Enough snow!! All of the melting snow is causing damage to Dr. Lehner's home. He needs to hire a couple of people to shovel off his decks, (if you have ever seen his house, you would know he has quite a few). Since Dr. L. enjoys seeing students take responsibility. . . he offers the job to Upper Unit students. Dr. L. says when the job is completed to his satisfaction; he will pay $48 to the shovelers to share as they see fair. Oh, yes, Dr. L. will not let the work begin until he hears the plan for sharing the money and makes sure that everyone agrees. If there are 3 decks and 6 shovelers, how do you think the work and money should be shared? The deck sizes: Deck A: half the size of deck B Deck B: 80 square feet Deck C: 120 square feet
The class was working on multiplication, so we did some beginning area concepts along with multiplication. I wanted to do a problem that appeared to be real world that involved area and that might also check students' division concept and equal parts. This task is a multi-step problem that has more than one strategy. It involves division as well as area and money. Drawing a diagram to help solve the problem seemed natural to many students. Most students started by thinking about what the decks might look like and to draw the decks on graph paper. The connection between sharing evenly and the division algorithm was clearer for some than others. 45 minutes
This task works well with discussions about money, sharing and work. If your area does not have snow, you might think about raking leaves off decks, painting or staining decks. Graph paper The $48 is divided evenly among six students so each student gets $8. And a total of 240 square feet is divided evenly among six students so each student needs to clear 40 square feet (in any arrangement of 40 square feet).
This student tried unsuccessfully to draw the decks and is applying inappropriate concepts to solve the problem. There is no evidence of reasoning. S/he has two shovelers working at each deck regardless of the size of the decks. The student also does not deal with the amount of money each student should receive.
This student does not have a complete solution indicating that part of the problem was not understood. S/he uses a strategy that is successful in figuring out how much each deck should be worth, but does not seem to understand that the money is going to go to individual students for clearing the decks. The decks are drawn correctly and there is evidence of mathematical reasoning as the student explains the rationale for sharing the $48.
This student has a broad understanding of the problem. They share the amount of money and the area of the decks evenly using division. S/he uses effective reasoning, there is a clear explanation of the strategy and the representation is accurate.
The solution shows a deep understanding of the problem. Notice there are two different solutions. And in fact, the second solution is made to a different scale. The first solution has one square = one square foot and the second solution has one square = four square feet. The second scale makes for a more efficient representation. There is a clear and effective explanation and connects division and fractions to their strategy.
|
