### Student Page 2.9.2 Analyzing Tile Patterns

Use tiles to model each pattern. Use color to show how each pattern grows. For example, choose a color for tiles that are new in Step 2 when compared to Step 1. Use the Step 2 color to show where these same tiles appear in all subsequent steps. Find a way to count each pattern of tiles so that the relationship between the number of tiles and the step number is evident.

Work on Pattern A. When you're done, share the different ways you colored the pattern with your group and when asked to do so, with the class. Use that information to draw Steps 0 and 4 and to find the equation.

Continue working on Patterns B through F.

When the class has finished work on Analyzing Tile Patterns, as a group, claim one pattern. You will share your coloring of the pattern and equation with the class.

Once all patterns are posted, study each group's work. Determine if you agree or disagree and why. When reporting, group members who did not put the pattern on the board will explain the work presented.

Study the visual patterns in Figure 2.9.2.1. Assume each pattern continues infinitely and grows predictably. Determine the following for each pattern:

#### 1.

How is the pattern growing? Use colors or numbers to show how tiles are added to the pattern from one step to the next. Show how the pattern builds from one step to the next.

#### 2.

Draw Step 4. Draw Step 0.

#### 3.

For each step, determine the number of tiles needed.

#### 4.

Determine if the pattern is proportional linear, linear, or other. Explain your decision.

#### 5.

For each linear and proportional linear pattern, find an equation that gives the number of tiles in a step based on its step number.

#### 6.

For linear and proportional linear patterns, determine what part of the pattern relates to the slope. Determine what part of the pattern relates to the \(y\)-intercept. Explain both.