Grade Level 3Ð5
Superbowl Sunday
Superbowl Sunday is the final day of the entire playoff season. The playoffs start with 16 teams. This is a single elimination tournament. That means if a team loses once, they are out. Determine the number of games that will have to be played by the time the Superbowl Champion is crowned.
Context
This task was given to students who had a lot of problem solving experience the first half of the year. These students had worked with situations where they were determining tournament winners and different combinations. They had also worked on how to represent solutions using diagrams, lists, and other representations.
What This Task Accomplishes
This task allows the teacher to assess studentsÕ representations of solutions, in that the problem requires organization to determine an accurate answer. The students can also be assessed for their ability to determine patterns in problemÐsolving solutions.
Time Required for Task
This task required 45 Ð 60 minutes to complete. Students spent an additional 15 minutes selfÐreflecting on their work.
Interdisciplinary Links
This type of problem that involves elimination can be used in a variety of settings. It doesnÕt always have to relate to sporting events. It could be used to figure out a mystery, character traits, or groupings of teams.
Teaching Tips
To help students be successful, be sure they have practiced different ways of making mathematical representations. For example, when graphing change over time, a line graph should be used. Students also need to experience situations where a list may be more useful than a graph. To make the task more complicated you could adapt the task to ask how many games would be played with 4 teams, 5 teams, 6 teams and any number or teams. For students with special needs, you could simply reduce the number of teams.
Suggested Materials
Most students will simply use paper and pencil. Some may choose to use manipulatives (i.e. color tiles), but then will transfer their solutions to paper.
Possible Solutions
Most students will use a chart or diagram to solve the problem. The correct solution is 15 games. Of course, there could also be a chance that some students may want to work in ties, but in playoff situations a tie is not possible.
Benchmark Descriptors
Novice
The expert will make mathematically relevant observations about the solution. The novice will create some sort of representation. The work will show few or no labels, so it will be difficult to follow the studentÕs approach and reasoning. Little or no mathematical understanding will be present.
Apprentice
The apprentice will have an approach that will lead to a partial solution. Parts of the studentÕs work will be labeled and clear. There may be a lack of organization that eventually leads to an incorrect solution. Some math language may be used to communicate.
Practitioner
The practitioner will have an approach that will lead to a correct solution. Work will show the approach and reasoning used. Math language will be used, and math representations will be clear and labeled.
Expert
The expertÕs solution will demonstrate a thorough understanding of the task, and the solution will be clearly communicated. All math work will be correct, representations will be labeled, and correct math language used. The expert will also make mathematically relevant observations about the solution.
Author
Shawn Parkhurst is a grade four teacher at the Canadian Academy in Kobe, Japan. He is on a leave of absence from his work as a multiÐage teacher at the Williston Central School in Williston, Vermont.