NCTM - Principals and Standards for School Mathematics (PSSM) * Teacher Notes
Students will: apply and adapt a variety of appropriate strategies to solve problems monitor and reflect on the process of mathematical problem solving communicate their mathematical thinking coherently and clearly to others
Ohio Academic Content Standards * Teacher Notes
* Number Sense - Grade 6 - Indicator 14: Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.
* Number Sense - Grade 8 - Indicator 6: Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.
* 5-7 Mathematical Process Benchmark B: Apply and adapt problem-solving strategies to solve a variety of problems, including unfamiliar and non-routine problem situations
* 5-7 Mathematical Process Benchmark C: Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods.
The Learning Target
I can apply a problem solving strategy to solve a problem that is not familiar to me.
The Instructions
Below is a story about some sailors and how they come to divide a pile of coconuts between them. This is a problem that will probably require some exploration and various trials before coming to a solution. You may want to recall the various problem solving strategies that we have talked about in your mathematics classes. If you need some help on what these strategies are, you can click here.Problem Solving Strategies.pdf
As you work toward your solution, please keep all your work, including those methods you may have tried and been unsuccessful. After you successfully get your solution, provide an explanation on why you think your solution is correct. You may use words, pictures, or numbers to construct this defense of your solution.
The Task
 The Sailors and Coconuts Problem 
Three sailors were marooned on a deserted island that was also inhabited by a band of monkeys. The sailors worked all day to collect coconuts but were too tired that night to count them, They agreed to divide them equally the next morning.
During the night, one sailor woke up and decided to take his share. He found that he could make three equal piles, with one coconut left over, which he threw to the monkeys. Thereupon, he put his own share in a pile down the beach, and left the remainder in a single pile near where they all slept.
Later that night, the second sailor awoke and, likewise, decided to take his share of coconuts. He also was able to make three equal piles, with one coconut left over, which he threw to the monkeys.
Somewhat later, the third sailor awoke and did exactly the same thing with the remaining coconuts. In the morning, all three sailors noticed that the pile was considerably smaller, but each thought that he knew why and said nothing. 
When they then divided what was left of the original pile of coconuts equally, each sailor received seven and one was left over, which they threw to the monkeys. How many coconuts were in the original pile?
The Product
Once you find your solution, provide an explanation on why you think your solution is correct. You may use words, pictures, or numbers to construct this defense of your solution. Explain the problem solving strategy you used and the reason you chose that strategy. You can present you explanation in a variety of ways. You can write a paper, create a video, record a podcast, or any other combination of writing and multimedia.
| 
