Gideon came up to me today with a toilet paper tube and told me that if you unrolled the cardboard, it would make a triangle.
This was incorrect, but it started a fun impromptu math lesson with all of the kids. (If you only unroll the tube part way, it does make a triangle.)
If you unroll the toilet paper tube, you get a parallelogram. The kids did not remember this shape, so it led to a nice discussion of what parallel means.
Since our kids had memorized the area of a rectangle (length times width), I showed them how to find the area of a parallelogram. If you cut off part of the parallelogram, you can rearrange the pieces into a rectangle.
The kids said that the area of the parallelogram would also be length times width. I agreed, but I told them that we don’t call them length and width, we call them base and height. So the area of parallelogram is base times height. (I was actually expecting to end the discussion here, but when the kids heard base times height, they said, “Oh, like a triangle is one half base times height.”)
So I taped the parallelogram back together and then cut in in half, going from one corner to another. As I was cutting the kids declared, “I see it. I see it. It is going to be triangles.”
So it makes sense that the area of a parallelogram is base times height and a triangle is one half base times height.
Taking the time to answer our kids questions and expand on them has helped build a culture of learning in our house.