Then the Pythagorean theorem ‘pops out’ even more clearly.

I reveal how at http://www.jonathancrabtree.com/mathematics/a-proof-of-pythagoras-via-the-chinese-chou-pei-suan-ching/

]]>I am sitting here in my Elementary Math Methods class and we are hashing out the details of division of fractions. We’re loving your blog posts, but we are confused about one section. Under SHARING you write, “In this problem, we have some number of objects (35) that we are dividing up into a known number of groups (7). We need to figure out how many are in each group. This first meaning for division is variously known as sharing, partitive and how many groups? division. These terms all mean the same thing.” And then under MEASURING you write, “In this case, we know how many are in each group, but we don’t know how many groups we can make. This meaning for division is referred to as measuring, measurement, quotative and how many in each group? division. These terms all mean the same thing.” I think you may have flipped the sharing/measurement “how many groups?division”/”how many in each group?division.” Sharing division is figuring out “how many in each group” and measurement division is figuring out “how many groups.”

Thanks for all your great posts!

Lucy