SMART SPINNERS:

This introduction to probability challenges students to make predictions and do physical experiments that develop an intuitive understanding of probability theory. Students will build their own spinners, and use them to conduct their explorations.

Time: 40 minutes
Materials: Materials for making spinners (xerox, cardboard, brass brads, scissors, markers), scratch paper and pencils.

Getting Started: Ask students to brainstorm where they've seen or used spinners before. What did the spinners look like? Explain that they're going to build their own spinners to do mathematical experiments.

Use materials provided to have each student make a spinner like this:

Encourage students to individualize their spinners...they may choose to use colors, animals, designs, etc. to designate each of their 3 areas. (This should take approximately 10 minutes, depending upon age and dexterity of students.)

NOW have students pair up to conduct the following explorations:

1. Ask each pair to make a prediction: If you spin your spinner 40 times, how many times will it land on EACH of your spinner's categories? Make sure students record their predictions on paper which they'll use to record their results in the next part.

2. Spin your spinner 40 times, keeping track of how many times it really DID land on each category by making some kind of chart. (Let each student decide how to design a chart of their results....charts which don't work very well are as important in the learning process as those which may work better!).

3. Repeat steps 1 and 2, and change the number of spins...try 20 or 80. Make sure students PREDICT and RECORD results!

To Discuss: Ask students how their predictions compared with real results. Ask "WHY!"...WHY did they predict as they did, and WHY do their real results look like they do? Encourage ALL students to participate in this discussion, especially students who are usually afraid to speak up in class.

You may want to explain that the data generated by their spinners simulates the kind of probability experiments done by real scientists and statisticians. The numbers are quirky, because they're not EXACTLY matched with the predictions (or theoretical numbers) , and this can be confusing. But early experiences like this will help develop later understanding of probability.

Extension:

Have students change the face of their spinners by adding a 4th category and label each one "Go West", "Go North", "Go South", and "Go East".

Ask students if they see how this is like a compass (for many, compasses will be a brand new concept, and you may want to talk about maps and explorers and regular people who use North, South, East, West directions all the time!)

1. Have students form groups of 2-4 players, and have each player find or make a player piece (a crumbled scrap of paper works fine!)

2. Explain that the xerox represents a fictional city and the goal is to be the first person out of the city, or off the xerox.

3. Players take turns spinning the spinner, and each moves 2 spaces in the direction identified by the spinner. Two or more players may occupy the same square at the same time.

4. Play until ALL players are out of the city! Have FUN!!