Walking Around Shapes

Est. Class Sessions: 3

Look around the school for a large equilateral triangle, hexagon, or square. Measure one side, and ask students to predict the perimeter using the patterns they found in this activity. Then measure the shape to check their predictions.
Give students a side length (10 cm) and ask them to find the perimeter of a regular triangle, square, and regular hexagon.
Give students a perimeter (48 cm) and ask them to find the side length of a regular triangle, square, and regular hexagon.
Make a class graph with all three lines (triangle, hexagon, and square) on the same graph and label each line with the appropriate shape. Use large graph paper or a display.

Ask students to compare the lines as you pose the following questions:

How are the lines the same? (They all start at (0,0) and are straight.)
How are they different? (Some are steeper than others, and some slant more than others.)
Which is the steepest? (The hexagon's line.)
Which is the next steepest? (The square's line.)
Why is the line for the hexagons the steepest? Prompt as needed: Which shape had the most sides? (The hexagon has the most sides.)
Where do you think the line for octagons will appear on the graph? (It will be even steeper than the line for the hexagons.)
Where do you think the line for pentagons will appear on the graph? (It will be between the lines for squares and hexagons.)

Lesson 6