Parallelograms

Contents || Math Lessons

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

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

## Objectives

- to continue developing the student's sense of area, especially the relation between the area of a parallelogram and the area of the corresponding rectangle
- to realize that all rectangles are parallelograms
- to review some geometric concepts (e.g.,
congruent,similar) in the context of parallelograms- to experiment with geometric pattern making
## Materials

5 x 5 geoboards (the kind that fit together to make a10 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 or three 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

- Make a rectangle with base 2 units on your geoboard. Without removing the rectangle, make a parallelogram with the same base.
- What is the area of the rectangle in the previous activity? What is the area of the parallelogram? How do you know?
- Find another parallelogram with the same area as the parallelogram in the previous activity.
- On a
5 x 5 geoboard, find all parallelograms with a base of 2 units. How many are there? (There are 12 such parallelograms, including four rectangles.)- Make a parallelogram with base 1 unit on your geoboard.
- Find three more parallelograms with base 1 unit having the same area as the parallelogram in the the previous activity. What is the area of each of these parallelograms?
- Find four more parallelograms with base 1 unit, all having the same area.
- How many different parallelograms with base 1 unit are there? (There are 16 such parallelograms, including four rectangles.)
- Find a parallelogram with smallest area. Can you find other parallelograms with this area?
- Find a parallelogram with next smallest area. Can you find others?
- Find the parallelogram with largest area.
- Find the parallelogram with next largest area.
## Main activity

Find all possible parallelograms on a

5 x 5 geoboard. (There are 26 non-rectangular parallelograms. Together with the 16 rectangles of Lesson 4, this gives a total of 42 parallelograms.)## Homework

Order each of the parallelograms found in the main activity by area. Here is a summary of the 26 non-rectangular parallelograms:

## Extended activities

- Make a parallelogram that has the same area as the following rectangle:

- Make a parallelogram that is congruent to the one below:

- Make a parallelogram that is similar to the one below:

- Continue this pattern of parallelograms on a
10 x 10 geoboard and complete the table:

Compare your results with extended activity 5 of our lesson on rectangles.

- Continue this pattern of parallelograms on a
10 x 10 geoboard and complete the table:

Compare your results with extended activity 6 of our lesson on rectangles.

- Continue this pattern of parallelograms on a
10 x 10 geoboard and complete the table:

Compare your results with extended activity 7 of our lesson on rectangles.

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

Compare your results with extended activity 8 of our lesson on rectangles.

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

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

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