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 increases by a single-digit step. Let's solve each sequence step by step.

---

Sequence 1:

```
_ 7 14 _ 28 _ 42 _
```
- The difference between 7 and 14 is 7.
- The difference between 14 and 28 is 14.
- The difference between 28 and 42 is 14.

The pattern appears to be increasing by 7, then 14, then 14, and so on. However, since the task specifies "single-digit steps," let's re-evaluate:
- The difference between 7 and 14 is 7.
- The next number should be 14 + 7 = 21.
- The next number after 28 should be 28 + 7 = 35.
- The next number after 42 should be 42 + 7 = 49.

So, the completed sequence is:
```
0 7 14 21 28 35 42 49
```

---

Sequence 2:

```
0 _ 8 12 _ 20 _ _
```
- The difference between 0 and 8 is 8.
- The difference between 8 and 12 is 4.
- The difference between 12 and 20 is 8.

The pattern alternates between adding 8 and adding 4. So:
- The number before 8 should be 0 + 4 = 4.
- The number after 12 should be 12 + 8 = 20 (already given).
- The number after 20 should be 20 + 4 = 24.
- The number after 24 should be 24 + 8 = 32.

So, the completed sequence is:
```
0 4 8 12 20 24 32
```

---

Sequence 3:

```
8 _ 12 _ 16 18 _ _
```
- The difference between 8 and 12 is 4.
- The difference between 12 and 16 is 4.
- The difference between 16 and 18 is 2.

The pattern seems to alternate between adding 4 and adding 2. So:
- The number after 8 should be 8 + 4 = 12 (already given).
- The number after 12 should be 12 + 4 = 16 (already given).
- The number after 18 should be 18 + 4 = 22.
- The number after 22 should be 22 + 2 = 24.

So, the completed sequence is:
```
8 10 12 14 16 18 22 24
```

---

Sequence 4:

```
12 15 _ 21 _ _ 30 _
```
- The difference between 12 and 15 is 3.
- The difference between 15 and 21 is 6.
- The difference between 21 and 30 is 9.

The pattern increases by multiples of 3 (3, 6, 9, ...). So:
- The number after 15 should be 15 + 6 = 21 (already given).
- The number after 21 should be 21 + 9 = 30 (already given).
- The number after 30 should be 30 + 12 = 42.
- The number after 42 should be 42 + 15 = 57.

So, the completed sequence is:
```
12 15 18 21 24 27 30 42 57
```

---

Sequence 5:

```
0 _ 18 27 _ _ 54 _
```
- The difference between 0 and 18 is 18.
- The difference between 18 and 27 is 9.
- The difference between 27 and 54 is 27.

The pattern alternates between adding 18 and adding 9. So:
- The number after 0 should be 0 + 9 = 9.
- The number after 27 should be 27 + 18 = 45.
- The number after 45 should be 45 + 9 = 54 (already given).
- The number after 54 should be 54 + 18 = 72.

So, the completed sequence is:
```
0 9 18 27 45 54 72
```

---

Sequence 6:

```
_ 17 22 _ 32 _ 42 _
```
- The difference between 17 and 22 is 5.
- The difference between 22 and 32 is 10.
- The difference between 32 and 42 is 10.

The pattern alternates between adding 5 and adding 10. So:
- The number before 17 should be 17 - 5 = 12.
- The number after 22 should be 22 + 5 = 27.
- The number after 32 should be 32 + 10 = 42 (already given).
- The number after 42 should be 42 + 5 = 47.

So, the completed sequence is:
```
12 17 22 27 32 42 47
```

---

Sequence 7:

```
_ 12 _ 24 _ 36 42 _
```
- The difference between 12 and 24 is 12.
- The difference between 24 and 36 is 12.
- The difference between 36 and 42 is 6.

The pattern alternates between adding 12 and adding 6. So:
- The number before 12 should be 12 - 6 = 6.
- The number after 12 should be 12 + 6 = 18.
- The number after 24 should be 24 + 6 = 30.
- The number after 42 should be 42 + 12 = 54.

So, the completed sequence is:
```
6 12 18 24 30 36 42 54
```

---

Sequence 8:

```
19 _ 23 _ 27 29 _ _
```
- The difference between 19 and 23 is 4.
- The difference between 23 and 27 is 4.
- The difference between 27 and 29 is 2.

The pattern alternates between adding 4 and adding 2. So:
- The number after 19 should be 19 + 2 = 21.
- The number after 23 should be 23 + 4 = 27 (already given).
- The number after 29 should be 29 + 4 = 33.
- The number after 33 should be 33 + 2 = 35.

So, the completed sequence is:
```
19 21 23 25 27 29 33 35
```

---

Sequence 9:

```
_ 24 32 _ 48 _ 64 _
```
- The difference between 24 and 32 is 8.
- The difference between 32 and 48 is 16.
- The difference between 48 and 64 is 16.

The pattern alternates between adding 8 and adding 16. So:
- The number before 24 should be 24 - 8 = 16.
- The number after 32 should be 32 + 8 = 40.
- The number after 48 should be 48 + 16 = 64 (already given).
- The number after 64 should be 64 + 8 = 72.

So, the completed sequence is:
```
16 24 32 40 48 64 72
```

---

Sequence 10:

```
17 _ _ 20 21 _ _ 24
```
- The difference between 20 and 21 is 1.
- The difference between 21 and 24 is 3.

The pattern alternates between adding 1 and adding 3. So:
- The number after 17 should be 17 + 3 = 20.
- The number after 20 should be 20 + 1 = 21 (already given).
- The number after 21 should be 21 + 3 = 24 (already given).

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

---

Final Answer:

```
1) 0 7 14 21 28 35 42 49
2) 0 4 8 12 20 24 32
3) 8 10 12 14 16 18 22 24
4) 12 15 18 21 24 27 30 42 57
5) 0 9 18 27 45 54 72
6) 12 17 22 27 32 42 47
7) 6 12 18 24 30 36 42 54
8) 19 21 23 25 27 29 33 35
9) 16 24 32 40 48 64 72
10) 17 20 21 20 21 24 25 24
```

\boxed{
\begin{array}{cccccccc}
1) & 0 & 7 & 14 & 21 & 28 & 35 & 42 & 49 \\
2) & 0 & 4 & 8 & 12 & 20 & 24 & 32 \\
3) & 8 & 10 & 12 & 14 & 16 & 18 & 22 & 24 \\
4) & 12 & 15 & 18 & 21 & 24 & 27 & 30 & 42 & 57 \\
5) & 0 & 9 & 18 & 27 & 45 & 54 & 72 \\
6) & 12 & 17 & 22 & 27 & 32 & 42 & 47 \\
7) & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 54 \\
8) & 19 & 21 & 23 & 25 & 27 & 29 & 33 & 35 \\
9) & 16 & 24 & 32 & 40 & 48 & 64 & 72 \\
10) & 17 & 20 & 21 & 20 & 21 & 24 & 25 & 24 \\
\end{array}
}