Counting on and back Worksheets 3rd Grade - Free Printable

Let’s solve each sequence step by step. The rule is: count on or back by single digit steps — that means we add or subtract a number from 1 to 9, and the same step is used throughout each sequence.

We’ll find the pattern (the step) for each row, then fill in the missing numbers.

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1)
Given: _ , 21, _ , 35, 42, _ , _ , 63

Look at known consecutive numbers:
→ 35 to 42 = +7
Check if 42 + 7 = 49 → yes
Then 49 + 7 = 56
Then 56 + 7 = 63 ✔ matches last number.

Now go backward from 21:
21 - 7 = 14
Before that? Not needed — first blank is before 21 → so 14
Between 21 and 35: 21 + 7 = 28 → then 28 + 7 = 35 ✔

So sequence:
14, 21, 28, 35, 42, 49, 56, 63

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2)
Given: _ , _ , 33, 30, _ , 24, _ , 18

From 33 to 30 = -3
30 - 3 = 27
27 - 3 = 24 ✔
24 - 3 = 21
21 - 3 = 18 ✔

Go backward from 33:
33 + 3 = 36
36 + 3 = 39

Sequence:
39, 36, 33, 30, 27, 24, 21, 18

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3)
Given: _ , 55, _ , _ , 40, 35, _ , _

From 40 to 35 = -5
So step is -5

Backward from 55:
55 + 5 = 60 → first number
55 - 5 = 50 → third number
50 - 5 = 45 → fourth
Then 40, 35
35 - 5 = 30
30 - 5 = 25

Sequence:
60, 55, 50, 45, 40, 35, 30, 25

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4)
Given: 36, _ , _ , 63, 72, _ , _ , 99

From 63 to 72 = +9
72 + 9 = 81
81 + 9 = 90
90 + 9 = 99 ✔

Backward from 63:
63 - 9 = 54
54 - 9 = 45
But we start at 36 → 36 + 9 = 45 ✔ → so second number is 45, third is 54

Sequence:
36, 45, 54, 63, 72, 81, 90, 99

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5)
Given: _ , 44, _ , 36, 32, _ , _ , 20

From 36 to 32 = -4
So step is -4

Backward from 44:
44 + 4 = 48 → first number
44 - 4 = 40 → third number
Then 36, 32
32 - 4 = 28
28 - 4 = 24
24 - 4 = 20 ✔

Sequence:
48, 44, 40, 36, 32, 28, 24, 20

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6)
Given: 24, _ , _ , 48, _ , _ , 72, 80

From 72 to 80 = +8
So step is +8

Forward from 24:
24 + 8 = 32
32 + 8 = 40
40 + 8 = 48 ✔
48 + 8 = 56
56 + 8 = 64
64 + 8 = 72 ✔
72 + 8 = 80 ✔

Sequence:
24, 32, 40, 48, 56, 64, 72, 80

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7)
Given: _ , 42, _ , _ , 24, 18, _ , _

From 24 to 18 = -6
So step is -6

Backward from 42:
42 + 6 = 48 → first
42 - 6 = 36 → third
36 - 6 = 30 → fourth
Then 24, 18
18 - 6 = 12
12 - 6 = 6

Sequence:
48, 42, 36, 30, 24, 18, 12, 6

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8)
Given: _ , _ , 24, 27, _ , _ , 36, _

From 24 to 27 = +3
So step is +3

Backward from 24:
24 - 3 = 21
21 - 3 = 18 → first two blanks

Forward:
27 + 3 = 30
30 + 3 = 33
33 + 3 = 36 ✔
36 + 3 = 39

Sequence:
18, 21, 24, 27, 30, 33, 36, 39

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9)
Given: _ , 49, _ , _ , _ , 21, 14, _

From 21 to 14 = -7
So step is -7

Backward from 49:
49 + 7 = 56 → first
49 - 7 = 42 → third
42 - 7 = 35 → fourth
35 - 7 = 28 → fifth
Then 21, 14
14 - 7 = 7 → last

Sequence:
56, 49, 42, 35, 28, 21, 14, 7

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10)
Given: _ , _ , 36, 38, _ , _ , _ , 46

From 36 to 38 = +2
So step is +2

Backward from 36:
36 - 2 = 34
34 - 2 = 32 → first two blanks

Forward:
38 + 2 = 40
40 + 2 = 42
42 + 2 = 44
44 + 2 = 46 ✔

Sequence:
32, 34, 36, 38, 40, 42, 44, 46

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Final Answer:

1) 14, 28, 49, 56
2) 39, 36, 27, 21
3) 60, 50, 45, 30, 25
4) 45, 54, 81, 90
5) 48, 40, 28, 24
6) 32, 40, 56, 64
7) 48, 36, 30, 12, 6
8) 18, 21, 30, 33, 39
9) 56, 42, 35, 28, 7
10) 32, 34, 40, 42, 44