Let’s solve each problem step by step.
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Problem 1: Rule = Subtract 4
In: 9 → Out: 9 - 4 =
5
In: 12 → Out: 12 - 4 =
8
In: 15 → Out: 15 - 4 =
11
In: 18 → Out: 18 - 4 =
14
✔ Check: All correct.
---
Problem 2: Rule = Subtract 5
In: 7 → Out: 7 - 5 =
2
In: 12 → Out: 12 - 5 =
7
In: 15 → Out: 15 - 5 =
10
In: 16 → Out: 16 - 5 =
11
✔ Check: All correct.
---
Problem 3: Rule = Subtract 1
In: 4 → Out: 4 - 1 =
3
In: 6 → Out: 6 - 1 =
5
In: 12 → Out: 12 - 1 =
11
In: 13 → Out: 13 - 1 =
12
✔ Check: All correct.
---
Problem 4: Rule = Subtract 3
In: 4 → Out: 4 - 3 =
1
In: 5 → Out: 5 - 3 =
2
In: 10 → Out: 10 - 3 =
7
In: 14 → Out: 14 - 3 =
11
✔ Check: All correct.
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Problem 5: Rule = Subtract 1
In: 6 → Out: 6 - 1 =
5
In: 10 → Out: 10 - 1 =
9
In: 13 → Out: 13 - 1 =
12
In: 14 → Out: 14 - 1 =
13
✔ Check: All correct.
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Problem 6: Rule = Add 2
In: 3 → Out: 3 + 2 =
5
In: 8 → Out: 8 + 2 =
10
In: 9 → Out: 9 + 2 =
11
In: 11 → Out: 11 + 2 =
13
✔ Check: All correct.
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Problem 7: Rule = Add 3
In: 0 → Out: 0 + 3 =
3
In: 6 → Out: 6 + 3 =
9
In: 9 → Out: 9 + 3 =
12
In: 12 → Out: 12 + 3 =
15
✔ Check: All correct.
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Problem 8: Rule = Add 2
In: 8 → Out: 8 + 2 =
10
In: 9 → Out: 9 + 2 =
11
In: 10 → Out: 10 + 2 =
12
In: 14 → Out: 14 + 2 =
16
✔ Check: All correct.
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Now, problems 9–14 ask us to find the rule AND fill in the boxes.
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Problem 9:
In | Out
0 → 4
2 → 6
6 → 10
7 → ?
Look at differences:
0 → 4: +4
2 → 6: +4
6 → 10: +4
So Rule =
Add 4
Then 7 + 4 =
11
✔ Final for #9: Rule = Add 4; last Out = 11
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Problem 10:
In | Out
2 → ?
6 → 10
14 → 18
15 → 19
Check known pairs:
6 → 10: +4
14 → 18: +4
15 → 19: +4
So Rule =
Add 4
Then 2 + 4 =
6
✔ Final for #10: Rule = Add 4; first Out = 6
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Problem 11:
In | Out
1 → 2
12 → ?
14 → 15
15 → 16
Check:
1 → 2: +1
14 → 15: +1
15 → 16: +1
So Rule =
Add 1
Then 12 + 1 =
13
✔ Final for #11: Rule = Add 1; second Out = 13
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Problem 12:
In | Out
4 → 1
9 → 6
11 → 8
17 → ?
Check:
4 → 1: -3
9 → 6: -3
11 → 8: -3
So Rule =
Subtract 3
Then 17 - 3 =
14
✔ Final for #12: Rule = Subtract 3; last Out = 14
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Problem 13:
In | Out
4 → ?
5 → 10
9 → 14
10 → 15
Check known:
5 → 10: +5
9 → 14: +5
10 → 15: +5
So Rule =
Add 5
Then 4 + 5 =
9
✔ Final for #13: Rule = Add 5; first Out = 9
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Problem 14:
In | Out
5 → 0
6 → 1
8 → ?
13 → 8
Check:
5 → 0: -5
6 → 1: -5
13 → 8: -5
So Rule =
Subtract 5
Then 8 - 5 =
3
✔ Final for #14: Rule = Subtract 5; third Out = 3
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All done! Now compile final answers as requested.
Final Answer:
1) 5, 8, 11, 14
2) 2, 7, 10, 11
3) 3, 5, 11, 12
4) 1, 2, 7, 11
5) 5, 9, 12, 13
6) 5, 10, 11, 13
7) 3, 9, 12, 15
8) 10, 11, 12, 16
9) Rule: Add 4; missing Out: 11
10) Rule: Add 4; missing Out: 6
11) Rule: Add 1; missing Out: 13
12) Rule: Subtract 3; missing Out: 14
13) Rule: Add 5; missing Out: 9
14) Rule: Subtract 5; missing Out: 3
Parent Tip: Review the logic above to help your child master the concept of 8th grade math functions worksheet.
