__Pow 10: Going Bananas __

For our exhibition, my group and I presented Pow (Problem of the week) number 10. Pow number 10 was in my opinion, the most complicated Pow we have done this year. This Pow was all about the concept of maximization and optimization. The question was about a camel and how many bananas could he get to the market from the grove. He could only carry a certain amount at a time, and he had to eat one banana for every mile he walked. This Pow proved to be even more complicated than we first thought because it involved multiple stops at random points, and going back to the market to grab more bananas to pile up. It was hard to keep track because we forgot we had to eat bananas on the way back to the market too. In Order to prepare to present this Pow after we had finished it, my group and I decided to make a poster with a timeline of the camels journey drawn out. This Pow was very complicated and hard to explain, so Teaching it really helped my group and I get a better

understanding of the problem.

understanding of the problem.

## __Cookies Problem Cover Letter __

The Cookies Problem Portfolio
By: Todd Laffaye When first introduced to this problem, I had no idea how in depth it would go. I assumed that it would only be a one-day activity but it ended up being a multiple month long project that taught me more life long skills than my whole 8th grade year in math. Starting with simple counting using addition and subtraction, and ending by solving systems of equations using elimination. I have made tremendous personal growth throughout this project as well, and learned how to do things with graphs that I never thought I could do. The central problem was to figure out how many of each kind of cookie they could make to have a maximum profit without going over there 4 constants; Dough, Time, Space, and Icing. In Order to do this we had to learn how to find and write constants, plot constants on graphs, find feasible regions on graphs, make and use profit lines, and calculate the number of each variables on any certain point on a graph. I had gone into this project without knowing anything about any of these topics, and came out feeling comfortable about all of them and being able to do them in order to solve the Big State U problem. This Portfolio will consist of all my build up work which allowed me to solve the Big State U problem along with the main Cookies Problem. |

__Pow #5 Process __

A Pow is simply a problem of the week. This pow (#5) was one that I did my best on.

This is my process:

At first glance at the problem, I could tell it was going to be a hard one. My first method turned out to be useless. I started by writing down all the weights the bales could be and the combinations they were listed in. The main problem with this was the assumption that the bail combinations and weights were listed in order. This wrong assumption turned out to make this method impossible, and I found myself confused. When I received help and saw the guess and check method, it felt like a stroke of luck. Knowing that the possible totals are: 80, 82, 83, 84, 85, 86, 87, 88, 90, and 91; it was clear if there was a pattern it was going to be hard to figure it out. I used the guess and check method by picking different numbers for bail #1 to be and then using that to plug in the other weights. I did this by using subtraction. For example, say I think bail #1 would be 35; knowing that bail #1+bail #2 should be the lowest possible answer (80) I did 80-35 to get bail #2. (Witch in this case would be 45) *[35+45=80.]

This is my process:

At first glance at the problem, I could tell it was going to be a hard one. My first method turned out to be useless. I started by writing down all the weights the bales could be and the combinations they were listed in. The main problem with this was the assumption that the bail combinations and weights were listed in order. This wrong assumption turned out to make this method impossible, and I found myself confused. When I received help and saw the guess and check method, it felt like a stroke of luck. Knowing that the possible totals are: 80, 82, 83, 84, 85, 86, 87, 88, 90, and 91; it was clear if there was a pattern it was going to be hard to figure it out. I used the guess and check method by picking different numbers for bail #1 to be and then using that to plug in the other weights. I did this by using subtraction. For example, say I think bail #1 would be 35; knowing that bail #1+bail #2 should be the lowest possible answer (80) I did 80-35 to get bail #2. (Witch in this case would be 45) *[35+45=80.]