching.

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Age band:Ages 7-9Ages 10-12

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Worksheet StudioPractice pack · Ages 10-12

Function machine rules

Take your time. Show your thinking.

  1. 1. A number machine multiplies the input by 3 and then adds 11. When the input is 4, what is the output?

    3+811+84+8?

  2. 2. A number machine multiplies the input by 9 and then adds 5. When the input is 11, what is the output?

    9-45-411-4?

  3. 3. A number machine multiplies the input by 3 and then adds 6. When the input is 11, what is the output?

    3+36+311+3?

  4. 4. A number machine multiplies the input by 2 and then adds 8. When the input is 8, what is the output?

    2+68+68+6?

  5. 5. A number machine multiplies the input by 2 and then adds 5. When the input is 15, what is the output?

    2+35+315+3?

  6. 6. A number machine multiplies the input by 2 and then adds 9. When the input is 10, what is the output?

    2+79+710+7?

  7. 7. A number machine multiplies the input by 7 and then adds 8. When the input is 9, what is the output?

    7+18+19+1?

  8. 8. A number machine multiplies the input by 2 and then adds 4. When the input is 3, what is the output?

    2+24+23+2?

  9. 9. A number machine multiplies the input by 7 and then adds 5. When the input is 13, what is the output?

    7-25-213-2?

  10. 10. A number machine multiplies the input by 4 and then adds 14. When the input is 11, what is the output?

    4+1014+1011+10?

  11. 11. A number machine multiplies the input by 6 and then adds 8. When the input is 9, what is the output?

    6+28+29+2?

  12. 12. A number machine multiplies the input by 8 and then adds 5. When the input is 7, what is the output?

    8-35-37-3?
12 questions · Seed 104730 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 10-12

Function machine rules

Answers and reasoning. Review before teaching.

  1. 1. A number machine multiplies the input by 3 and then adds 11. When the input is 4, what is the output?

    23

    First multiply: 4 × 3 = 12. Then add 11: 12 + 11 = 23.

  2. 2. A number machine multiplies the input by 9 and then adds 5. When the input is 11, what is the output?

    104

    First multiply: 11 × 9 = 99. Then add 5: 99 + 5 = 104.

  3. 3. A number machine multiplies the input by 3 and then adds 6. When the input is 11, what is the output?

    39

    First multiply: 11 × 3 = 33. Then add 6: 33 + 6 = 39.

  4. 4. A number machine multiplies the input by 2 and then adds 8. When the input is 8, what is the output?

    24

    First multiply: 8 × 2 = 16. Then add 8: 16 + 8 = 24.

  5. 5. A number machine multiplies the input by 2 and then adds 5. When the input is 15, what is the output?

    35

    First multiply: 15 × 2 = 30. Then add 5: 30 + 5 = 35.

  6. 6. A number machine multiplies the input by 2 and then adds 9. When the input is 10, what is the output?

    29

    First multiply: 10 × 2 = 20. Then add 9: 20 + 9 = 29.

  7. 7. A number machine multiplies the input by 7 and then adds 8. When the input is 9, what is the output?

    71

    First multiply: 9 × 7 = 63. Then add 8: 63 + 8 = 71.

  8. 8. A number machine multiplies the input by 2 and then adds 4. When the input is 3, what is the output?

    10

    First multiply: 3 × 2 = 6. Then add 4: 6 + 4 = 10.

  9. 9. A number machine multiplies the input by 7 and then adds 5. When the input is 13, what is the output?

    96

    First multiply: 13 × 7 = 91. Then add 5: 91 + 5 = 96.

  10. 10. A number machine multiplies the input by 4 and then adds 14. When the input is 11, what is the output?

    58

    First multiply: 11 × 4 = 44. Then add 14: 44 + 14 = 58.

  11. 11. A number machine multiplies the input by 6 and then adds 8. When the input is 9, what is the output?

    62

    First multiply: 9 × 6 = 54. Then add 8: 54 + 8 = 62.

  12. 12. A number machine multiplies the input by 8 and then adds 5. When the input is 7, what is the output?

    61

    First multiply: 7 × 8 = 56. Then add 5: 56 + 5 = 61.

