The Friday Fave has featured
before, but it’s just so much fun! Plus, it’s pomegranate season
One of the more important things that mathematicians do is pay attention to a single attribute at a time. How is 2 like 10? They’re both even. How is 2 different from 10? 2 is prime; 10 is composite. So is 2 like 10 or different from it? It depends on the attribute you care about.
In math when two things are the same, we say they are equivalent, and the way they are the same is an equivalence relation.
Fractions depend on equivalence. Similarity and congruence are kinds of equivalence. Abstract algebra depends on equivalence.
In Pomegraphit, we ask students to consider one attribute at a time of various fruits. First up is tastiness.
Then comes difficulty.
Next, students place their fruits on coordinate axes where one axis is tastiness and the other is difficulty. They argue (another important mathematical practice!) about the placement, and they decide which fruit is most controversial in their class.
So go work on mathematical abstraction and equivalence with your students. Then maybe you’ll be inspired to do the same thing with other familiar things in your lives—school lunches, perhaps. Or writing implements (How are gel pens like #2 pencils? How are they different?. Or….
And while you’re thinking about variables with your students, here are three more favorite activities for working with meaningful variables: