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
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
- one package of M&M's per group
(four students in a group)
- one white paper plate per group
- round coffee filters (enough for each
- construction paper
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.
- 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
Part One: Reviewing the parts
of a circle
- The students are seated in groups of four.
- Each group receives one small bag of M&M's
and a paper plate.
- Begin by asking the students to measure
the diameter in M&M's.
- Next have them measure the radius
- Have them find the circumference
Part Two: Relating the circle
to a parallelogram
- Pass out a round coffee filter to each
- Begin by having the student Fold the filter
in half. Remind them to press on the fold to make it very crisp.
- With young students you can discuss the
diameter, 1/2 of the circle and so on.
- The students then cut on the fold. You
should now have two parts.
- Fold each half of the circle in half and
again remind the students to press on the fold to make it very
- 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.
- Discuss the arc at this time. The students
could color with a marker or crayon the arc.
- 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.)
- Now have the students glue their triangles
onto the construction paper in an alternating up and down pattern.
(Click here to view and example.)
- 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
- 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.
- The students read the information "The
Geometry of Gears". (Click
here for a print copy.)