# 6.14: Growing Patterns

**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 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.

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