This is a good activity for your students to explore what happens to perimeters of shapes made from squares that have been cut apart and then pieced together in a different way.
- White index cards for each student.
- Chart paper for each group.
- Graph paper for each student.
- Scissors, glue, tape, rulers.
- 5cm x 5cm index card.
- Hold a 5cm x 5cm square up and over the grid paper.
- The area of this square is 25 square centimeters.
- How did I figure that out? A different way to find the area? What is the area formula for a square? L x W or L2.
- How long is the distance around the square? What is the perimeter formula for a square? 4 x L or 2 x (L + W).
- How can I cut this square in 2 or more pieces?
- Some of the ways you could cut the card are in the picture below. Select one of the ways to cut the card.
Students work in groups to complete the activity. Below are the steps your students will need to follow.
1. At the top of the chart paper write the names of the members of your group, the date and the heading ‘The Area Stays the Same’.
2. Each person in the group cut a 5cm by 5cm square from your white index card.
3. Cut your square into two or more pieces and put the pieces together to create a new shape. You cannot place one piece partially or completely over another. Each piece must touch the edge of another piece. Edges (not corners) must touch.
4. Work out the length of the perimeter of your new shape.
5. Display your group’s shapes on the chart paper. Draw a straight line underneath each shape equal to the length of its perimeter.
6. Discuss and write down (on the chart paper) what you notice.
7. As a group, repeat with another additional square. This time predict the length of the perimeter before you measure it.
Have students share their charts and report on what they found. Ask them how a square could be cut to get a really long perimeter.
Graphic Credits: Graphics From the Pond