You are looking for a job after school and you look in the local paper. You see the following 3 jobs that seem interesting. (1) Baby-sitting 2 young children: Work after school 2 hours per day Monday, Wednesday and Friday; pays $4.50 per hour. (2) Delivery route: Deliver 100 papers each day after school Monday through Friday; it should take 45 minutes per day using a bike and 1 hour 15 minutes per day if you walk. It pays 5 cents per paper. (3) Work for the Green Mountain Bank: mow lawn, shovel snow, empty trash, etc. Work 5 hours per week; pays $3 per hour. This job pays $10 per week overtime for special projects (rake leaves, trim bushes, file papers, etc.) which amounts to $10 extra (you can count on this overtime). If you had your choice of any of these jobs, which job would you decide to take? Compare each job - maybe for a few months (you decide how many months are necessary for you to be sure you are getting the best job). Show all your data and give mathematical reasons why you are choosing one job over the other two jobs.
I was surprised at how engaged my students were in this problem. I noticed, however, that a good deal of their discussions were about which job would allow them to do sports after school or that they like kids or that they did not like raking leaves. I had to make it clear that I wanted to see the mathematics in their solution as well as other ideas. I stressed that they would mainly be graded on their mathematical ideas. They walked out the door talking about which job they wanted to take. This task will show what students can keep track of and work with a couple of variables: time working per week and amount of money earned. Each job presents this information differently. The student will need to find a way to compare the jobs. They will have to figure out how much they will earn for each job. They will also have to compare the amount of time each job will take. They will need to juggle these variables with their own after school schedules and interests. The first job description is straight forward. The newspaper job does not give the amount earned per hour and the bank job indicates overtime, but the student will need to determine how much overtime they think they will need to do for $10. 1-2 hours The task takes 45 minutes to present to students and allow them to get started thinking about strategies. It takes another 30 minutes for them to complete their responses (or complete for homework). This problem can be given to students in a guidance program to talk about life skills and interests. Spend a fair amount of time discussing each job so all students understand each constraint. Discuss how hard it is to compare jobs because the information is given in different forms. Talk about the need to get the jobs described in a similar way.
This is an open-ended problem. There is no one correct answer. However, the mathematics they do and how they compare each job determines their level of performance. Here is some of the mathematics: Baby-Sitting: 2 hours/day x 3 days (Monday, Wednesday, Friday) x $4.50/hour = $27 per week. Newspaper Route: 100 newspapers/day x 5 cents/newspaper x 5 days = $25 per week. Average one hour per day so this job earns about $5/hour. Bank Job: 5 hours per week x $3/hour = $15 per week. Plus overtime: about 2 - 3 hours a week for $10/week. For a total of 5 - 6 hours/week and $25/week. This job earns between $4.17 and $5/ hour.
The student does not have the correct money earned for the bank job. There is no evidence of a strategy or procedure. There is little evidence of mathematical reasoning since there is no explanation of the solution. There is inappropriate use of the dollar sign and no use of mathematical representation.
The solution is not complete. The student did not choose which job s/he thought was the best and why. The student did use a strategy that is partially useful. S/he found out how much s/he would earn for the first and second job. S/he did not complete the amount earned in the third job. There is some evidence of mathematical reasoning. There is some use of mathematical notation (however the dollar sign is used incorrectly).
The solution shows that the student has a broad understanding of the problem and the major concepts necessary for its solution (except the hours for the bank job). S/he uses a strategy that leads to a solution and uses effective mathematical reasoning. There is a clear explanation, appropriate use of mathematical representation, terminology and notation.
The solution shows a deep understanding of the problem including the ability to identify the appropriate mathematical concepts and the information necessary for its solution. Uses refined reasoning. There is a clear, effective explanation detailing how the problem was solved. All the steps are included so that the reader does not need to infer how and why decisions were made. Mathematical representation is accurate and communicates ideas related to the solution of the problem. There is appropriate use of mathematical terminology and notation.
|
