Matchstick Patterns Worksheets | Grade1to6.com - Free Printable

Problem: Matchstick Patterns

The task is to complete the table for each sequence of matchstick shapes and determine the function rule for finding the number of matchsticks needed for the shape in the 50th position. Let's solve each part step by step.

---

#### Part 1:
Shapes:
- The pattern shows a series of shapes that increase in size, with each new shape adding a consistent number of matchsticks.

Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 7 | 12 | 17 | 22 | 27 | ? | ? | ? | ? | ? |
| Function Rule | | | | | | | | | | |

Step 1: Identify the pattern.
- From the given numbers:
- Shape 1: 7 matchsticks
- Shape 2: 12 matchsticks
- Shape 3: 17 matchsticks
- Shape 4: 22 matchsticks
- Shape 5: 27 matchsticks

The difference between consecutive terms is:
\[
12 - 7 = 5, \quad 17 - 12 = 5, \quad 22 - 17 = 5, \quad 27 - 22 = 5
\]
This indicates a linear pattern where each new shape adds 5 matchsticks.

Step 2: Determine the function rule.
- The general form of a linear function is:
\[
\text{Number of Matchsticks} = an + b
\]
where \( n \) is the shape number, \( a \) is the common difference, and \( b \) is the initial value adjusted for the pattern.

- Here, \( a = 5 \) (the common difference).
- To find \( b \), use the first term:
\[
7 = 5(1) + b \implies b = 7 - 5 = 2
\]
So, the function rule is:
\[
\text{Number of Matchsticks} = 5n + 2
\]

Step 3: Fill in the missing values.
- For \( n = 6 \):
\[
5(6) + 2 = 30 + 2 = 32
\]
- For \( n = 7 \):
\[
5(7) + 2 = 35 + 2 = 37
\]
- For \( n = 8 \):
\[
5(8) + 2 = 40 + 2 = 42
\]
- For \( n = 9 \):
\[
5(9) + 2 = 45 + 2 = 47
\]
- For \( n = 50 \):
\[
5(50) + 2 = 250 + 2 = 252
\]

Completed Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 7 | 12 | 17 | 22 | 27 | 32 | 37 | 42 | 47 | 252 |
| Function Rule | | | | | | | | | | \( 5n + 2 \) |

---

#### Part 2:
Shapes:
- The pattern shows a series of shapes that increase in size, with each new shape adding a consistent number of matchsticks.

Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 6 | 9 | 12 | 15 | 18 | ? | ? | ? | ? | ? |
| Function Rule | | | | | | | | | | |

Step 1: Identify the pattern.
- From the given numbers:
- Shape 1: 6 matchsticks
- Shape 2: 9 matchsticks
- Shape 3: 12 matchsticks
- Shape 4: 15 matchsticks
- Shape 5: 18 matchsticks

The difference between consecutive terms is:
\[
9 - 6 = 3, \quad 12 - 9 = 3, \quad 15 - 12 = 3, \quad 18 - 15 = 3
\]
This indicates a linear pattern where each new shape adds 3 matchsticks.

Step 2: Determine the function rule.
- The general form of a linear function is:
\[
\text{Number of Matchsticks} = an + b
\]
where \( n \) is the shape number, \( a \) is the common difference, and \( b \) is the initial value adjusted for the pattern.

- Here, \( a = 3 \) (the common difference).
- To find \( b \), use the first term:
\[
6 = 3(1) + b \implies b = 6 - 3 = 3
\]
So, the function rule is:
\[
\text{Number of Matchsticks} = 3n + 3
\]

Step 3: Fill in the missing values.
- For \( n = 6 \):
\[
3(6) + 3 = 18 + 3 = 21
\]
- For \( n = 7 \):
\[
3(7) + 3 = 21 + 3 = 24
\]
- For \( n = 8 \):
\[
3(8) + 3 = 24 + 3 = 27
\]
- For \( n = 9 \):
\[
3(9) + 3 = 27 + 3 = 30
\]
- For \( n = 50 \):
\[
3(50) + 3 = 150 + 3 = 153
\]

Completed Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 153 |
| Function Rule | | | | | | | | | | \( 3n + 3 \) |

---

#### Part 3:
Shapes:
- The pattern shows a series of shapes that increase in size, with each new shape adding a consistent number of matchsticks.

Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 5 | 8 | 11 | 14 | 17 | ? | ? | ? | ? | ? |
| Function Rule | | | | | | | | | | |

Step 1: Identify the pattern.
- From the given numbers:
- Shape 1: 5 matchsticks
- Shape 2: 8 matchsticks
- Shape 3: 11 matchsticks
- Shape 4: 14 matchsticks
- Shape 5: 17 matchsticks

The difference between consecutive terms is:
\[
8 - 5 = 3, \quad 11 - 8 = 3, \quad 14 - 11 = 3, \quad 17 - 14 = 3
\]
This indicates a linear pattern where each new shape adds 3 matchsticks.

Step 2: Determine the function rule.
- The general form of a linear function is:
\[
\text{Number of Matchsticks} = an + b
\]
where \( n \) is the shape number, \( a \) is the common difference, and \( b \) is the initial value adjusted for the pattern.

- Here, \( a = 3 \) (the common difference).
- To find \( b \), use the first term:
\[
5 = 3(1) + b \implies b = 5 - 3 = 2
\]
So, the function rule is:
\[
\text{Number of Matchsticks} = 3n + 2
\]

Step 3: Fill in the missing values.
- For \( n = 6 \):
\[
3(6) + 2 = 18 + 2 = 20
\]
- For \( n = 7 \):
\[
3(7) + 2 = 21 + 2 = 23
\]
- For \( n = 8 \):
\[
3(8) + 2 = 24 + 2 = 26
\]
- For \( n = 9 \):
\[
3(9) + 2 = 27 + 2 = 29
\]
- For \( n = 50 \):
\[
3(50) + 2 = 150 + 2 = 152
\]

Completed Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 5 | 8 | 11 | 14 | 17 | 20 | 23 | 26 | 29 | 152 |
| Function Rule | | | | | | | | | | \( 3n + 2 \) |

---

#### Part 4:
Shapes:
- The pattern shows a series of shapes that increase in size, with each new shape adding a consistent number of matchsticks.

Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 6 | 10 | 14 | 18 | 22 | ? | ? | ? | ? | ? |
| Function Rule | | | | | | | | | | |

Step 1: Identify the pattern.
- From the given numbers:
- Shape 1: 6 matchsticks
- Shape 2: 10 matchsticks
- Shape 3: 14 matchsticks
- Shape 4: 18 matchsticks
- Shape 5: 22 matchsticks

The difference between consecutive terms is:
\[
10 - 6 = 4, \quad 14 - 10 = 4, \quad 18 - 14 = 4, \quad 22 - 18 = 4
\]
This indicates a linear pattern where each new shape adds 4 matchsticks.

Step 2: Determine the function rule.
- The general form of a linear function is:
\[
\text{Number of Matchsticks} = an + b
\]
where \( n \) is the shape number, \( a \) is the common difference, and \( b \) is the initial value adjusted for the pattern.

- Here, \( a = 4 \) (the common difference).
- To find \( b \), use the first term:
\[
6 = 4(1) + b \implies b = 6 - 4 = 2
\]
So, the function rule is:
\[
\text{Number of Matchsticks} = 4n + 2
\]

Step 3: Fill in the missing values.
- For \( n = 6 \):
\[
4(6) + 2 = 24 + 2 = 26
\]
- For \( n = 7 \):
\[
4(7) + 2 = 28 + 2 = 30
\]
- For \( n = 8 \):
\[
4(8) + 2 = 32 + 2 = 34
\]
- For \( n = 9 \):
\[
4(9) + 2 = 36 + 2 = 38
\]
- For \( n = 50 \):
\[
4(50) + 2 = 200 + 2 = 202
\]

Completed Table:
| Shapes Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 50 |
|---------------|---|---|---|---|---|---|---|---|---|----|
| Number of Matchsticks | 6 | 10 | 14 | 18 | 22 | 26 | 30 | 34 | 38 | 202 |
| Function Rule | | | | | | | | | | \( 4n + 2 \) |

---

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{Part 1: } 5n + 2 \\
\text{Part 2: } 3n + 3 \\
\text{Part 3: } 3n + 2 \\
\text{Part 4: } 4n + 2 \\
\end{array}
}
\]