POW #3
This problem asks us to create formulas for each question. Every question had it's own requirements. Question 1 gives us 4 sub questions. For an example here is what it says.
1a. Find a formula for the area of polygons with no pegs in the interior you formula show use the number of pegs on the boundary as the IN and should give you the areas as the OUT. Make specific examples on the geoboard to get data.
1b. Find a different formula that works for with exactly on peg in the interior. Again, use the number of pegs as the IN and the area as the OUT.
1c.Pick a number bigger than 1, and find the formula for the area of polygons with that number of pegs on the interior.
1d. Do more cases like Question 1c.
So as you can see above each question is pretty long and takes some time to figure out, so question 2 was some what like that but it just had different requirements. My process for each and every question that was asked was I would take the requirement and make sure that it was included in the shape I was trying to make, So lets say question one says that I must have a perimeter of pegs of at least 4, then I would make a shape with at least 4 pegs on the outside and I tried to make sure that I would at least have an area of 1 or higher because if for each shape I had 0 as my area there would be no real formula to come up with. But each question had different requirements and it was kinda hard to included each requirement and find different data then was able to create a strong formula. These were my formulas for all the problems:
The solutions that we had to find was formulas so each question we had to come up with a formula.I came up with the solutions to every question and these were the formulas I created:
1a. P/2-1 1b. P/2
1c. P-4 1d. a. (p/2)+2 b. (p/2) +3
2a. I +1 2b. I+2
2c. a. I=2.5 b. I+3 c. I+3.5
Those are the Formula's I had, The last 3 are a little more simple but it was because I had to use big numbers so it was harder to find different data that would have given me a good formula. Reflecting on this problem I think it was a good way to refresh our minds about formula's, but I think it would have been a better learning lesson if we were a little more challenged with the requirements and possible having to create 2 formula's per problem I think would have been more challenging. A few HOHAM's I feel I developed was Cooperation. I think I did very well at helping my fellowing group members at my table understand the formulas I got and how they fit in I also think I developed perspective. I know I was very strong in this because I felt that to get a strong formula I needed strong data so I was constantly reminding myself that I can't just have the same data for each shape, I need something different and new. So that's what I did. I looked at my results ahead of time and focused on what needed to get done. Below are the images of work that I had done for this problem. Each geoboard shows a shape or 2 of the shapes I used for my data table.
1a. Find a formula for the area of polygons with no pegs in the interior you formula show use the number of pegs on the boundary as the IN and should give you the areas as the OUT. Make specific examples on the geoboard to get data.
1b. Find a different formula that works for with exactly on peg in the interior. Again, use the number of pegs as the IN and the area as the OUT.
1c.Pick a number bigger than 1, and find the formula for the area of polygons with that number of pegs on the interior.
1d. Do more cases like Question 1c.
So as you can see above each question is pretty long and takes some time to figure out, so question 2 was some what like that but it just had different requirements. My process for each and every question that was asked was I would take the requirement and make sure that it was included in the shape I was trying to make, So lets say question one says that I must have a perimeter of pegs of at least 4, then I would make a shape with at least 4 pegs on the outside and I tried to make sure that I would at least have an area of 1 or higher because if for each shape I had 0 as my area there would be no real formula to come up with. But each question had different requirements and it was kinda hard to included each requirement and find different data then was able to create a strong formula. These were my formulas for all the problems:
The solutions that we had to find was formulas so each question we had to come up with a formula.I came up with the solutions to every question and these were the formulas I created:
1a. P/2-1 1b. P/2
1c. P-4 1d. a. (p/2)+2 b. (p/2) +3
2a. I +1 2b. I+2
2c. a. I=2.5 b. I+3 c. I+3.5
Those are the Formula's I had, The last 3 are a little more simple but it was because I had to use big numbers so it was harder to find different data that would have given me a good formula. Reflecting on this problem I think it was a good way to refresh our minds about formula's, but I think it would have been a better learning lesson if we were a little more challenged with the requirements and possible having to create 2 formula's per problem I think would have been more challenging. A few HOHAM's I feel I developed was Cooperation. I think I did very well at helping my fellowing group members at my table understand the formulas I got and how they fit in I also think I developed perspective. I know I was very strong in this because I felt that to get a strong formula I needed strong data so I was constantly reminding myself that I can't just have the same data for each shape, I need something different and new. So that's what I did. I looked at my results ahead of time and focused on what needed to get done. Below are the images of work that I had done for this problem. Each geoboard shows a shape or 2 of the shapes I used for my data table.