This activity has students build patterns with square tiles. 

They will be asked to count the number of tiles in the first, second, and third pictures and predict the number of tiles in the fourth and fifth pictures.  Students will study how the pictures are changing and look to see if the chart is changing the same way.  The students will be asked to write arithmetic expressions to represent how the number of tiles for each picture can be found.  This will lead to students writing expressions for the 10th, 20th, 50th, and 100th pictures.  Students should then be able to write the expression for the nth picture. 

Students can then be challenged to re-look at other ways the patterns could be made.