Counting on in 100s worksheet with number sequences and a grid for practice.

Problem Description:

The task involves completing sequences of numbers by counting on in increments of 100. The goal is to fill in the missing numbers in each sequence and observe any patterns.

Solution:

#### Part 1: Completing the Sequences
We need to fill in the missing numbers in each sequence by adding or subtracting 100 as needed.

---

#### Sequence (a):
```
100, 200, 300, ____, 500, ____
```
- The pattern is increasing by 100.
- Missing number after 300: \( 300 + 100 = 400 \)
- Missing number after 500: \( 500 + 100 = 600 \)

Completed Sequence (a):
```
100, 200, 300, 400, 500, 600
```

---

#### Sequence (b):
```
700, 600, ____, 400, ____, 200
```
- The pattern is decreasing by 100.
- Missing number after 600: \( 600 - 100 = 500 \)
- Missing number after 400: \( 400 - 100 = 300 \)

Completed Sequence (b):
```
700, 600, 500, 400, 300, 200
```

---

#### Sequence (c):
```
____, 900, 1000, ____, 1300
```
- The pattern is increasing by 100.
- Missing number before 900: \( 900 - 100 = 800 \)
- Missing number after 1000: \( 1000 + 100 = 1100 \)

Completed Sequence (c):
```
800, 900, 1000, 1100, 1300
```

---

#### Sequence (d):
```
1100, ____, ____, 800, 700, 600
```
- The pattern is decreasing by 100.
- Missing number after 1100: \( 1100 - 100 = 1000 \)
- Missing number after 1000: \( 1000 - 100 = 900 \)

Completed Sequence (d):
```
1100, 1000, 900, 800, 700, 600
```

---

#### Sequence (e):
```
900, ____, 1100, 1200, ____, 1400
```
- The pattern is increasing by 100.
- Missing number after 900: \( 900 + 100 = 1000 \)
- Missing number after 1200: \( 1200 + 100 = 1300 \)

Completed Sequence (e):
```
900, 1000, 1100, 1200, 1300, 1400
```

---

#### Sequence (f):
```
____, 1400, 1300, ____, 1100, 1000
```
- The pattern is decreasing by 100.
- Missing number before 1400: \( 1400 + 100 = 1500 \)
- Missing number after 1300: \( 1300 - 100 = 1200 \)

Completed Sequence (f):
```
1500, 1400, 1300, 1200, 1100, 1000
```

---

#### Sequence (g):
```
800, 900, 1100, ____, 1300
```
- The pattern is increasing by 100.
- Missing number after 1100: \( 1100 + 100 = 1200 \)

Completed Sequence (g):
```
800, 900, 1100, 1200, 1300
```

---

#### Sequence (h):
```
1900, ____, 2200
```
- The pattern is increasing by 100.
- Missing number after 1900: \( 1900 + 100 = 2000 \)

Completed Sequence (h):
```
1900, 2000, 2200
```

---

#### Sequence (i):
```
____, 3100, 3200, 3300, 3400
```
- The pattern is increasing by 100.
- Missing number before 3100: \( 3100 - 100 = 3000 \)

Completed Sequence (i):
```
3000, 3100, 3200, 3300, 3400
```

---

Final Answer:

```
(a) 100, 200, 300, 400, 500, 600
(b) 700, 600, 500, 400, 300, 200
(c) 800, 900, 1000, 1100, 1300
(d) 1100, 1000, 900, 800, 700, 600
(e) 900, 1000, 1100, 1200, 1300, 1400
(f) 1500, 1400, 1300, 1200, 1100, 1000
(g) 800, 900, 1100, 1200, 1300
(h) 1900, 2000, 2200
(i) 3000, 3100, 3200, 3300, 3400
```

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
(a) \, 100, 200, 300, 400, 500, 600 \\
(b) \, 700, 600, 500, 400, 300, 200 \\
(c) \, 800, 900, 1000, 1100, 1300 \\
(d) \, 1100, 1000, 900, 800, 700, 600 \\
(e) \, 900, 1000, 1100, 1200, 1300, 1400 \\
(f) \, 1500, 1400, 1300, 1200, 1100, 1000 \\
(g) \, 800, 900, 1100, 1200, 1300 \\
(h) \, 1900, 2000, 2200 \\
(i) \, 3000, 3100, 3200, 3300, 3400 \\
\end{array}
}
\]