a) Draw the next two figures in the tile pattern.
b) Write a pattern rule using an algebraic expression for the
number of tiles in any figure.
c) Identify the constant term and the numerical coefficient in
d) What do the constant term and the numerical coefficient
tell you about how the pattern grows?
Each of the following figures that you draw would have one more column of 4 tiles to the left.
So, the fourth diagram would have 3 columns of 4 tiles (on the left) and the one tile on the bottom right.
The fifth diagram would have 4 columns of 4 tiles (on the left) and the one tile on the bottom right.
Tiles = 4n + 1 (where n is the number of columns of four tiles)
or: Tiles = 4(n - 1) + 1 (where n represents which picture you are looking at)
The constant term is 1 and the numerical coefficient is 4.
The constant term tells you how many tiles that you originally started with.
The numerical coefficient tells you how many more tiles you get as you go from picture to picture.