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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 1. When the input is 14, what is the output?

    7-61-614-6?

  2. 2. A number machine multiplies the input by 2 and then adds 14. When the input is 5, what is the output?

    2+1214+125+12?

  3. 3. A number machine multiplies the input by 7 and then adds 10. When the input is 11, what is the output?

    7+310+311+3?

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

    9+211+211+2?

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

    5+38+37+3?

  6. 6. A number machine multiplies the input by 8 and then adds 8. When the input is 10, what is the output?

    8+08+010+0?

  7. 7. A number machine multiplies the input by 6 and then adds 9. When the input is 7, what is the output?

    6+39+37+3?

  8. 8. A number machine multiplies the input by 8 and then adds 9. When the input is 3, what is the output?

    8+19+13+1?

  9. 9. A number machine multiplies the input by 4 and then adds 9. When the input is 10, what is the output?

    4+59+510+5?

  10. 10. A number machine multiplies the input by 5 and then adds 6. When the input is 15, what is the output?

    5+16+115+1?

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

    2+35+311+3?

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

    7-25-212-2?
12 questions · Seed 42 · 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 1. When the input is 14, what is the output?

    99

    First multiply: 14 × 7 = 98. Then add 1: 98 + 1 = 99.

  2. 2. A number machine multiplies the input by 2 and then adds 14. When the input is 5, what is the output?

    24

    First multiply: 5 × 2 = 10. Then add 14: 10 + 14 = 24.

  3. 3. A number machine multiplies the input by 7 and then adds 10. When the input is 11, what is the output?

    87

    First multiply: 11 × 7 = 77. Then add 10: 77 + 10 = 87.

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

    110

    First multiply: 11 × 9 = 99. Then add 11: 99 + 11 = 110.

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

    43

    First multiply: 7 × 5 = 35. Then add 8: 35 + 8 = 43.

  6. 6. A number machine multiplies the input by 8 and then adds 8. When the input is 10, what is the output?

    88

    First multiply: 10 × 8 = 80. Then add 8: 80 + 8 = 88.

  7. 7. A number machine multiplies the input by 6 and then adds 9. When the input is 7, what is the output?

    51

    First multiply: 7 × 6 = 42. Then add 9: 42 + 9 = 51.

  8. 8. A number machine multiplies the input by 8 and then adds 9. When the input is 3, what is the output?

    33

    First multiply: 3 × 8 = 24. Then add 9: 24 + 9 = 33.

  9. 9. A number machine multiplies the input by 4 and then adds 9. When the input is 10, what is the output?

    49

    First multiply: 10 × 4 = 40. Then add 9: 40 + 9 = 49.

  10. 10. A number machine multiplies the input by 5 and then adds 6. When the input is 15, what is the output?

    81

    First multiply: 15 × 5 = 75. Then add 6: 75 + 6 = 81.

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

    27

    First multiply: 11 × 2 = 22. Then add 5: 22 + 5 = 27.

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

    89

    First multiply: 12 × 7 = 84. Then add 5: 84 + 5 = 89.

12 questions · Seed 42 · 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 1. When the input is 14, what is the output?

    7-61-614-6?

  2. 2. A number machine multiplies the input by 2 and then adds 14. When the input is 5, what is the output?

    2+1214+125+12?

  3. 3. A number machine multiplies the input by 7 and then adds 10. When the input is 11, what is the output?

    7+310+311+3?

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

    9+211+211+2?

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

    5+38+37+3?

  6. 6. A number machine multiplies the input by 8 and then adds 8. When the input is 10, what is the output?

    8+08+010+0?

  7. 7. A number machine multiplies the input by 6 and then adds 9. When the input is 7, what is the output?

    6+39+37+3?

  8. 8. A number machine multiplies the input by 8 and then adds 9. When the input is 3, what is the output?

    8+19+13+1?

  9. 9. A number machine multiplies the input by 4 and then adds 9. When the input is 10, what is the output?

    4+59+510+5?

  10. 10. A number machine multiplies the input by 5 and then adds 6. When the input is 15, what is the output?

    5+16+115+1?

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

    2+35+311+3?

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

    7-25-212-2?
12 questions · Seed 42 · 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 1. When the input is 14, what is the output?

    99

    First multiply: 14 × 7 = 98. Then add 1: 98 + 1 = 99.

  2. 2. A number machine multiplies the input by 2 and then adds 14. When the input is 5, what is the output?

    24

    First multiply: 5 × 2 = 10. Then add 14: 10 + 14 = 24.

  3. 3. A number machine multiplies the input by 7 and then adds 10. When the input is 11, what is the output?

    87

    First multiply: 11 × 7 = 77. Then add 10: 77 + 10 = 87.

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

    110

    First multiply: 11 × 9 = 99. Then add 11: 99 + 11 = 110.

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

    43

    First multiply: 7 × 5 = 35. Then add 8: 35 + 8 = 43.

  6. 6. A number machine multiplies the input by 8 and then adds 8. When the input is 10, what is the output?

    88

    First multiply: 10 × 8 = 80. Then add 8: 80 + 8 = 88.

  7. 7. A number machine multiplies the input by 6 and then adds 9. When the input is 7, what is the output?

    51

    First multiply: 7 × 6 = 42. Then add 9: 42 + 9 = 51.

  8. 8. A number machine multiplies the input by 8 and then adds 9. When the input is 3, what is the output?

    33

    First multiply: 3 × 8 = 24. Then add 9: 24 + 9 = 33.

  9. 9. A number machine multiplies the input by 4 and then adds 9. When the input is 10, what is the output?

    49

    First multiply: 10 × 4 = 40. Then add 9: 40 + 9 = 49.

  10. 10. A number machine multiplies the input by 5 and then adds 6. When the input is 15, what is the output?

    81

    First multiply: 15 × 5 = 75. Then add 6: 75 + 6 = 81.

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

    27

    First multiply: 11 × 2 = 22. Then add 5: 22 + 5 = 27.

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

    89

    First multiply: 12 × 7 = 84. Then add 5: 84 + 5 = 89.

12 questions · Seed 42 · Age guidance, not curriculum certification