Math worksheet for extending number sequences and practicing counting in sevens.

Let’s solve each part of this worksheet step by step.

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1. 14, 20, 26, 32, __, __

Look at the differences:
- 20 - 14 = 6
- 26 - 20 = 6
- 32 - 26 = 6

✔ Pattern: Add 6 each time.

So:
- 32 + 6 = 38
- 38 + 6 = 44

Answer: 38, 44

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2. 47, 54, 61, 68, __, __

Differences:
- 54 - 47 = 7
- 61 - 54 = 7
- 68 - 61 = 7

✔ Pattern: Add 7 each time.

So:
- 68 + 7 = 75
- 75 + 7 = 82

Answer: 75, 82

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3. 9, 17, __, 33, __, 49

Differences:
- 17 - 9 = 8
- Let’s assume pattern is +8 each time.

Check:
- 17 + 8 = 25
- 25 + 8 = 33 ✔
- 33 + 8 = 41
- 41 + 8 = 49 ✔

Answer: 25, 41

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4. 27, 34, __, __, __

Differences:
- 34 - 27 = 7

Assume +7 each time.

So:
- 34 + 7 = 41
- 41 + 7 = 48
- 48 + 7 = 55

Answer: 41, 48, 55

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5. 67, 58, 49, __, 31, __

Differences:
- 58 - 67 = -9
- 49 - 58 = -9

✔ Pattern: Subtract 9 each time.

So:
- 49 - 9 = 40
- 31 - 9 = 22

Check: 40 → 31? 40 - 9 = 31 ✔
Then 31 - 9 = 22

Answer: 40, 22

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6. 99, 92, __, 78, __, 64

Differences:
- 92 - 99 = -7

Assume subtract 7 each time.

So:
- 92 - 7 = 85
- 85 - 7 = 78 ✔
- 78 - 7 = 71
- 71 - 7 = 64 ✔

Answer: 85, 71

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7. __, 42, 36, 30, __, 18

Differences:
- 36 - 42 = -6
- 30 - 36 = -6

Pattern: Subtract 6.

So:
- Before 42: 42 + 6 = 48
- After 30: 30 - 6 = 24

Check: 24 - 6 = 18 ✔

Answer: 48, 24

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8. __, __, 78, 70, 62, 54

Differences:
- 70 - 78 = -8
- 62 - 70 = -8
- 54 - 62 = -8

Pattern: Subtract 8.

So:
- Before 78: 78 + 8 = 86
- Before 86: 86 + 8 = 94

Check: 94 → 86 → 78 → 70 → 62 → 54 ✔

Answer: 94, 86

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9. Take a 9 x 9 square. Starting at 1 count on in sevens. Circle or colour the numbers you land on.

We start at 1, then add 7 repeatedly:

Sequence:
- 1
- 1 + 7 = 8
- 8 + 7 = 15
- 15 + 7 = 22
- 22 + 7 = 29
- 29 + 7 = 36
- 36 + 7 = 43
- 43 + 7 = 50
- 50 + 7 = 57
- 57 + 7 = 64
- 64 + 7 = 71
- 71 + 7 = 78
- 78 + 7 = 85
- 85 + 7 = 92 → But 92 is beyond 81 (the last number in the 9x9 grid), so we stop at 85.

✔ Numbers to circle: 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85

You can locate them in the grid — they form a diagonal pattern going down-right.

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10. What do you notice? If you went on, would 100 be in your sequence? How do you know?

What do you notice?

The numbers are all 1 more than a multiple of 7, because:

- 1 = 0×7 + 1
- 8 = 1×7 + 1
- 15 = 2×7 + 1
- ...
- So general term: 7n + 1, where n starts from 0.

They form a diagonal line in the 9x9 grid, moving one row down and one column right each time (since adding 7 moves you down one row in a 9-column grid).

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Would 100 be in your sequence?

Check if 100 fits the pattern: Is 100 = 7n + 1 for some whole number n?

→ 100 - 1 = 99
→ 99 ÷ 7 = 14.142... → Not a whole number

So, no, 100 is NOT in the sequence.

✔ Because 100 is not 1 more than a multiple of 7.

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## ✔ Final Answers Summary:

1. 38, 44
2. 75, 82
3. 25, 41
4. 41, 48, 55
5. 40, 22
6. 85, 71
7. 48, 24
8. 94, 86
9. Circle: 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85
10. Notice: All numbers are 1 more than multiples of 7; they form a diagonal.
100? No, because 100 - 1 = 99 is not divisible by 7.

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Let me know if you’d like a visual of the circled numbers in the grid!