Thursday Tool School: Measurement Tools- Area and Perimeter with Pentominoes

26 Shares

This month, Thursday Tool School will feature measurement activities. The first activity is one of my favorites and features the use of pentominoes– five square unit two-dimensional shapes. See the image to the right for a picture of the set. Pentominoes can be used in many ways, including how they all fit together to make one large rectangle. Give that one a try! Today’s activity reinforces area and perimeter concepts.

Specifically, this activity addresses the following Common Core State Standard for Mathematics:

3.MD.D.8- Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Pentominoes can be purchased at any of the major math manipulative suppliers; however, there is a link to a free reproducible set below. Looking for a real challenge? Have your students find all of the shapes that can be created using 5 square units– there are 12 of them.

Once students have a set of pentominoes from which to work, have them complete the activity below.

Freebie Alert! Click here for a free printable of this activity.

For part I, students find the perimeter of each pentomino. They are each identified by the letter their shape resembles. After students find the perimeter of each pentomino, students analyze the shapes to answer questions about their perimeters and then compare the perimeters to the fixed area.

For part II, students create a new shape by putting two shapes together. The goal is to create a new figure with the smallest possible perimeter and the largest possible perimeter. Again, students can compare how the perimeters compare to the fixed area– what attributes does the shape with the larger perimeter have that the smaller perimeter does not?

The objective for both parts is to provide students with some experiences comparing the perimeter of shapes that have the same area. Students can then begin to make conjectures about what attributes shapes with smaller perimeters have when compared to shapes with larger perimeters.