Tag Archives: Volume of Pyramids
In earlier posts I’ve mentioned Friedrich Froebel and his geometric gifts. The third of his geometric gifts was a box containing eight cubes. Instead of the students simply opening the lid and dumping the cubes on the table, he would have the students place the box with the lid down on the table, slide the lid out from under the box, and then carefully pick up the box leaving the eight cubes themselves in the form of a two-by-two-by-two cube.
I was struck by something Froebel said about his primary objective for this early geometric gift and how it came about. The following is from the book I just showed you by Edward Wiebe, written in about 1869. Wiebe was a disciple of Froebel and helped to bring his ideas to the United States.
“A prominent desire in the mind of every child is to divide things (takes things apart), in order to examine the parts of which they consist. This natural instinct is observable at a very early period. The little one tries to change its toy by breaking it, desirous of looking at its inside, and is sadly disappointed in finding itself incapable of reconstructing the fragments. Froebel’s third gift is founded on this observation. In it the child receives a whole, whose parts he can easily separate, and put together again at pleasure. Thus he is able to do that which he could not in the case of the toys—restore to its original form that which was broken—making a perfect whole. And not only this—he can use the parts also for the construction of other wholes.”
Does any of this sound familiar? How many times do the words composing and decomposing appear in the Common Core Standards? This idea of taking apart and putting together, whether it be with geometric shapes in two and three dimensions or sets of objects or numbers expressed as a sum in different ways, is a common thread running through the standards.
Let’s jump ahead to eighth grade and show you a couple of ways that taking a cube apart can help us think about the volume of pyramids.
Well, there is much more that can be found by taking a cube apart. We’ve only just scratched the surface. For anyone interested, you can click here to find nets (pyramids for cube, cube corners, and tetrahedron) that will let you build the pieces that I’ve just shown you.