 # Perimeter Challenge

#### Curriculum Goals

Overall expectation:

Determine the relationships among units and measurable attributes, including the area and perimeter of rectangles.

Specific expectations:

• Determine, through investigation, the relationship between the side lengths of a rectangle and its perimeter and area
• Determine the relationships among units and measurable attributes, including the area and perimeter of rectangles Context

• Students have previously measured shapes, and determined the perimeter of shapes
• Full class lesson, moving to partner work

Materials

• Math Tiles
• Graph Paper
• Pencils
• Smartboard/Whiteboard

Summary

An exploratory lesson related to perimeter.

Lesson

1. Have the students review how to find the perimeter of a shape.
2. Explain to the students that today we will be learning to find the perimeter of shapes that are made up of units. For these shapes, we aren’t using centimetres or metres like we are used to.
3. Present the students a shape such as the one below. Ask students how we could we find the perimeter of this shape?  Explain to the students that we can count the outside edges of this shape by looking at the units. Explain that some of the units we may count two sides to find the perimeter. In this case, the perimeter would be P= 14 units. 4. Explain to the students that this concept of units is important because we will be working on a fun math challenge where you will need to find the perimeter of shapes using units.

Activity

1. For this activity, students will work with a partner. Each partner pairing will have 24 math tiles.
2. Students will make as many different shapes as they can. The challenge is that each shape has to have a different perimeter. If you have already found a shape with this perimeter, then the shape doesn’t count towards the challenge. Students will need to reconfigure it so that it has a different perimeter that students haven’t found yet in their pairing.
3. Once a shape has been found that has a new perimeter, it will be recorded on the groups graph paper, with the corresponding perimeter that was found.
4. Each shape has to use all 24 tiles.
5. Units connect edge to edge.

Questions to Extend Student Thinking

1. Was it difficult finding shapes that had different perimeters?
2. If you found a shape with the same perimeter that you had already found, how did you make it so that it had a new perimeter?
3. Does anyone have examples of shapes that looked very different, but had similar perimeters?
4. Consider the area of the shapes. What was the area? Did it change? Why?
5. How many different perimeters can we find?
6. While using all 24 tiles, what is the biggest perimeter was can find? What is the smallest perimeter we can find?
7. Once they discover the biggest perimeter possible, how many different ways can this perimeter be made?
8. What would happen if we increased the challenge, and allowed for shapes to connect at the vertices and not edge to edge?

Assessing the Learning

• Are students properly determining the perimeter of the shape? Are they forgetting to count sides?
• Are students coming up with strategies for the challenge?
• What do students discover during the activity?