There are 3 boats. There are 4 people fishing on each boat. Each person may catch up to 3 fish. How many fish could be caught? Be sure to explain your reasoning using words, numbers, diagrams and/or charts.
This problem was given to a first grade class. I looked over the results and was intrigued. What would a fourth grade class do with this problem? Would I be able to see any differences in their reasoning? This task looks at a problem with many solutions. Most students started by drawing a diagram. Many then went to a chart. Many found the extremes - the most and the least number of fish that could be caught. 45 minutes This task can be used with units on science, social studies and art. The problem is slightly different from the Pre-K-2 version. This problem asks students to consider how many fish could be caught, not how many were caught. Students need to be made sensitive to thinking about problems this way. Graph paper You can get any number of fish caught from 0 to 36. This is assuming you do not consider 12 solutions for one person catching a fish - Person "A" on first boat and no one else, Person "B" on first boat and no one else, etc.
The solution does not have a relationship to the task (did 21 mean 12?). There is not an explanation of the solution so no reasoning is given.
This solution, although beautifully drawn, is not complete. The student did not understand that more than one solution could be found.
This student understands that there is more than one solution, "I think I could do this a lot more times, but I'm getting tired of it." S/he indicates the least and most number of fish to be caught. If s/he had made an organized list, s/he could have found all the combinations. They also realize that the same number of fish does not have to be caught on each boat.
This student went immediately to the number sentences that would tell him/her that there are 36 possible solutions. The solution shows a deep understanding of the problem and the communication is very clear.
|
