Before I get into my solution, I would like to explain the problem that my group was give. We were assigned the “Broken Eggs” problem where a farmer was taking her eggs to be sold at a market when her cart hit a pothole and broke all her eggs. She went to her insurance agent and asked about getting reimbursed for the money that she lost in her little “accident.” The insurance agent asked her how many eggs she had and she didn’t remember. All she knew was that she put them in groups of 2, 3, 4, 5, and 6 and each group had one left over. But when she put them in groups of 7, there were an even amount of groups.
We were told to figure out how many eggs she had, and here is what we did.
1. "Solution Section":
After taking a little bit of time to look at this problem, we found that the smallest amount of eggs that the farmer could have was 301. We found this by writing out factors of 7, up to 350. We determined that the answer could not be an even number since that would make even groups of 2 and 4. Then we realized that it had to be a number that ended in 1 since it had to be a factor of 5, which is 5 or 10, plus 1. And since 5+1=6, it couldn’t be 6, so it had to be 10+1=11. So a number ending in 1. We looked at the multiples of 7 that ended in 1, and then divided that number by 2,3,4,5 and 6 to make sure that they were all evenly divisible with a remainder of 1. The numbers that we tried were 21, 91, 161, 231 and 301. After trying all of these numbers, we found that only 301 was divisible by all of them leaving a remainder of one. And that is how we settled on 301 being the answer. Although this is only the smallest answer possible, we did not look into any further answers.
2. "Personal Pride"
This problem was not incredibly difficult, so it did not push me to incredible lengths of confusion. But it didn't push me in the area of problem-solving. I started with doing what I know was a good starting place, which was just writing out multiples of seven. This was the best place for me to start, so I can get a look at what I was supposed to be working with. This started a kind of process in my brain, where I started to understand the pattern for the problem. Once I had a place to go off of I was able to push myself in the right direction for finding a solution to this problem.
The way that I went about this problem can next to one of the "Mathematical practices and expectations." The one that this connects to the most seems to be "reason abstractly and quantitatively." This make sense to me because the further I got into this problem I had to be able to give the reason behind my supposed answer. And this being an open-ended problem there had to be some sort of abstract reasoning behind my supposed solution. And the quantitative bit make sense because this problem is surrounding numbers which are quantitative. I may be completely reading this wrong, but that is what makes sense in my brain.
3. "Group Gauge"
My group did not really have the option of working through the entire problem together. That is because I was absent for the first day working on the problem and when we came back together half of our group had already determined a solution. We did however, work as a group once we were able to come back together and talk about the problem. Not sure if this group had any really considerable strengths since we did not really have the option of working together as much as we should have. But this doesn't leave us a room for improvement. Next time, if we all work together again, we could improve our group work if we get the chance to work together from the beginning.
Our group did consider working on further questions. One question we considered starting was if the total amount of eggs was made up of groups of two, three, four, five, six and seven with the remainder of one. But we didn't really get time enough to start work on this problem.
We were told to figure out how many eggs she had, and here is what we did.
1. "Solution Section":
After taking a little bit of time to look at this problem, we found that the smallest amount of eggs that the farmer could have was 301. We found this by writing out factors of 7, up to 350. We determined that the answer could not be an even number since that would make even groups of 2 and 4. Then we realized that it had to be a number that ended in 1 since it had to be a factor of 5, which is 5 or 10, plus 1. And since 5+1=6, it couldn’t be 6, so it had to be 10+1=11. So a number ending in 1. We looked at the multiples of 7 that ended in 1, and then divided that number by 2,3,4,5 and 6 to make sure that they were all evenly divisible with a remainder of 1. The numbers that we tried were 21, 91, 161, 231 and 301. After trying all of these numbers, we found that only 301 was divisible by all of them leaving a remainder of one. And that is how we settled on 301 being the answer. Although this is only the smallest answer possible, we did not look into any further answers.
2. "Personal Pride"
This problem was not incredibly difficult, so it did not push me to incredible lengths of confusion. But it didn't push me in the area of problem-solving. I started with doing what I know was a good starting place, which was just writing out multiples of seven. This was the best place for me to start, so I can get a look at what I was supposed to be working with. This started a kind of process in my brain, where I started to understand the pattern for the problem. Once I had a place to go off of I was able to push myself in the right direction for finding a solution to this problem.
The way that I went about this problem can next to one of the "Mathematical practices and expectations." The one that this connects to the most seems to be "reason abstractly and quantitatively." This make sense to me because the further I got into this problem I had to be able to give the reason behind my supposed answer. And this being an open-ended problem there had to be some sort of abstract reasoning behind my supposed solution. And the quantitative bit make sense because this problem is surrounding numbers which are quantitative. I may be completely reading this wrong, but that is what makes sense in my brain.
3. "Group Gauge"
My group did not really have the option of working through the entire problem together. That is because I was absent for the first day working on the problem and when we came back together half of our group had already determined a solution. We did however, work as a group once we were able to come back together and talk about the problem. Not sure if this group had any really considerable strengths since we did not really have the option of working together as much as we should have. But this doesn't leave us a room for improvement. Next time, if we all work together again, we could improve our group work if we get the chance to work together from the beginning.
Our group did consider working on further questions. One question we considered starting was if the total amount of eggs was made up of groups of two, three, four, five, six and seven with the remainder of one. But we didn't really get time enough to start work on this problem.