Counting on and back Worksheets 3rd Grade - Free Printable

To solve the problem, we need to identify the pattern in each sequence and fill in the missing numbers. Each sequence goes up by single-digit steps, so we will determine the step size for each sequence and use it to fill in the blanks.

Sequence 1:

```
_ 7 _ 14 _ 28 _ 42 _
```
- The difference between 14 and 7 is 7.
- The difference between 28 and 14 is 14.
- The difference between 42 and 28 is 14.
- The pattern seems to be increasing by 7, then 14, then 14, and so on.
- Filling in the blanks:
- First blank: \(7 - 7 = 0\)
- Second blank: \(14 + 7 = 21\)
- Third blank: \(28 + 14 = 42\) (already given)
- Fourth blank: \(42 + 14 = 56\)

So, the sequence is:
```
0 7 21 14 28 42 56
```

Sequence 2:

```
0 _ 8 12 _ 20 _ _
```
- The difference between 8 and 0 is 8.
- The difference between 12 and 8 is 4.
- The difference between 20 and 12 is 8.
- The pattern alternates between adding 8 and adding 4.
- Filling in the blanks:
- First blank: \(0 + 8 = 8\)
- Second blank: \(12 + 8 = 20\) (already given)
- Third blank: \(20 + 4 = 24\)
- Fourth blank: \(24 + 8 = 32\)

So, the sequence is:
```
0 8 8 12 20 20 24 32
```

Sequence 3:

```
8 _ 12 _ 16 18 _ _
```
- The difference between 12 and 8 is 4.
- The difference between 16 and 12 is 4.
- The difference between 18 and 16 is 2.
- The pattern seems to be increasing by 4, then 4, then 2, and so on.
- Filling in the blanks:
- First blank: \(8 + 4 = 12\) (already given)
- Second blank: \(12 + 4 = 16\) (already given)
- Third blank: \(18 + 2 = 20\)
- Fourth blank: \(20 + 2 = 22\)

So, the sequence is:
```
8 12 12 16 16 18 20 22
```

Sequence 4:

```
12 15 _ 21 _ _ 30 _
```
- The difference between 15 and 12 is 3.
- The difference between 21 and 15 is 6.
- The difference between 30 and 21 is 9.
- The pattern seems to be increasing by 3, then 6, then 9, and so on.
- Filling in the blanks:
- First blank: \(15 + 6 = 21\) (already given)
- Second blank: \(21 + 9 = 30\) (already given)
- Third blank: \(30 + 12 = 42\)
- Fourth blank: \(42 + 15 = 57\)

So, the sequence is:
```
12 15 21 21 30 30 42 57
```

Sequence 5:

```
0 _ 18 27 _ _ 54 _
```
- The difference between 18 and 0 is 18.
- The difference between 27 and 18 is 9.
- The difference between 54 and 27 is 27.
- The pattern seems to be increasing by 18, then 9, then 27, and so on.
- Filling in the blanks:
- First blank: \(0 + 18 = 18\) (already given)
- Second blank: \(27 + 9 = 36\)
- Third blank: \(36 + 27 = 63\)
- Fourth blank: \(63 + 9 = 72\)

So, the sequence is:
```
0 18 18 27 36 63 54 72
```

Sequence 6:

```
_ 17 22 _ _ 32 _ 42 _
```
- The difference between 22 and 17 is 5.
- The difference between 32 and 22 is 10.
- The difference between 42 and 32 is 10.
- The pattern seems to be increasing by 5, then 10, then 10, and so on.
- Filling in the blanks:
- First blank: \(17 - 5 = 12\)
- Second blank: \(22 + 10 = 32\) (already given)
- Third blank: \(32 + 10 = 42\) (already given)
- Fourth blank: \(42 + 10 = 52\)

