# 6.14: Growing Patterns

**At Grade**Created by: CK-12

**Growing Patterns - Patterns and Functions**

**Teacher Notes**

Growing Patterns require students to analyze the first 3 or 4 figures of a pattern, identify relationships between the pattern number and the number of items, describe the \begin{align*}10^{th}\end{align*} figure, and write the rule that relates the pattern number and the number of items. Encourage students to make a table to organize their data. The table will help them to observe the relationship and write the rule.

Solutions

1. 12 circles in Figure 10.

Rule: Number of circles is 2 more than the Figure Number.

2. 14 tiles in Figure 10.

Rule: Number of Tiles is 4 more than the Figure Number.

3. 11 circles in Figure 10.

Rule: Number of Circles is 1 more than the Figure Number.

4. 13 trapezoids in Figure 10.

Rule: Number of Trapezoids is 3 more than the Figure Number.

5. 20 circles in Figure 10.

Rule: Number of Circles is the Figure Number plus the Figure Number, or 2 times the Figure Number.

6. 30 purple tiles in Figure 10.

Rule: Number of Purple Tiles is 3 times the Figure Number.

7. 20 checkered tiles in Figure 10.

Rule: Number of Checkered Tiles is 2 times the Figure Number.

8. 50 tiles in Figure 10.

Rule: Number of Square Tiles is 5 times the Figure Number.

9. The perimeter of Figure 10 is 30 units.

Rule: Perimeter in Number of Units is 3 times the Figure Number.

10. The perimeter of Figure 10 is 40 units.

Rule: Perimeter in Number of Units is 4 times the Figure Number.

\begin{align*}& \mathbf{Describe:} && \text{Each figure is made of square tiles.}\\ &&& \text{Figure} \ 1 \ \text{has} \ 8 \ \text{tiles.}\\ &&& \text{Figure} \ 2 \ \text{has} \ 9 \ \text{tiles.}\\ &&& \text{Figure} \ 3 \ \text{has} \ 10 \ \text{tiles.}\\ &&& \text{The number of square tiles changes only on the left side of the figure.}\\ & \mathbf{My \ Job:} && \text{Determine the number of tiles in Figure} \ 10. \ \text{Write the rule.}\\ & \mathbf{Plan:} && \text{Collect information in a table. Look for the relationship between the Figure}\\ &&& \text{Number and the Number of Tiles}\\ & \mathbf{Solve:}\end{align*}

\begin{align*}{\;} \qquad \quad \mathbf{Check:}\!\\ {\;} \qquad \quad \quad \text{Figure} \ 1: \qquad 1 + 7 = 8 \ \text{tiles}\!\\ {\;} \qquad \quad \quad \text{Figure} \ 2: \qquad 2 + 7 = 9 \ \text{tiles}\!\\ {\;} \qquad \quad \quad \text{Figure} \ 3: \qquad 3 + 7 = 10 \ \text{tiles}\!\\ {\;} \qquad \quad \quad \text{Figure} \ 10: \quad \ 10 + 7 = 17 \ \text{tiles}\end{align*}

Rule: Number of Tiles is 7 more than the Figure Number.

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