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Tom Scavo's

Rectangles

Contents || Math Lessons

[Materials] [Length] [Area] [Pick's Theorem] [Dot Paper] [Epilogue]

[Lines] [Squares] [Rectangles] [Parallelograms] [Right Triangles] [Bibliography]

## Find all rectangles

### Objectives

• to continue developing a sense of area on the geoboard
• to realize that all squares are rectangles
• to experiment with geometric pattern making

### Materials

• 5 x 5 geoboards (the kind that fit together to make a 10 x 10 geoboard) and rubber bands (various sizes and colors)
• at least five geoboards for the teacher and one for each student
• 5 x 5 geoboard dot paper (two sheets for each student)
• 10 x 10 geoboard dot paper (for extended activities)
• overhead projector; transparent geoboard or dot paper (with marking pens)

### Warm-up activities

1. Make a rectangle on your geoboard. What is its area?
2. How many rectangles are there with base 1 unit long?
3. How many rectangles are there with base 2 units long?

### Main activity

Find all possible rectangles on a 5 x 5 geoboard. (There is a total of 16 such rectangles, half of which are squares.)

### Homework

Order each of the rectangles in the main activity by area. (The non-square rectangles have area 2, 3, 4, 4, 6, 6, 8, and 12 square units.)

### Extended activities

1. Make a rectangle with area 2 square units. Can you find another rectangle with this area?

2. Can you find a rectangle and a square with the same area?

3. There are three rectangles with area 4 square units. Can you find them?

4. Find the perimeter of each of the rectangles in the main activity.

5. Continue this pattern of rectangles on a 10 x 10 geoboard and complete the table:

6. Continue this pattern of rectangles on a 10 x 10 geoboard and complete the table:

7. Continue this pattern of rectangles on a 10 x 10 geoboard and complete the table:

8. Continue this pattern of rectangles on a 10 x 10 geoboard and complete the table:

[Materials] [Length] [Area] [Pick's Theorem] [Dot Paper] [Epilogue]

[Lines] [Squares] [Rectangles] [Parallelograms] [Right Triangles] [Bibliography]

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The Math Forum * * Tom Scavo * * 3 August 1997

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