With your team, discuss which shapes have the same side lengths and which ones have different side lengths. Be prepared to share your ideas with the class. On your traced drawings, color-code lengths that are the same. Each type of tile is named for its area. In this course, the smallest square will have a side length of 1 unit, so its area is 1 square unit. This tile will be called “one” or the “unit tile.” Can you use the unit tile to find the side lengths of the other rectangles? Why or why not?

If the side lengths of a tile can be measured exactly, then the area of the tile can be calculated by multiplying these two lengths together. The area is measured in square units. For example, the tile at right measures 1 unit by 5 units, so it has an area of 5 square units.

The next tile at right has one side length that is exactly one unit long. If the other side length cannot have a numerical value, what can it be called?

A rectangle divided into 5 squares, labeled 1 on the short edge.

A rectangle, labeled 1 on the short edge and question mark on the long edge.

If the unknown length is called “r,” label the side lengths of each of the four algebra tiles you traced. Find each area and use it to name each tile. Be sure to include the name of the type of units it represents.