ETSC: No LIMIT! Project - Classroom Activities
Eight People in a Boat
This is good as an icebreaker and/or problem-solving situation.
Folding the Circle
This activity was adapted from a session in Paper Folding in Geometry at a Northwest Mathematics Conference in Portland.
Tennis Ball Toss
This is a great way to help students/participants learn names and problem solve.
Random Number Activity
Participants draw a number and think of ways their random number connects to them and their life.
Eight People in a Boat
Use 9 chairs with 4 men seated on one end, 4 women seated on the other end, and 1 empty chair in the middle.
How many moves will it take change positions so 4 women and 4 men are on the opposite side from where they started?
Legal moves:
- Slide into an empty chair
- Only jump over one person of the opposite sex
- Can't move backwards
This activity is good as an icebreaker and/or problem solving situation.
After explaining the challenge ask participants for predictions of the number of moves needed.
Results should be recorded.
Discuss thinking and patterns participants noticed.
Folding the Circle
- Begin with a circle about 20 cm in diameter. (Wax paper may be useful for
teacher demonstration.)
- Find and mark the center of the circle.
- Choose any point on the circle and fold to the center.
- What does it look like?
- How do you get the center diameter, radius, and 90?
- How many degrees are in a circle?
- Repeat the process using one endpoint of the arc as an endpoint
of the next arc.
- What does it look like?
- Show me a chord.
- What is the distance around a circle? (Circumference)
- Fold the remaining part into the center so you have an equilateral
triangle.
- Possible terms to bring up: vertex, vertices, isosceles, equiangular, area, and perimeter.
- Find the midpoint of one side by creasing lightly. Fold the opposite vertex
to the midpoint. Crease and you have an isosceles trapezoid.
- What does it look like?
- Fold one of the side triangles over on top of the middle one. Crease
and you have a rhombus.
- What does it look like?
- Fold the remaining triangle over on top of the other two. Crease and a smaller equilateral triangle is formed.
- Let the three triangles folded over in steps 2, 3 and 4 open up and come to a point. A tetrahedron is formed (also called a triangular pyramid).
- Open the shape back up to the large triangle you made in step 1. Fold each vertex in turn into the center of the circle. Crease as you go and you have a trapezoid, a pentagon and a regular hexagon.
- Let the small triangles raise up a little bit and push gently into the center. A truncated (cut-off) tetrahedron is formed.
- Open the shape to the hexagon. Look at one side of the hexagon and you will see three line segments formed by previous creases. Fold back along each of those creases and you will have a nonagon (9-sided), a unidecagon (11-sided), and a dodecagon (12-sided). The last shape is a 12 pointed star.
- Let the sides of the shape raise up to form a paper clip holder!
Other Comments
- At each stage of the folding process try to get students to respond with as many different names for the shapes as is appropriate for the level of students you are working with. For example, the trapezoid can also be called a quadrilateral and a polygon.
- Use the model formed to also talk about other names for shapes. For example when talking about the equilateral triangle you can talk about the following triangles: isosceles, scalene, equiangular, right, obtuse.
- Use the model to talk about the parts of a shape. For example, with the circle you could talk about the center, radius, diameter, chord, inscribed angles, central angles, arcs, etc.
- Use the model to talk about the circumference (or perimeter) and area. If appropriate have students state the formulas for those measurements.
- Many places along the folding process yield nice places to stop and use the model as a start for an art project. Use your own imagination. In particular, after all the folding has been completed you can unfold back to the original circle. The creases from the folds have created many "polygons" on the circle. Students could use crayons or felt tip markers to color in the regions. If a teacher has a nice, bright window, the circles can be exhibited almost like stained glass panels. For some students, the extra challenge of using the fewest number of colors possible makes an interesting investigation.
Supplies:
- Copies of the circle for each student
- Scissors
- (Optional) Masking tape, scotch tape
This activity was adapted from a session in Paper Folding in Geometry at a Northwest Mathematics Conference in Portland.
Tennis Ball Toss
This is a great way to help students/participants learn names and problem solve.
Participants stand in a circle. Begin by calling out the name of a person and tossing a tennis ball to them. The individual continues by calling out someone else's name and tossing them the ball. Continue around the circle.
Start the process again by calling out the name of a person and tossing a tennis ball to them. Each person receives and tosses the tennis ball only once. Introduce a 2nd ball and continue in the same order. With a 3rd and 4th ball continue the process. Have participants predict how fast they can do the toss. Keep trying to do it faster. (Participants may decide to rearrange themselves to get a faster time.)
Variation: Toss the ball 2 people to the right. How many times does the ball go around the circle before each person has touched it at least once? Continue with the same pattern: Toss the ball 3 people to the right. How many times does the ball go around the circle before each person has touched it at least once? Toss the ball 4 people to the right. How many times does the ball go around the circle before each person has touched it at least once? What patterns do you see?
(A pair of clean socks could be used instead of tennis ball.)
Random Number Activity
Print random numbers between 1 and 100 for the participants.
Participants draw a number and think of ways their random number connects to them and their life.
Find another person whose number connects to their number and talk about the connections.
Find a person whose number doesn't connect to their number and talk about the lack of connections.
Participants finish the activity by sharing their name and how the number is connected to them.
Variation: Use fractions, decimal or percents for the random numbers.