Name__________________________

Rectangle Families

8^th Grade Open Response Question

THE PROBLEM

You work in a gift shop and have been asked, by your manager, to arrange a new shipment of picture frames into three different display groups, based on their shape. You find the 12 new frames are all rectangles with the following dimensions: (the first number is the width in inches and the second number is the height in inches) 6 X 10; 8 X 12; 4 X 6; 4 X 8; 3 X 5; 5 X 10; 2 X 3; 9 X 15; 3 X 6; 6 X 9; 1 X 2; 12 X 20.

a) Arrange the frames into three groups/families, each group containing rectangles of similar shape.

Family A Dimensions

Family B Dimensions

Family C Dimensions

b) Explain how you know that each group contains only similar rectangles.

c) On a separate sheet of grid paper, graph the dimensions of each frame/rectangle with the width recorded as the “x” variable and the height recorded as the “y” variable. Draw three lines, each containing one of the rectangle families.

d) Find the dimensions of an additional, similar frame size that would fit into each rectangle family. Explain your method.