Sorting and Math Teachers at Play 15

The new carnival is up.

Some of my favorite items: Kindergarten sequences (good for older kids, too) and the math skits idea.

I'm not crazy about the fractions or quadrilaterals activities, as I think both fall into some common pitfalls of the traditional thinking on these topics.

Sorting
As we started class this week, one activity we did in both my classes (geometry for K-8 and math student teacher assisting) is a Piece of Me. Students come up with one question about the class and one question about the teacher(s). They then get together in pairs/groups and decide on one of each to ask. They never ask the sort of thing you'd expect, or the sort of thing I used to share in my own introductions. It's an excellent quick pre-assessment of where they are with the class and what they care about. And, they get to discuss with other students what makes a good question. I got this activity from Dave Coffey, but I can't remember from where he got it.

The first activity I had the geometry students do was a game, that I've played with many levels of students.

In or Out
Materials: rope or chalk circle (For 20ish students a 40-50 ft rope will suffice. Of course, divide by 6 to estimate the diameter of the circle formed.)

Students stand outside of the circle. To demonstrate how a circle sorts, have a few different rules, and students who fit the rule step in. I usually use the old riddle: how many sides does a circle have? (Highlight for the answer: Two - inside and outside)

The game is a guess the rule game. Someone has a rule for the circle and people guess whether they are in or out. If they are correct, they can guess at the rule. If you guess the rule, you can make up the next rule.

I usually demonstrate the first three rules. One that is obvious, one a bit more subtle, and then a hard rule. The hardest rules are ones that change: in or out depends on body position, or on what the person before says. (Almost a guaranteed rule stumper is - you're out or in based on what the person before you guessed.) This can also be used to demonstrate the concept of function. (That's when I'm using the game in a college algebra class.)

Mostly the point is to get students thinking about characteristics. With upper elementary students or middle school students you could ask the questions I asked this time, after playing the game for awhile:

Activity: Work your way through some of the following questions.
1) What were some of the rules used?
2) Was there a rule that was easy to guess? Why?
3) Was there a rule that was difficult to guess? Why?
4) What is a rule that would divide our class into two groups of roughly the same size?
5) What are two rules that would divide our class into 4 groups of roughly the same size?
6) Why do two rules divide a population into 4 groups? Give an example.
Extension: Into how many groups would 5 rules divide a population? N Rules?

Reflection:
• Whole class: Share some of the ideas from (5). Try them out.
• Analysis: What are you doing when you’re sorting?
• Inference: What does this lesson have to do with geometry?