5th Grade Patterns Worksheets - Free Printable

Problem Analysis:

The task involves identifying patterns in sequences of numbers and completing the missing values. The worksheet is divided into two sections:

1. Column and pattern (Rows 1–6): Here, we need to identify the rule or pattern for each sequence and fill in the missing values.
2. Input and output (Rows 7–12): Here, we need to determine the relationship between the input and output values and use it to complete the missing outputs.

Let's solve each section step by step.

---

Section 1: Column and Pattern (Rows 1–6)

#### Row 1:
- Sequence: `0, 10, 20, __, __`
- Pattern: Each number increases by 10.
- Missing values: `30, 40`
- Completed sequence: `0, 10, 20, 30, 40`

#### Row 2:
- Sequence: `0, 8, __, __, __`
- Pattern: Each number increases by 8.
- Missing values: `16, 24, 32`
- Completed sequence: `0, 8, 16, 24, 32`

#### Row 3:
- Sequence: `0, 5, __, __, __`
- Pattern: Each number increases by 5.
- Missing values: `10, 15, 20`
- Completed sequence: `0, 5, 10, 15, 20`

#### Row 4:
- Sequence: `0, 4, __, __, __`
- Pattern: Each number increases by 4.
- Missing values: `8, 12, 16`
- Completed sequence: `0, 4, 8, 12, 16`

#### Row 5:
- Sequence: `0, 3, __, __, __`
- Pattern: Each number increases by 3.
- Missing values: `6, 9, 12`
- Completed sequence: `0, 3, 6, 9, 12`

#### Row 6:
- Sequence: `0, 2, __, __, __`
- Pattern: Each number increases by 2.
- Missing values: `4, 6, 8`
- Completed sequence: `0, 2, 4, 6, 8`

---

Section 2: Input and Output (Rows 7–12)

#### Row 7:
- Input: `0, 1, 2, 3, 4`
- Output: `0, 10, 20, __, __`
- Pattern: Each output is 10 times the input.
- Missing values: `30, 40`
- Completed output: `0, 10, 20, 30, 40`

#### Row 8:
- Input: `0, 1, 2, 3, 4`
- Output: `0, 8, __, __, __`
- Pattern: Each output is 8 times the input.
- Missing values: `16, 24, 32`
- Completed output: `0, 8, 16, 24, 32`

#### Row 9:
- Input: `0, 1, 2, 3, 4`
- Output: `0, 5, __, __, __`
- Pattern: Each output is 5 times the input.
- Missing values: `10, 15, 20`
- Completed output: `0, 5, 10, 15, 20`

#### Row 10:
- Input: `0, 1, 2, 3, 4`
- Output: `0, 4, __, __, __`
- Pattern: Each output is 4 times the input.
- Missing values: `8, 12, 16`
- Completed output: `0, 4, 8, 12, 16`

#### Row 11:
- Input: `0, 1, 2, 3, 4`
- Output: `0, 3, __, __, __`
- Pattern: Each output is 3 times the input.
- Missing values: `6, 9, 12`
- Completed output: `0, 3, 6, 9, 12`

#### Row 12:
- Input: `0, 1, 2, 3, 4`
- Output: `0, 2, __, __, __`
- Pattern: Each output is 2 times the input.
- Missing values: `4, 6, 8`
- Completed output: `0, 2, 4, 6, 8`

---

Final Answer:

For Section 1 (Column and Pattern):
1. `0, 10, 20, 30, 40`
2. `0, 8, 16, 24, 32`
3. `0, 5, 10, 15, 20`
4. `0, 4, 8, 12, 16`
5. `0, 3, 6, 9, 12`
6. `0, 2, 4, 6, 8`

For Section 2 (Input and Output):
7. `0, 10, 20, 30, 40`
8. `0, 8, 16, 24, 32`
9. `0, 5, 10, 15, 20`
10. `0, 4, 8, 12, 16`
11. `0, 3, 6, 9, 12`
12. `0, 2, 4, 6, 8`

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Section 1:} \\
1. \, 0, 10, 20, 30, 40 \\
2. \, 0, 8, 16, 24, 32 \\
3. \, 0, 5, 10, 15, 20 \\
4. \, 0, 4, 8, 12, 16 \\
5. \, 0, 3, 6, 9, 12 \\
6. \, 0, 2, 4, 6, 8 \\
\\
\text{Section 2:} \\
7. \, 0, 10, 20, 30, 40 \\
8. \, 0, 8, 16, 24, 32 \\
9. \, 0, 5, 10, 15, 20 \\
10. \, 0, 4, 8, 12, 16 \\
11. \, 0, 3, 6, 9, 12 \\
12. \, 0, 2, 4, 6, 8 \\
\end{array}
}
\]