Des-blog

The Friday Fave has featured Pomegraphit before, but it’s just so much fun! Plus, it’s pomegranate season (no joke!)

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:

Lawnmower Math

Central Park

Pool Border Problem

The Friday Fave has featured Point Collector: Lines before, but now that this activity includes Challenge Creator, it’s like a Friday Extra Fave!

In case you’re not familiar, Challenge Creator allows students to create their own challenges, to share these challenges with their classmates, to try their classmates’ challenges, and to see their classmates’ solutions to each challenge.

The Fave wagers that your students will create far more devious challenges than the Des-authors would dare, and that your students will invest far more effort in solving those devious challenges because of their social connection to the challenge’s creator.

In case you’re not familiar, the premise of Point Collector: Lines is that you need to write a linear inequality that captures more blue points than red ones. How many more blue ones you capture than red ones determines your score. You are invited to revise in order to maximize your score.

Now with the addition of Challenge Creator, this already faved activity is even more interesting and challenging. Which, of course, makes it this week’s Friday Fave.

While you’re thinking about inequalities, have a look at these other activities involving transitive relations:

Polygraph: Systems of Linear Inequalities

Des-Pet

Domain and Range Introduction

Do you know what the Friday Fave wishes there were more of in the world?

Trapezoids!

Isosceles trapezoids, to be specific.

Build the Arch—this week’s Friday Fave—has you building arches from isosceles trapezoids. Perhaps you’ll use just a few isosceles trapezoids; perhaps you’ll use many.

You’ll definitely be thinking about relationships in the trapezoid’s angles, and probably you’ll be noticing a relationship between the cut angle and the number of trapezoids you’ll need to build the arch.

In any case, your goal is to describe a good cut angle with algebraic formality. The experimentation and analysis you do up front is going to be the proverbial keystone in your process.

Isosceles trapezoids, angle relationships, algebraic symbols, and a chance to be the stone mason; these all add up to this week’s Friday Fave.

While you’re thinking about trapezoids and angles, the Friday Fave recommends these additional activities.

Polygraph: Shape Bucket

Polygraph: Advanced Quadrilaterals

Lines, Transversals, and Angles