Algebra and equations · Ages 9–10
Number machines worksheet
Part of: Patterns and rules
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Number machines worksheet
Algebra and equations · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The number machine turns the input into the output by the rule shown. What is the output?
Answer:
2.This number machine has two steps, done in order from left to right. What is the output?
Answer:
3.The machine's rule and output are shown. What is the input?
Answer:
4.Each input in the table goes to its output by the same rule. What is the ? in the table?
Answer:
5.Each input in the table goes to its output by the same rule. Which input gives the output 113?
Answer:
6.Each input in the table goes to its output by the same rule. Which input gives the output 80?
Answer:
7.Each input in the table goes to its output by the same rule. Which input gives the output 51?
Answer:
8.Each input in the table goes to its output by the same rule. Which input gives the output 105?
Answer:
9.Each input in the table goes to its output by the same rule. Which input gives the output 125?
Answer:
10.Each input in the table goes to its output by the same rule. Which input gives the output 33?
Answer:
11.Each input in the table goes to its output by the same rule. Which input gives the output 91?
Answer:
Part B: Choose, or true or false (2 marks each)
12.Every input and output in the table follow the same rule. Which rule is it?
- A. + 7
- B. × 4, then + 4
- C. × 5, then + 3
- D. × 8
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Tsz-ching thinks of a number, multiplies it by 6, then subtracts 3, and gets 69. What number did Tsz-ching think of?
Working:
Answer:
14.A cha chaan teng sells takeaway rice at $39 a box, plus $14 delivery on each order. Chi-keung pays $209 for one order. How many boxes did Chi-keung buy?
Working:
Answer:
15.A fun fair has two number machines: A multiplies by 5 and B adds 1. Put 10 through A, then B, and you get ; through B, then A, and you get .
Fill in each blank
Working:
Answer:
16.A number machine at the fun fair: put in 3 and out comes 8, 4 gives 10, 5 gives 12. By the same rule, what comes out for 14?
Working:
Answer:
17.A number machine at the fun fair: put in 3 and out comes 15, 4 gives 18, 5 gives 21. By the same rule, what comes out for 18?
Working:
Answer:
18.A cha chaan teng sells takeaway rice at $32 a box, plus $5 delivery on each order. Ka-yee pays $197 for one order. How many boxes did Ka-yee buy?
Working:
Answer:
Show the answers and working
Number machines worksheet: Answers and working
Part A: Working out and filling in
1. 26
Read the rule in the box and do it to 24.
Put 24 into the machine and do what the box says: 26.
2. 55
Go from left to right and do only the first step to 8. What does it become?
First step: 8 becomes 11. Second step: 11 becomes 55.
3. 13
Work backwards: start from the output 71 and undo the last step first.
Work backwards from the last step, doing the opposite each time: first 71 − 6 = 65, then 65 ÷ 5 = 13.
4. 40
See how much the output goes up when the input goes up by 1: that tells you what to multiply by. Then see what is still missing.
Each time the input goes up 1, the output goes up 3: so × 3. 5 × 3 is 1 short: so + 1. 13 × 3 + 1 = 40.
5. 18
Find the rule first: how much does the output go up for each 1 more in? Then work backwards from 113.
The rule is “× 6, then + 5”. Work backwards: 113 − 5 = 108, 108 ÷ 6 = 18.
6. 15
Find the rule first: how much does the output go up for each 1 more in? Then work backwards from 80.
The rule is “× 5, then + 5”. Work backwards: 80 − 5 = 75, 75 ÷ 5 = 15.
7. 8
Find the rule first: how much does the output go up for each 1 more in? Then work backwards from 51.
The rule is “× 6, then + 3”. Work backwards: 51 − 3 = 48, 48 ÷ 6 = 8.
8. 17
Find the rule first: how much does the output go up for each 1 more in? Then work backwards from 105.
The rule is “× 6, then + 3”. Work backwards: 105 − 3 = 102, 102 ÷ 6 = 17.
9. 20
Find the rule first: how much does the output go up for each 1 more in? Then work backwards from 125.
The rule is “× 6, then + 5”. Work backwards: 125 − 5 = 120, 120 ÷ 6 = 20.
10. 9
Find the rule first: how much does the output go up for each 1 more in? Then work backwards from 33.
The rule is “× 3, then + 6”. Work backwards: 33 − 6 = 27, 27 ÷ 3 = 9.
11. 15
Find the rule first: how much does the output go up for each 1 more in? Then work backwards from 91.
The rule is “× 6, then + 1”. Work backwards: 91 − 1 = 90, 90 ÷ 6 = 15.
Part B: Choose, or true or false
12. B. × 4, then + 4
How much does the output go up for each 1 more in? Then check the rules on every pair, not just the first.
The output goes up 4 each time: × 4. 1 × 4 = 4, 4 short: + 4. Every pair fits.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 12
Work backwards from 69: the last step was − 3, so undo that first.
Work backwards: + 3 first, 69 + 3 = 72; then ÷ 6, 72 ÷ 6 = 12.
14. 5 boxes
The rule is boxes × 39, then + 14. Work backwards: take off the $14 delivery first.
The rule is “boxes × 39, then + 14”. Work backwards: 209 − 14 = 195, 195 ÷ 39 = 5.
15. 51, 55
Follow the machines in order: A then B means 10 is multiplied by 5 first; B then A means 1 is added first.
A then B: 10 × 5 + 1 = 51. B then A: (10 + 1) × 5 = 55. A different order gives a different result.
16. 30
Each time 1 more goes in, how much more comes out? Compare 8 and 10.
Each 1 more in gives 2 more out: × 2. 3 × 2 is 2 short: + 2. 14 × 2 + 2 = 30.
17. 60
Each time 1 more goes in, how much more comes out? Compare 15 and 18.
Each 1 more in gives 3 more out: × 3. 3 × 3 is 6 short: + 6. 18 × 3 + 6 = 60.
18. 6 boxes
The rule is boxes × 32, then + 5. Work backwards: take off the $5 delivery first.
The rule is “boxes × 32, then + 5”. Work backwards: 197 − 5 = 192, 192 ÷ 32 = 6.
Numsprite · numsprite.com/en/worksheets/patterns-and-rules/function-machines
Practise it in the gameNumber machines · Unlimited questions, no download