12 questions · Seed 104730 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 10-12

Function machine rules

Take your time. Show your thinking.

  1. 1. A number machine multiplies the input by 3 and then adds 11. When the input is 4, what is the output?

    3+811+84+8?

  2. 2. A number machine multiplies the input by 9 and then adds 5. When the input is 11, what is the output?

    9-45-411-4?

  3. 3. A number machine multiplies the input by 3 and then adds 6. When the input is 11, what is the output?

    3+36+311+3?

  4. 4. A number machine multiplies the input by 2 and then adds 8. When the input is 8, what is the output?

    2+68+68+6?

  5. 5. A number machine multiplies the input by 2 and then adds 5. When the input is 15, what is the output?

    2+35+315+3?

  6. 6. A number machine multiplies the input by 2 and then adds 9. When the input is 10, what is the output?

    2+79+710+7?

  7. 7. A number machine multiplies the input by 7 and then adds 8. When the input is 9, what is the output?

    7+18+19+1?

  8. 8. A number machine multiplies the input by 2 and then adds 4. When the input is 3, what is the output?

    2+24+23+2?

  9. 9. A number machine multiplies the input by 7 and then adds 5. When the input is 13, what is the output?

    7-25-213-2?

  10. 10. A number machine multiplies the input by 4 and then adds 14. When the input is 11, what is the output?

    4+1014+1011+10?

  11. 11. A number machine multiplies the input by 6 and then adds 8. When the input is 9, what is the output?

    6+28+29+2?

  12. 12. A number machine multiplies the input by 8 and then adds 5. When the input is 7, what is the output?

    8-35-37-3?
12 questions · Seed 104730 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 10-12

Function machine rules

Answers and reasoning. Review before teaching.

  1. 1. A number machine multiplies the input by 3 and then adds 11. When the input is 4, what is the output?

    23

    First multiply: 4 × 3 = 12. Then add 11: 12 + 11 = 23.

  2. 2. A number machine multiplies the input by 9 and then adds 5. When the input is 11, what is the output?

    104

    First multiply: 11 × 9 = 99. Then add 5: 99 + 5 = 104.

  3. 3. A number machine multiplies the input by 3 and then adds 6. When the input is 11, what is the output?

    39

    First multiply: 11 × 3 = 33. Then add 6: 33 + 6 = 39.

  4. 4. A number machine multiplies the input by 2 and then adds 8. When the input is 8, what is the output?

    24

    First multiply: 8 × 2 = 16. Then add 8: 16 + 8 = 24.

  5. 5. A number machine multiplies the input by 2 and then adds 5. When the input is 15, what is the output?

    35

    First multiply: 15 × 2 = 30. Then add 5: 30 + 5 = 35.

  6. 6. A number machine multiplies the input by 2 and then adds 9. When the input is 10, what is the output?

    29

    First multiply: 10 × 2 = 20. Then add 9: 20 + 9 = 29.

  7. 7. A number machine multiplies the input by 7 and then adds 8. When the input is 9, what is the output?

    71

    First multiply: 9 × 7 = 63. Then add 8: 63 + 8 = 71.

  8. 8. A number machine multiplies the input by 2 and then adds 4. When the input is 3, what is the output?

    10

    First multiply: 3 × 2 = 6. Then add 4: 6 + 4 = 10.

  9. 9. A number machine multiplies the input by 7 and then adds 5. When the input is 13, what is the output?

    96

    First multiply: 13 × 7 = 91. Then add 5: 91 + 5 = 96.

  10. 10. A number machine multiplies the input by 4 and then adds 14. When the input is 11, what is the output?

    58

    First multiply: 11 × 4 = 44. Then add 14: 44 + 14 = 58.

  11. 11. A number machine multiplies the input by 6 and then adds 8. When the input is 9, what is the output?

    62

    First multiply: 9 × 6 = 54. Then add 8: 54 + 8 = 62.

  12. 12. A number machine multiplies the input by 8 and then adds 5. When the input is 7, what is the output?

    61

    First multiply: 7 × 8 = 56. Then add 5: 56 + 5 = 61.

12 questions · Seed 104730 · Age guidance, not curriculum certification