So, the sequence is:
```
12 17 22 32 32 32 42 52
```

Sequence 7:

```
_ 12 _ 24 _ 36 42 _
```
- The difference between 24 and 12 is 12.
- The difference between 36 and 24 is 12.
- The difference between 42 and 36 is 6.
- The pattern seems to be increasing by 12, then 12, then 6, and so on.
- Filling in the blanks:
- First blank: \(12 - 12 = 0\)
- Second blank: \(12 + 12 = 24\) (already given)
- Third blank: \(24 + 12 = 36\) (already given)
- Fourth blank: \(36 + 6 = 42\) (already given)
- Fifth blank: \(42 + 6 = 48\)

So, the sequence is:
```
0 12 24 24 36 36 42 48
```

Sequence 8:

```
19 _ 23 _ 27 29 _ _
```
- The difference between 23 and 19 is 4.
- The difference between 27 and 23 is 4.
- The difference between 29 and 27 is 2.
- The pattern seems to be increasing by 4, then 4, then 2, and so on.
- Filling in the blanks:
- First blank: \(19 + 4 = 23\) (already given)
- Second blank: \(23 + 4 = 27\) (already given)
- Third blank: \(29 + 2 = 31\)
- Fourth blank: \(31 + 2 = 33\)

So, the sequence is:
```
19 23 23 27 27 29 31 33
```

Sequence 9:

```
_ 24 32 _ 48 _ 64 _
```
- The difference between 32 and 24 is 8.
- The difference between 48 and 32 is 16.
- The difference between 64 and 48 is 16.
- The pattern seems to be increasing by 8, then 16, then 16, and so on.
- Filling in the blanks:
- First blank: \(24 - 8 = 16\)
- Second blank: \(32 + 16 = 48\) (already given)
- Third blank: \(48 + 16 = 64\) (already given)
- Fourth blank: \(64 + 16 = 80\)

So, the sequence is:
```
16 24 32 48 48 64 64 80
```

Sequence 10:

```
17 _ _ 20 21 _ _ 24
```
- The difference between 20 and 17 is 3.
- The difference between 21 and 20 is 1.
- The difference between 24 and 21 is 3.
- The pattern seems to be increasing by 3, then 1, then 3, and so on.
- Filling in the blanks:
- First blank: \(17 + 3 = 20\)
- Second blank: \(20 + 1 = 21\) (already given)
- Third blank: \(21 + 3 = 24\) (already given)
- Fourth blank: \(24 + 1 = 25\)

So, the sequence is:
```
17 20 21 20 21 24 25 24
```

Final Answer:

```
1) 0 7 21 14 28 42 56
2) 0 8 8 12 20 20 24 32
3) 8 12 12 16 16 18 20 22
4) 12 15 21 21 30 30 42 57
5) 0 18 18 27 36 63 54 72
6) 12 17 22 32 32 32 42 52
7) 0 12 24 24 36 36 42 48
8) 19 23 23 27 27 29 31 33
9) 16 24 32 48 48 64 64 80
10) 17 20 21 20 21 24 25 24
```

\boxed{
\begin{array}{cccccccc}
1) & 0 & 7 & 21 & 14 & 28 & 42 & 56 \\
2) & 0 & 8 & 8 & 12 & 20 & 20 & 24 & 32 \\
3) & 8 & 12 & 12 & 16 & 16 & 18 & 20 & 22 \\
4) & 12 & 15 & 21 & 21 & 30 & 30 & 42 & 57 \\
5) & 0 & 18 & 18 & 27 & 36 & 63 & 54 & 72 \\
6) & 12 & 17 & 22 & 32 & 32 & 32 & 42 & 52 \\
7) & 0 & 12 & 24 & 24 & 36 & 36 & 42 & 48 \\
8) & 19 & 23 & 23 & 27 & 27 & 29 & 31 & 33 \\
9) & 16 & 24 & 32 & 48 & 48 & 64 & 64 & 80 \\
10) & 17 & 20 & 21 & 20 & 21 & 24 & 25 & 24 \\
\end{array}
}