## Pow #5

Problem statement In this problem we had to find that maximum number of pieces of pie that was possible with a certain amount of linear cuts. I drew two different circles. On one of them I drew 4 lines across the pie in a way I thought would make the most amount pieces. The amount of pieces I got with 4 cuts was 5 pieces but I do not believe that was the maximum amount of cuts I could have gotten. It was the same case with the second circle except I drew 5 cuts and got 6 pieces. If had had drawn more circles and attempted to put the cuts in different places then I probably would have gotten more variety in numbers and found a greater number than the ones I have. I also did not find a pattern but, again, if I had experimented more with the number of cuts and places of the cuts I might have found a pattern.

## Pow #4

The highest impossible score for the Free Thinkers Football League is 7. All scores higher than 7 are possible because after that point any combination of the scores adds up to a certain number that appears after 7, as shown by the data. The other score system that I tried was 4 points for field goals and 3 points for touchdowns. According to the data the highest impossible score is 5, anything after that number is a possible score. While these two sets of number have a highest impossible score there is not always one. For example, if the field goals were worth 4 points and the touchdowns were worth 2 then there would be no highest impossible score. All odd numbered scores would be impossible and all even numbered scores would be possible. In the other two sets of data that have a highest possible score there is no clear pattern.

In conclusion, 7 is the highest impossible score the Free Thinkers can get with the average point system. It is proven by my data that any score after 7 is possible. For the scoring system where field goals were worth 4 points and touchdown are worth three points the highest impossible score was 5. The scoring system where field goals were worth 4 points and touchdowns were worth 2 there was no highest impossible score

In conclusion, 7 is the highest impossible score the Free Thinkers can get with the average point system. It is proven by my data that any score after 7 is possible. For the scoring system where field goals were worth 4 points and touchdown are worth three points the highest impossible score was 5. The scoring system where field goals were worth 4 points and touchdowns were worth 2 there was no highest impossible score

## Pow #3

The first method that I tried was putting 6 bags on one side of the scale and 2 on the other, but then I remembered that the scale only compares weight and doesn't tell you the actual weight of the object. Then I realized you could put 6 bags on each side and have 2 leftover bags. If the three bags were even then you would add the other two bags one on each side. Whichever side rose would be the side that had the bag with the missing gold, which would be the bag that was just added. If that method was used then the scale would only be needed two times to figure out which bag had the missing gold.

Extension: Reuben had twelve bags of scones and his sister took some scones out of one of his bags. He needs to know which bag she took the scones out of but all he has is a pan scale. What is the least amount of times he can use the pan scale to find out which bag is missing the scones.

Extension: Reuben had twelve bags of scones and his sister took some scones out of one of his bags. He needs to know which bag she took the scones out of but all he has is a pan scale. What is the least amount of times he can use the pan scale to find out which bag is missing the scones.

## Cookies Unit Cover Letter

In this unit our main goal was to find out how many of each type of cookie Abbey and Bing Woo should make to maximize their profit. We learned how to graph and made graphs. The specific skills we learned were feasible regions, inequalities, reordering equations, substitution and elimination. When we first started this unit I had learned a lot of this before. However, I didn't understand it very well and was really bad at graphing. I have improved my skills in graphing, substitution, and elimination the most. The only new skill I learned is feasible regions. Before I had never heard of that before and I didn’t know how to find a feasible region on a graph. Something I have also never done is make a portfolio of all my math work from a unit. I am not very good at organization so I lost a lot of the work that should have been in the portfolio. I need to work on my organization and advocating for myself. This is mainly because when we started that unit I missed the first three days of the beginning so I was really confused for days. I did the work but I didn’t understand it. That could have been avoided if I had just asked for help.