Suppose you have pennies, nickels, and dimes in your pocket. If you pull out four coins, what amount of money could you get?
Guidelines for working on the problem that match the homework rubric:
1. Okay, you know what the problem is asking as this is like what we did in class. So write a concise restatement of the problem in your own words. Think about what you are given in the problem, what you know about the problem and what you are trying to figure out.
2. Find some solutions as we did with three coins. You know there are several from what was investigated in class. What is the largest you could have, the smallest? Thinking about things like this will give you some ideas of what you might do next.
3. Use pictures, manipulatives, charts, and/or graphs to help explain your thinking and move along to a solution. After you have some solutions, arrange them in some systematic fashion so that you can look for patterns.
4. Identify and describe any patterns that you discovered in the problem. Even if you think they might not help you towards a solution – it may be helpful to write them down.
5. When you find a pattern, you can use this to generate more solutions. It is much easier. However, check to make sure that the solutions you generate with your pattern really are solutions. If they aren’t, go back and take a careful look at your pattern. This is an important step!
6. Find all the possible amounts of money you can have when you pick four coins out of your pocket (remember the coins in your pocket are pennies, nickels and dimes). How do you know that you have them all?
7. Provide a complete justification for your solution. That is, explain why your solution(s) makes sense.
8. Discuss what worked, what didn’t work and what you did if you got stuck. Did you get help from anyone or anything? What did you find or learn in this problem that you didn’t think about before? (This is your reflection.)