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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 3. When the input is 8, what is the output?

    7-43-48-4?

  2. 2. A number machine multiplies the input by 6 and then adds 2. When the input is 4, what is the output?

    6-42-44-4?

  3. 3. A number machine multiplies the input by 2 and then adds 1. When the input is 13, what is the output?

    2-11-113-1?

  4. 4. A number machine multiplies the input by 7 and then adds 10. When the input is 2, what is the output?

    7+310+32+3?

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

    4-22-23-2?

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 10, what is the output?

    2+1113+1110+11?

  7. 7. A number machine multiplies the input by 6 and then adds 14. When the input is 12, what is the output?

    6+814+812+8?

  8. 8. A number machine multiplies the input by 8 and then adds 5. When the input is 6, what is the output?

    8-35-36-3?

  9. 9. A number machine multiplies the input by 3 and then adds 12. When the input is 6, what is the output?

    3+912+96+9?

  10. 10. A number machine multiplies the input by 5 and then adds 12. When the input is 11, what is the output?

    5+712+711+7?

  11. 11. A number machine multiplies the input by 3 and then adds 5. When the input is 12, what is the output?

    3+25+212+2?

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

    9+312+36+3?
12 questions · Seed 43 · 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 3. When the input is 8, what is the output?

    59

    First multiply: 8 × 7 = 56. Then add 3: 56 + 3 = 59.

  2. 2. A number machine multiplies the input by 6 and then adds 2. When the input is 4, what is the output?

    26

    First multiply: 4 × 6 = 24. Then add 2: 24 + 2 = 26.

  3. 3. A number machine multiplies the input by 2 and then adds 1. When the input is 13, what is the output?

    27

    First multiply: 13 × 2 = 26. Then add 1: 26 + 1 = 27.

  4. 4. A number machine multiplies the input by 7 and then adds 10. When the input is 2, what is the output?

    24

    First multiply: 2 × 7 = 14. Then add 10: 14 + 10 = 24.

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

    14

    First multiply: 3 × 4 = 12. Then add 2: 12 + 2 = 14.

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 10, what is the output?

    33

    First multiply: 10 × 2 = 20. Then add 13: 20 + 13 = 33.

  7. 7. A number machine multiplies the input by 6 and then adds 14. When the input is 12, what is the output?

    86

    First multiply: 12 × 6 = 72. Then add 14: 72 + 14 = 86.

  8. 8. A number machine multiplies the input by 8 and then adds 5. When the input is 6, what is the output?

    53

    First multiply: 6 × 8 = 48. Then add 5: 48 + 5 = 53.

  9. 9. A number machine multiplies the input by 3 and then adds 12. When the input is 6, what is the output?

    30

    First multiply: 6 × 3 = 18. Then add 12: 18 + 12 = 30.

  10. 10. A number machine multiplies the input by 5 and then adds 12. When the input is 11, what is the output?

    67

    First multiply: 11 × 5 = 55. Then add 12: 55 + 12 = 67.

  11. 11. A number machine multiplies the input by 3 and then adds 5. When the input is 12, what is the output?

    41

    First multiply: 12 × 3 = 36. Then add 5: 36 + 5 = 41.

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

    66

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

12 questions · Seed 43 · 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 3. When the input is 8, what is the output?

    7-43-48-4?

  2. 2. A number machine multiplies the input by 6 and then adds 2. When the input is 4, what is the output?

    6-42-44-4?

  3. 3. A number machine multiplies the input by 2 and then adds 1. When the input is 13, what is the output?

    2-11-113-1?

  4. 4. A number machine multiplies the input by 7 and then adds 10. When the input is 2, what is the output?

    7+310+32+3?

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

    4-22-23-2?

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 10, what is the output?

    2+1113+1110+11?

  7. 7. A number machine multiplies the input by 6 and then adds 14. When the input is 12, what is the output?

    6+814+812+8?

  8. 8. A number machine multiplies the input by 8 and then adds 5. When the input is 6, what is the output?

    8-35-36-3?

  9. 9. A number machine multiplies the input by 3 and then adds 12. When the input is 6, what is the output?

    3+912+96+9?

  10. 10. A number machine multiplies the input by 5 and then adds 12. When the input is 11, what is the output?

    5+712+711+7?

  11. 11. A number machine multiplies the input by 3 and then adds 5. When the input is 12, what is the output?

    3+25+212+2?

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

    9+312+36+3?
12 questions · Seed 43 · 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 3. When the input is 8, what is the output?

    59

    First multiply: 8 × 7 = 56. Then add 3: 56 + 3 = 59.

  2. 2. A number machine multiplies the input by 6 and then adds 2. When the input is 4, what is the output?

    26

    First multiply: 4 × 6 = 24. Then add 2: 24 + 2 = 26.

  3. 3. A number machine multiplies the input by 2 and then adds 1. When the input is 13, what is the output?

    27

    First multiply: 13 × 2 = 26. Then add 1: 26 + 1 = 27.

  4. 4. A number machine multiplies the input by 7 and then adds 10. When the input is 2, what is the output?

    24

    First multiply: 2 × 7 = 14. Then add 10: 14 + 10 = 24.

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

    14

    First multiply: 3 × 4 = 12. Then add 2: 12 + 2 = 14.

  6. 6. A number machine multiplies the input by 2 and then adds 13. When the input is 10, what is the output?

    33

    First multiply: 10 × 2 = 20. Then add 13: 20 + 13 = 33.

  7. 7. A number machine multiplies the input by 6 and then adds 14. When the input is 12, what is the output?

    86

    First multiply: 12 × 6 = 72. Then add 14: 72 + 14 = 86.

  8. 8. A number machine multiplies the input by 8 and then adds 5. When the input is 6, what is the output?

    53

    First multiply: 6 × 8 = 48. Then add 5: 48 + 5 = 53.

  9. 9. A number machine multiplies the input by 3 and then adds 12. When the input is 6, what is the output?

    30

    First multiply: 6 × 3 = 18. Then add 12: 18 + 12 = 30.

  10. 10. A number machine multiplies the input by 5 and then adds 12. When the input is 11, what is the output?

    67

    First multiply: 11 × 5 = 55. Then add 12: 55 + 12 = 67.

  11. 11. A number machine multiplies the input by 3 and then adds 5. When the input is 12, what is the output?

    41

    First multiply: 12 × 3 = 36. Then add 5: 36 + 5 = 41.

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

    66

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

12 questions · Seed 43 · Age guidance, not curriculum certification