Des-blog

The Fave is feeling lucky, which is why Chance Experiments is this week’s Friday Fave.

Your students analyze a spinner, and they spin it virtually. But then they’ll design a spinner and test that out.

What does it mean for something to be “almost impossible” or “almost certain”? Does “almost impossible” differ from “unlikely”? How exactly? These are some of the big questions of probability and statistics–questions that Chance Encounters seeks to raise in your classroom.

And along the way, many other important questions will probably surface. How should I subdivide the spinner if I want to get exactly one red in 36 spins? Will a fair spinner always give 50% red? Will an unfair spinner ever give 50% red? Whether you are feeling lucky or not, these questions matter. Linger on them in your classroom.

And if spinners have you thinking about circles, here are three circle-based activities for you and your students.

Polygraph: Conics

Circle Patterns

Lawnmower Math

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