Dominoes

There are two ways to fill a 2x2 rectangle using 1x2 dominoes:

There are three ways to fill a 2x3 rectangle using 1x2 dominoes:

How many ways are there to fill ...

a 2x4 rectangle _______________

 

a 2x5 rectangle _______________

 

a 2x6 rectangle _______________

 

a 2x7 rectangle _______________

On a sheet of graph paper, draw each of these ways to fill a rectangle using dominoes.

Is there a pattern to these numbers? Use this pattern to predict how many ways there are to fill …

a 2x 8 rectangle _______________

 

a 2x 9 rectangle _______________

 

a 2x10 rectangle _______________

What is this pattern of numbers called?

As the number of patterns increases it becomes much more difficult to be sure you have every possible pattern without using any pattern twice. Describe a strategy for creating these patterns in an orderly way that will insure that you get every possible one.