There is talk of having a Colchester Middle School school-wide triathlon featuring 1 competitor from each of the teams in the school. The 3 events will be discus throw, long jump and a 220 yard dash. There must be 1 representative from each team performing in all 3 events. Looking at the results of your recent PE test scores, decide which member of the Challenger Team should be chosen to represent our team in this triathlon.
This task was given during the last week of school to all members of our multi-age, six-seven team. The students were in the midst of our interdisciplinary Olympics Unit, which included studying the history of the Olympic games, as well as preparing to enjoy the 1996 Summer Games. The physical education classes had just completed their track and field testing. This was a big topic of conversation and an inspiration for this task. The students had to organize and analyze the data and make mathematical decisions that involved comparing results measured in time and in distance. There is good opportunity for mathematical representations in the solution of this task. Students were given the results of three track and field events for 15 team members. They were asked to compare these results and select the best candidate to compete in a triathlon featuring these three events. Most students made some form of graphical representation of the data for comparison purposes. Others assigned a point system to the leaders in each field and compared point totals to determine a winner. Check with your physical educator. Your students probably do some activities that would give you similar results that you could use, or you could conduct a set of events to generate your own data. If there had been another week of school, we would have actually had the school-wide event described. To reduce the anxiety around physical competition between students, you could hold mock Olympic events such as "The cotton ball throw" which might be less threatening to students who are not as athletically inclined. Get your physical educator to help you generate the data set needed for this task. I suggest having a variety of events as opposed to having all events based on speed, strength or jump length, as it makes more interesting comparisons if the units of measure are varied. I adapted this task for special education students by having them work with a subset of only five competitors. I believe that the brevity of all student responses may be a result of assigning this task during the final week of the school year. They did seem very engaged in finding solutions. There might have been more interesting examples of student work if one student's event results had not been as outstanding as Adam's.
- Stopwatches (for gathering data)
- Tapes (for gathering data)
- Calculators
- Graph paper
50 minutes
Some students used extra time at home or in the computer room to create graphs or word process their responses.
See Expert solution
This student added the times and distances for the top placeholders to get the "highest" score. This is not a workable approach. S/he made a poor attempt at a graph, which is inappropriate to the task and poorly constructed. There is no mathematical language used in his/her solution.
This student used no mathematics in coming to his/her solution. S/he says s/he made a chart, but in fact only made a few x's on the given list of results. There is no math language used in the student's solution. While s/he seems to have understood the task, s/he did not put much energy into finding a solution.
Rearranging the results in a chart as this student did is a workable approach to solving this problem. This is a good example of a solution that did not require a lengthy narrative for the reader to understand what was done to solve the problem. The student makes an interesting observation about the median score in each event. This shows that this student has a concrete understanding of how to find the median, but lacks conceptual understanding of its appropriate use. It is unclear why s/he did not mention David as an alternate candidate based on David's scores.
This student had an interesting approach to solving the problem by assigning points for the best scores in each event and comparing the competitors based on these totals. S/he used a computer spreadsheet to create an interesting stacked bar graph. The original was easier to read as it was in color. It is apparent that this student understood the task and was able to solve it efficiently.
|
