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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 7 and then adds 10. When the input is 9, what is the output?

    7+310+39+3?

  2. 2. A number machine multiplies the input by 9 and then adds 11. When the input is 7, what is the output?

    9+211+27+2?

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

    4+610+611+6?

  4. 4. A number machine multiplies the input by 7 and then adds 4. When the input is 3, what is the output?

    7-34-33-3?

  5. 5. A number machine multiplies the input by 6 and then adds 12. When the input is 9, what is the output?

    6+612+69+6?

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 13, what is the output?

    2+1113+1113+11?

  7. 7. A number machine multiplies the input by 9 and then adds 3. When the input is 13, what is the output?

    9-63-613-6?

  8. 8. A number machine multiplies the input by 9 and then adds 12. When the input is 12, what is the output?

    9+312+312+3?

  9. 9. A number machine multiplies the input by 2 and then adds 12. When the input is 13, what is the output?

    2+1012+1013+10?

  10. 10. A number machine multiplies the input by 3 and then adds 10. When the input is 6, what is the output?

    3+710+76+7?

  11. 11. A number machine multiplies the input by 4 and then adds 1. When the input is 7, what is the output?

    4-31-37-3?

  12. 12. A number machine multiplies the input by 6 and then adds 15. When the input is 12, what is the output?

    6+915+912+9?
12 questions · Seed 46 · 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 7 and then adds 10. When the input is 9, what is the output?

    73

    First multiply: 9 × 7 = 63. Then add 10: 63 + 10 = 73.

  2. 2. A number machine multiplies the input by 9 and then adds 11. When the input is 7, what is the output?

    74

    First multiply: 7 × 9 = 63. Then add 11: 63 + 11 = 74.

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

    54

    First multiply: 11 × 4 = 44. Then add 10: 44 + 10 = 54.

  4. 4. A number machine multiplies the input by 7 and then adds 4. When the input is 3, what is the output?

    25

    First multiply: 3 × 7 = 21. Then add 4: 21 + 4 = 25.

  5. 5. A number machine multiplies the input by 6 and then adds 12. When the input is 9, what is the output?

    66

    First multiply: 9 × 6 = 54. Then add 12: 54 + 12 = 66.

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 13, what is the output?

    39

    First multiply: 13 × 2 = 26. Then add 13: 26 + 13 = 39.

  7. 7. A number machine multiplies the input by 9 and then adds 3. When the input is 13, what is the output?

    120

    First multiply: 13 × 9 = 117. Then add 3: 117 + 3 = 120.

  8. 8. A number machine multiplies the input by 9 and then adds 12. When the input is 12, what is the output?

    120

    First multiply: 12 × 9 = 108. Then add 12: 108 + 12 = 120.

  9. 9. A number machine multiplies the input by 2 and then adds 12. When the input is 13, what is the output?

    38

    First multiply: 13 × 2 = 26. Then add 12: 26 + 12 = 38.

  10. 10. A number machine multiplies the input by 3 and then adds 10. When the input is 6, what is the output?

    28

    First multiply: 6 × 3 = 18. Then add 10: 18 + 10 = 28.

  11. 11. A number machine multiplies the input by 4 and then adds 1. When the input is 7, what is the output?

    29

    First multiply: 7 × 4 = 28. Then add 1: 28 + 1 = 29.

  12. 12. A number machine multiplies the input by 6 and then adds 15. When the input is 12, what is the output?

    87

    First multiply: 12 × 6 = 72. Then add 15: 72 + 15 = 87.

12 questions · Seed 46 · 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 7 and then adds 10. When the input is 9, what is the output?

    7+310+39+3?

  2. 2. A number machine multiplies the input by 9 and then adds 11. When the input is 7, what is the output?

    9+211+27+2?

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

    4+610+611+6?

  4. 4. A number machine multiplies the input by 7 and then adds 4. When the input is 3, what is the output?

    7-34-33-3?

  5. 5. A number machine multiplies the input by 6 and then adds 12. When the input is 9, what is the output?

    6+612+69+6?

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 13, what is the output?

    2+1113+1113+11?

  7. 7. A number machine multiplies the input by 9 and then adds 3. When the input is 13, what is the output?

    9-63-613-6?

  8. 8. A number machine multiplies the input by 9 and then adds 12. When the input is 12, what is the output?

    9+312+312+3?

  9. 9. A number machine multiplies the input by 2 and then adds 12. When the input is 13, what is the output?

    2+1012+1013+10?

  10. 10. A number machine multiplies the input by 3 and then adds 10. When the input is 6, what is the output?

    3+710+76+7?

  11. 11. A number machine multiplies the input by 4 and then adds 1. When the input is 7, what is the output?

    4-31-37-3?

  12. 12. A number machine multiplies the input by 6 and then adds 15. When the input is 12, what is the output?

    6+915+912+9?
12 questions · Seed 46 · 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 7 and then adds 10. When the input is 9, what is the output?

    73

    First multiply: 9 × 7 = 63. Then add 10: 63 + 10 = 73.

  2. 2. A number machine multiplies the input by 9 and then adds 11. When the input is 7, what is the output?

    74

    First multiply: 7 × 9 = 63. Then add 11: 63 + 11 = 74.

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

    54

    First multiply: 11 × 4 = 44. Then add 10: 44 + 10 = 54.

  4. 4. A number machine multiplies the input by 7 and then adds 4. When the input is 3, what is the output?

    25

    First multiply: 3 × 7 = 21. Then add 4: 21 + 4 = 25.

  5. 5. A number machine multiplies the input by 6 and then adds 12. When the input is 9, what is the output?

    66

    First multiply: 9 × 6 = 54. Then add 12: 54 + 12 = 66.

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 13, what is the output?

    39

    First multiply: 13 × 2 = 26. Then add 13: 26 + 13 = 39.

  7. 7. A number machine multiplies the input by 9 and then adds 3. When the input is 13, what is the output?

    120

    First multiply: 13 × 9 = 117. Then add 3: 117 + 3 = 120.

  8. 8. A number machine multiplies the input by 9 and then adds 12. When the input is 12, what is the output?

    120

    First multiply: 12 × 9 = 108. Then add 12: 108 + 12 = 120.

  9. 9. A number machine multiplies the input by 2 and then adds 12. When the input is 13, what is the output?

    38

    First multiply: 13 × 2 = 26. Then add 12: 26 + 12 = 38.

  10. 10. A number machine multiplies the input by 3 and then adds 10. When the input is 6, what is the output?

    28

    First multiply: 6 × 3 = 18. Then add 10: 18 + 10 = 28.

  11. 11. A number machine multiplies the input by 4 and then adds 1. When the input is 7, what is the output?

    29

    First multiply: 7 × 4 = 28. Then add 1: 28 + 1 = 29.

  12. 12. A number machine multiplies the input by 6 and then adds 15. When the input is 12, what is the output?

    87

    First multiply: 12 × 6 = 72. Then add 15: 72 + 15 = 87.

12 questions · Seed 46 · Age guidance, not curriculum certification