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

    9+110+110+1?

  2. 2. A number machine multiplies the input by 4 and then adds 10. When the input is 5, what is the output?

    4+610+65+6?

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

    7+07+014+0?

  4. 4. A number machine multiplies the input by 2 and then adds 12. When the input is 5, what is the output?

    2+1012+105+10?

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

    8-35-35-3?

  6. 6. A number machine multiplies the input by 4 and then adds 1. When the input is 5, what is the output?

    4-31-35-3?

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

    3+710+74+7?

  8. 8. A number machine multiplies the input by 9 and then adds 8. When the input is 15, what is the output?

    9-18-115-1?

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

    3-21-213-2?

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

    4+610+63+6?

  11. 11. A number machine multiplies the input by 5 and then adds 7. When the input is 2, what is the output?

    5+27+22+2?

  12. 12. A number machine multiplies the input by 2 and then adds 7. When the input is 5, what is the output?

    2+57+55+5?
12 questions · Seed 104729 · 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 9 and then adds 10. When the input is 10, what is the output?

    100

    First multiply: 10 × 9 = 90. Then add 10: 90 + 10 = 100.

  2. 2. A number machine multiplies the input by 4 and then adds 10. When the input is 5, what is the output?

    30

    First multiply: 5 × 4 = 20. Then add 10: 20 + 10 = 30.

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

    105

    First multiply: 14 × 7 = 98. Then add 7: 98 + 7 = 105.

  4. 4. A number machine multiplies the input by 2 and then adds 12. When the input is 5, what is the output?

    22

    First multiply: 5 × 2 = 10. Then add 12: 10 + 12 = 22.

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

    45

    First multiply: 5 × 8 = 40. Then add 5: 40 + 5 = 45.

  6. 6. A number machine multiplies the input by 4 and then adds 1. When the input is 5, what is the output?

    21

    First multiply: 5 × 4 = 20. Then add 1: 20 + 1 = 21.

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

    22

    First multiply: 4 × 3 = 12. Then add 10: 12 + 10 = 22.

  8. 8. A number machine multiplies the input by 9 and then adds 8. When the input is 15, what is the output?

    143

    First multiply: 15 × 9 = 135. Then add 8: 135 + 8 = 143.

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

    40

    First multiply: 13 × 3 = 39. Then add 1: 39 + 1 = 40.

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

    22

    First multiply: 3 × 4 = 12. Then add 10: 12 + 10 = 22.

  11. 11. A number machine multiplies the input by 5 and then adds 7. When the input is 2, what is the output?

    17

    First multiply: 2 × 5 = 10. Then add 7: 10 + 7 = 17.

  12. 12. A number machine multiplies the input by 2 and then adds 7. When the input is 5, what is the output?

    17

    First multiply: 5 × 2 = 10. Then add 7: 10 + 7 = 17.

12 questions · Seed 104729 · 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 9 and then adds 10. When the input is 10, what is the output?

    9+110+110+1?

  2. 2. A number machine multiplies the input by 4 and then adds 10. When the input is 5, what is the output?

    4+610+65+6?

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

    7+07+014+0?

  4. 4. A number machine multiplies the input by 2 and then adds 12. When the input is 5, what is the output?

    2+1012+105+10?

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

    8-35-35-3?

  6. 6. A number machine multiplies the input by 4 and then adds 1. When the input is 5, what is the output?

    4-31-35-3?

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

    3+710+74+7?

  8. 8. A number machine multiplies the input by 9 and then adds 8. When the input is 15, what is the output?

    9-18-115-1?

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

    3-21-213-2?

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

    4+610+63+6?

  11. 11. A number machine multiplies the input by 5 and then adds 7. When the input is 2, what is the output?

    5+27+22+2?

  12. 12. A number machine multiplies the input by 2 and then adds 7. When the input is 5, what is the output?

    2+57+55+5?
12 questions · Seed 104729 · 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 9 and then adds 10. When the input is 10, what is the output?

    100

    First multiply: 10 × 9 = 90. Then add 10: 90 + 10 = 100.

  2. 2. A number machine multiplies the input by 4 and then adds 10. When the input is 5, what is the output?

    30

    First multiply: 5 × 4 = 20. Then add 10: 20 + 10 = 30.

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

    105

    First multiply: 14 × 7 = 98. Then add 7: 98 + 7 = 105.

  4. 4. A number machine multiplies the input by 2 and then adds 12. When the input is 5, what is the output?

    22

    First multiply: 5 × 2 = 10. Then add 12: 10 + 12 = 22.

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

    45

    First multiply: 5 × 8 = 40. Then add 5: 40 + 5 = 45.

  6. 6. A number machine multiplies the input by 4 and then adds 1. When the input is 5, what is the output?

    21

    First multiply: 5 × 4 = 20. Then add 1: 20 + 1 = 21.

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

    22

    First multiply: 4 × 3 = 12. Then add 10: 12 + 10 = 22.

  8. 8. A number machine multiplies the input by 9 and then adds 8. When the input is 15, what is the output?

    143

    First multiply: 15 × 9 = 135. Then add 8: 135 + 8 = 143.

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

    40

    First multiply: 13 × 3 = 39. Then add 1: 39 + 1 = 40.

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

    22

    First multiply: 3 × 4 = 12. Then add 10: 12 + 10 = 22.

  11. 11. A number machine multiplies the input by 5 and then adds 7. When the input is 2, what is the output?

    17

    First multiply: 2 × 5 = 10. Then add 7: 10 + 7 = 17.

  12. 12. A number machine multiplies the input by 2 and then adds 7. When the input is 5, what is the output?

    17

    First multiply: 5 × 2 = 10. Then add 7: 10 + 7 = 17.

12 questions · Seed 104729 · Age guidance, not curriculum certification