1. 2-1. TILE PATTERN INVESTIGATION
Complete the following tasks for Pattern A, recording your work on the resource page.
What do you notice about Pattern A?
Sketch the next figure in the sequence (Figure 4) for Pattern A on your resource page. Sketch Figure 0.  
By how much is Pattern A growing?  Where are the tiles being added with each new figure?  Color in the new tiles in each figure.  
What would Figure 100 look like for Pattern A?  Describe it in words.  How many tiles would be in the 100th figure? 
Assume the starting value of any tile pattern is the number of tiles in Figure 0.  Assume the growth is the number of tiles that are added from one figure to the next.  What are the growth and starting value for Pattern A?  
Write an equation that relates the figure number, x, to the number of tiles, y.
Figure 4 has 16 tiles; Figure 0 has 4 horizontal tiles.
Grows by adding 3 tiles. One tile is being stacked on the left, and two tiles are being stacked on the right.
The left tower has 100 tiles, the right tower has 200 tiles, and there are 4 horizontal tiles between the towers. Figure 100 has 304 tiles. 
starting value = 4, growth = 3
y = 3x + 4

2. Speak with appropriate language, tone and volume.

3. 2.1.1 Seeing Growth in Linear Functions
September 9, 2018
HW: 2-6 through 2-10

4. Objectives
CO: SWBAT write linear equations relating the figure number of a geometric pattern and its number of tiles.
LO: SWBAT discuss about patterns with their teammates.

5. 2-2. Complete all of 2-1 for Pattern B.
What do you notice about Pattern B?
Sketch the next figure in the sequence (Figure 4) for Pattern A on your resource page. Sketch Figure 0.  
By how much is Pattern A growing?  Where are the tiles being added with each new figure?  Color in the new tiles in each figure.  
What would Figure 100 look like for Pattern A?  Describe it in words.  How many tiles would be in the 100th figure? 
Assume the starting value of any tile pattern is the number of tiles in Figure 0.  Assume the growth is the number of tiles that are added from one figure to the next.  What are the growth and starting value for Pattern A?  
Write an equation that relates the figure number, x, to the number of tiles, y.
Figure 4 has 11 tiles. Figure 0 has 3 tiles.  
Grows by adding 2 tiles.
Figure 100 has 203 tiles.
starting value = 3, growth = 2
y = 2x + 3

6. Copy and fill in the table for Pattern C.
2-3. The growth of Pattern C is represented by the equation y = 3x + 1.
Copy and fill in the table for Pattern C.
By how many tiles is each figure in Pattern C growing?  What is the starting value?     
How can you use the table to determine the growth and starting value?    
Where do you look in the equation to see the growth and starting value?
Growth: 3 Starting Value: 1
Look for the zero term (starting value) & see how much is being added as the figure goes up by 1
Growth is in front of the x (multiplication)
Starting value is added on

7. 2-5. Now consider Pattern D.
Draw Figures 0 and 4 for this pattern on the resource page.  
Write an equation for the number of tiles in this pattern.  Use color to show where the numbers in your equation appear in the tile pattern.  Use x for the figure number and y for the number of tiles in the figure.
Make a table for the equation you wrote in part (b).  Does the information in your table match the figures in the tile pattern?
What is the same about this pattern and Pattern C?  What is different?  What would those similarities and differences look like in a tile pattern?   
What do the similarities and differences in part (d) look like in the equations?   
What do the similarities and differences look like in the table? 
Figure 0 has 1 tile, and Figure 4 has 17 tiles.
y = 4x + 1
Both patterns would have 1 tile in Figure 0.  Pattern C grows by adding 3, while Pattern D grows by 4.
The similarities can be seen at the “+1” in both equations; the differences can be seen at the coefficient of x in the equations.
The similarities can be seen at Figure 0 in the table; the differences can be seen by the increase in number of tiles from figure to figure in the table.
Figure # 1 2 3 4 5
Tiles 9 13 17