Description:

Gears were invented so that large forces could be transmitted between two rotating shafts. There are a few simple geometric relationships which govern the operation of gears. First, moving gears in mesh act like wheels that are rolling against each other without slipping. Gear teeth are much more effective in preventing slipping than friction between smooth wheels.

This activity is meant to review the parts of a circle. Then armed with this knowledge the students will adapt their knowledge of a circle to the geometry of the gear.

Materials:

Part One

• one package of M&M's™ per group (four students in a group)
• one white paper plate per group

Part Two

• round coffee filters (enough for each student)
• scissors
• construction paper

Purpose:

The learner will explain the parts of a circle using a paper plate and M&M's™ and report orally to the rest of their class their findings.

Advanced Preparation:

• purchase the supplies you will need
• The small package of M&M™'s will work. There may not be enough to go all the way around the plate but this is a good activity to watch the students and see how creative they can be to find the circumference in M&M™'s.
• This is just a review activity. If you haven't introduced the circle to your class their are many activities you can use.
• Try out all of the activities ahead of time.

Procedure:

Part One: Reviewing the parts of a circle

1. The students are seated in groups of four.
2. Each group receives one small bag of M&M™'s and a paper plate.
3. Begin by asking the students to measure the diameter in M&M™'s.
4. Next have them measure the radius in M&M™'s.
5. Have them find the circumference in M&M™'s.

Part Two: Relating the circle to a parallelogram

1. Pass out a round coffee filter to each student.
2. Begin by having the student Fold the filter in half. Remind them to press on the fold to make it very crisp.
3. With young students you can discuss the diameter, 1/2 of the circle and so on.
4. The students then cut on the fold. You should now have two parts.
5. Fold each half of the circle in half and again remind the students to press on the fold to make it very crisp.
6. They cut on the fold again. There should now be four parts. (You can discuss the triangular shape; how many of these shapes equal a whole etc.) If you are doing this with young students you can stop there.
7. Discuss the arc at this time. The students could color with a marker or crayon the arc.
8. If you are doing this with older students continue making the folds and cutting them. (Each triangular shape will get smaller and smaller. It is up to you how many times you want your students to fold and cut. This is a good activity for fractional parts also.)
9. Now have the students glue their triangles onto the construction paper in an alternating up and down pattern. (Click here to view and example.)
10. Finally the students discuss in their groups all of the patterns they have found. They should begin to notice that the glued triangular shapes make a parallelogram.

Art and Other Connection:

• The coffee filters could be dyed and then used in this activity.
• In science you could use the filters for chromatography first then this activity next.
• Students could create a collage of their work.
• The M&M™ 's could be glued to the paper plate. It is very colorful.
• There is a children's book called M&M's. You can read this to the students before this entire activity.

Part Three

1. The students read the information "The Geometry of Gears". (Click here for a print copy.)