Today in class we talked about problem solving. we learned about different types of strategies: make a drawling, guess and check, make a table, use a model, and working the problem backwards. All these are ways that could help you to solve a problem, however not all these will work for everyone. I have learned that not all these strategies will work for me, and they might not work for every problem. Our instructor gave us this problem to try. This is how it read:
- How many different amounts can you pay using 4 coins of dimes, nickels, and quarters?
When I started out I was just writing out the possible combinations of the money; for example: 4 quarters, 4 dimes, and 4 nickels. However this is not what they wanted; they wanted to know the amount of money you could make with the coins. When I was informed of this I went back to look at what I had written for answers, then started to figure out the money value. When doing so I realized that many of the amounts repeated.
Our instructor showed us the way she had figured the problem out. She told us to think about in the most and the least amount of money that you can make and then fill in rest. This was a much more piratical approach to solving this problem. So with the least amount of money being $0.20 and the most being $1.00, you can take all the possibilities between the two and figure out what amounts work and which one do not.
(*- all possibilities)
So in conclusion to the problem there are 14 different amounts.
After having done the problem on our own and then having help doing it seemed less confusing. which brings me to the article Observing demos hurts learning, and confusion is a sign of understanding by Eric Mazur. The article talks about confusion being a sign of understanding. Through out my own struggles in math I believe this to be true. When I struggle with something I want to become better at it and therefor understand it.