Tuesday, February 26, 2008

8.1 Areas of Rectangles and Parallelograms

In this chapter students are visited by an old friend, the area of a rectangle. Something students should know from early days of multiplication. But a new friend comes to join the party, the parallelogram hangs out to mix things up a bit.

The parallelogram and the rectangle have the same area formula: A = bh

I tried to look at two reasons why this is true.

The first uses translations, just like we did last unit with tessellations. We can translate part of a parallelogram to make a rectangle, by translating a triangle. This doesn't work as easily for some parallelograms, so another idea is important to look at.

I looked at skewing a parallelogram. I showed this by looking at a stack of calculators, when I skew the stack the area stays the same. The same thing would be true if I skewed a stack of paper. I like this idea because it starts a more calculus based way of thinking.

I'd like to hear more thoughts on this.

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