Exploring Area

Last week we explored area. We were given a certain area and then asked to create a geometric shape on a geoboard to represent that area. We then had to color in our shape on grid paper. Here is some of our work:

This irregular polygon has an area of 8.5 square inches



This irregular polygon has an area of 7 square inches



This irregular polygon has an area of 10 square inches




Here is one sample of completed work.
This student chose to label each square so that it was very clear what the area was.




Here is another work sample.
You can see there are some irregular polygons and two rectangles.


We noticed that there are often many ways to represent the same area. For example if you are making a figure with an area of 12 square inches, you could have a 1" x 12" rectangle, 3" x 4" rectangle, or a 2" x 6" rectangle. It is also possible to create an irregular polygon with an area of 12 square inches.

We also noticed that when working backwards from a given area, the rectangles you can make are the same as the factors for that number. For example, the factors of 12 are 1 and 12, 3 and 4, and 2 and 6. We also made a connection between area and arrays (a way we use to solve multiplication problems before we memorized our math facts). It is neat to see how it all goes together.

Is there anything you notice that you would like to share with us?