Fish Dilemma
Task
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.
Alternate Versions of Task
| More Accessible Version:
There are 3 boats. There are 4 people fishing on each boat. Each person catches 3 fish. How many fish have been caught?
More Challenging Version:
There are 3 boats. There are 4 people fishing on each boat. Each person may catch up to 3 fish. There are 10 different types of fish in the lake.
What are all of the different numbers of fish that could have been caught?
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Context
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?
What This Task Accomplishes
This task looks at a problem with many solutions.
What the Student Will Do
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. Time Required for Task
45 minutes
Interdisciplinary Links
This task can be used with units on science, social studies and art.
Teaching Tips
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.
Suggested Materials
Graph paper
Possible Solutions
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.
| More Accessible Version Solution:
4 x 4 x 3 = 36 fish
More Challenging Version Solution:
3 x 4 x 3 = 36 different fish caught.
Now, if there are 10 different types of fish, so 36 x 10 x 9 x 8 = 25,920 different possible combinations
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Task Specific Assessment Notes
Novice:
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.
Apprentice:
This solution, although beautifully drawn, is not complete. The student did not understand that more than one solution could be found.
Practitioner:
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.
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Expert:
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.
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