A Math Forum Web Unit
Tom Scavo's

Squares

Contents || Math Lessons

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

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

## Find all squares

### Objectives

• to begin to develop a sense of area on the geoboard
• to develop a working knowledge of order attributes (e.g. between) with respect to area of squares
• 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 (one sheet 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. With one rubber band, make a square on your geoboard. What is its area?
2. Find the square on your geoboard with smallest area.
3. Find the square on your geoboard with next smallest area.
4. Find the square on your geoboard with largest area.

### Main activity

Find all possible squares on a 5 x 5 geoboard. (There is a total of 8 such squares.)

### Homework

Order each of the squares in the main activity by area. (In order, the 8 squares have area 1, 2, 4, 5, 8, 9, 10, and 16 square units.)

### Extended activities

1. On a 5 x 5 geoboard, find the square with next to largest area.

2. Find a square with area between 4 and 9 square units. Can you find another square with area between 4 and 9 square units?

3. What is the area of the shaded region below?

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

5. On a 10 x 10 geoboard, make a square using each of the line segments in Lesson 2. Which of these squares do not fit on a 5 x 5 geoboard?

6. Continue the pattern below on a 10 x 10 geoboard and complete the following table:

7. Continue these patterns on a 10 x 10 geoboard:

8. Order each of the squares in the previous activity by area.

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

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