TILE PATTERN TEAM CHALLENGE

Your teacher will assign your team a tile pattern (one of the patterns labeled (a) through (e) on the next page).  Your team’s task is to create a poster showing every way you can represent your pattern and highlighting all of the connections between the representations that you can find.  For this activity, finding and showing the connections are the most important parts.  Clearly presenting the connections between representations on your poster will help you convince your classmates that your description of the pattern makes sense.  

Pattern Analysis:

• Extend the pattern: Draw Figures $0$, $4$, and $5$.  Then describe Figure $100$.  Give as much information as you can.  What will it look like?  How will the tiles be arranged?  How many tiles will it have?

• Generalize the pattern by writing a rule that will give the number of tiles in any figure in the pattern.  Show how you got your answer.

• Find the number of tiles in each figure.  Record your data in a table and on a graph.

• Demonstrate how the pattern grows using color, arrows, labels, and other math tools to help you show and explain.  Show growth in each representation.

• What connections do you see between the different representations (graph, figures, and $x→y$ table)?  How can you show these connections?

Presenting the Connections:

As a team, organize your work into a large poster that clearly shows each representation of your pattern, as well as a description of Figure $100$.  When your team presents your poster to the class, you will need to support each statement with a reason from your observations.  Each team member must explain something mathematical as part of your presentation.

1. Tile
   	Tile	Tile	Tile
   	Tile	Tile	Tile
   	Tile	Tile	Tile
   	Tile	Tile

   Figure 1

   Tile
   	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile

   Figure 2

   Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile

   Figure 3

2. 	Tile	Tile	Tile
   Tile	Tile
   Tile	Tile
   Tile	Tile	Tile	Tile

   Figure 1

   	Tile	Tile	Tile	Tile
   Tile	Tile	Tile
   Tile	Tile	Tile
   Tile	Tile	Tile
   Tile	Tile	Tile	Tile	Tile

   Figure 2

   	Tile	Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile	Tile	Tile

   Figure 3

3. Tile	Tile	Tile
   Tile	Tile
   Tile	Tile
   Tile
   Tile

   Figure 1

   Tile	Tile	Tile	Tile	Tile
   Tile	Tile	Tile
   Tile	Tile	Tile
   Tile	Tile	Tile
   Tile
   Tile

   Figure 2

   Tile	Tile	Tile	Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile	Tile	Tile	Tile
   Tile
   Tile

   Figure 3

4. 	Tile
   	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile
   Tile

   Figure 1

   	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile
   Tile

   Figure 2

   	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile	Tile
   	Tile	Tile	Tile	Tile	Tile	Tile
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   Tile

   Figure 3

5. 		Tile
   Tile	Tile	Tile	Tile	Tile	Tile
   		Tile	Tile

   Figure 1

   			Tile
   Tile	Tile	Tile	Tile	Tile	Tile	Tile	Tile	Tile
   			Tile	Tile	Tile
   			Tile	Tile	Tile

   Figure 2

   				Tile
   Tile	Tile	Tile	Tile	Tile	Tile	Tile	Tile	Tile	Tile	Tile	Tile
   				Tile	Tile	Tile	Tile
   				Tile	Tile	Tile	Tile
   				Tile	Tile	Tile	Tile

   Figure 3