16 Categories Defined by More Than One Property

In the previous lesson you learned that in a “IS-A” hierarchy or “TAXONOMY” a broad category at the top is sub-divided into narrower categories by property tests.  We used the example of dividing the ANIMALS category into BIRDS, DOGS, and so on.   In this lesson you’ll learn a very important idea — THE ORDER OF THE PROPERTY TESTS CREATES THE HIERARCHY.

Here are some figures to organize. What properties could we use to organize them?

IMPORTANT IDEA: the order in which we use these properties makes a big difference!  Let’s group the figures by color first, and then by shape.
This order of the property tests creates this hierarchy:

Now let’s do the tests in the other order.  Group by shape first, and then  by color:

This order of the property tests creates a different hierarchy: