This morning we looked at Chapter 3 in Count like and Egyptian. This chapter discusses how to calculate areas of triangles and the area of a circle using Egyptian ideas of multiplication and division.

Since it had been a couple of weeks since we last looked at the book, we started with a quick review of Egyptian multiplication. Most of the ideas had stayed with the boys, which was actually pretty nice to see, but one little piece of the process got reversed in their mind. There’s more detail on this process in our first project from the book linked above.

To get going with the ideas in chapter 3 of the book, we spent a little bit of time talking through how to divide by 2. My younger son listed some procedures that he knows for dividing by 2 – long division, for example – and my older son showed how to reduce a complex division problem into pieces that you already knew how to do. This second approach is pretty similar to the approach discussed in the book:

One time you might find yourself dividing by two is when you are calculating the area of a triangle. We work through several examples of using Egyptian multiplication to calculate the area of a triangle:

The last part of the project was using Egyptian multiplication to find the area of a circle. The book claims that the Egyptians used the approximation , so in order to calculate (or approximate, I guess) the area of a circle we need to learn how to divide by 8.

We talk through how to do that building off of dividing by 2 and then find an approximate value for the area of a circle with radius 10.

The math history that we are learning in this book is really fun. What I really like about going through this book with kids, though, is all of the conversations about arithmetic help them build up their number sense. I’d definitely recommend this book to anyone looking for fun and different ways to talk about arithmetic with kids.