|Badminton or Basketball?|
Assumed prior experience with:
No previous experience with a particular topic is required.
This lesson addresses the availability misconception about general number sense. The misconception is that things that come to mind more quickly (for example, groups of 2) are more numerous than things that don’t come to mind as quickly (for example, groups of 4). This lesson can also serve as a precursor to thinking through more complicated counting techniques.
Students will be able to explain in their own words why for a group of n people, there are an equal number of possibilities for subgroups of size k (such that k < n) and size n - k.
Materials & Technology Needed:
1. Explain to class... "We’re going to do an activity in which you’re going to help a gym teacher plan a lesson. Mrs. Fibonacci is trying to decide which would be more efficient: having the class play badminton or having them play two on two basketball. Every time she has to take time to stop and start a new game, class time is wasted. First I want you all to figure out how many rotations of players she’s going to have in each game. We’re going to divide into groups...each group will get a handout that will help us start off the activity."
2. Divide the class into groups of two or three students.
4. Circulate while students complete handouts.
NOTE TO TEACHER: Make sure that the basketball groups understand that their groups must be unique. That is, the group of Ruby, Tinika, Juan, and Calloway may only be listed once. Their may be an inclination to have these same participants switch teams, thus constituting another game and another grouping...explain to them that those exact four names may only be used together one time in their list.
5. Have a student in one of the badminton groups put their list on the board. Have a student in one of the basketball groups put their list on the board.
6. As a group, come to an agreement about each of the lists (that is, make sure that the lists are comprehensive and do not have repetitions).
7. "Which lesson plan would be the best use of her classtime?"
8. What if the teacher wanted to have both games going on at once so that everyone could participate, "How many ways can the gym teacher group the students to have both games going on at once?"
9. Starting with the first badminton group on the board..."What if Juan and Ruby were assigned to play badminton...who would be playing basketball?"...indicate on the board that these two groups go together.
10. Continue associating each badminton group with a basketball group to show that the two are related.
11. Discuss how the sizes of the badminton and basketball groups effect this outcome (that is, would this have worked for groups of 3 and groups of 5?) Make a list on the board of the conditions for this situation.
VII. Assessment:Provide each student with a copy of the Journal Entry handout. Have students read the situation detailed by the handout and write a response. Read and provide feedback for each individual’s reasoning.