House Hunting
1. Problem Statement
- The problem "house hunting" is a very complicated word problem. Essentially, it is one of those problems where you are given circumstances, then given hints, and then given a task. The circumstances of the problem are that there are five different houses in a particular order that are five different colors that house five different people of five different nationalities that drink five different beverages that smoke five different types of cigarettes that own five different pets. Sounds complicated? This is barely even the beginning. Next, we look at the hints:
- The problem "house hunting" is a very complicated word problem. Essentially, it is one of those problems where you are given circumstances, then given hints, and then given a task. The circumstances of the problem are that there are five different houses in a particular order that are five different colors that house five different people of five different nationalities that drink five different beverages that smoke five different types of cigarettes that own five different pets. Sounds complicated? This is barely even the beginning. Next, we look at the hints:
After the hints were given, there is a task. The task is to find who keeps the fish. We were also told that utilizing charts for this problem was advised. Immediately, we made a chart. We thought okay there are five different people with five different circumstances, so naturally we started with a 5X5 chart.
2. Process Description
- We started with the 5X5 chart shown below. We filled in everything we knew for sure using the hints from the problem above. We labeled each row with each of the circumstances, then labeled each column with each of the circumstances, then filled in what we knew for sure.
We got stuck when we started to notice that things started to overlap and we could not make any more conclusions. We got stuck with the chart and started to move towards other methods of solving the problem. We tried doing a bubble match chart but also found that we still got stuck. After, we were very frustrated because we could not figure it out. I then suggested that we go back to the chart and try again. We tried to organize it better and it still did not work out. Jack then tried to use a similar, but different chart. We ended up using the chart below. It is a modified chart of the one I suggested. We call it an intersect chart. We circled everything we knew for sure and Xed out everything we knew was not right. We also added houses at the bottom to determine the order of the houses. After this, we critically thoug about each hint and bounced off of eachother's ideas to complete our chart.
2. Process Description
- We started with the 5X5 chart shown below. We filled in everything we knew for sure using the hints from the problem above. We labeled each row with each of the circumstances, then labeled each column with each of the circumstances, then filled in what we knew for sure.
We got stuck when we started to notice that things started to overlap and we could not make any more conclusions. We got stuck with the chart and started to move towards other methods of solving the problem. We tried doing a bubble match chart but also found that we still got stuck. After, we were very frustrated because we could not figure it out. I then suggested that we go back to the chart and try again. We tried to organize it better and it still did not work out. Jack then tried to use a similar, but different chart. We ended up using the chart below. It is a modified chart of the one I suggested. We call it an intersect chart. We circled everything we knew for sure and Xed out everything we knew was not right. We also added houses at the bottom to determine the order of the houses. After this, we critically thoug about each hint and bounced off of eachother's ideas to complete our chart.
3. Solution
After an extremely long process of elimination, we came to the conclusion that the German in the fourth green house who drank coffee and smoked prince cigarettes, owns the fish. Simply put, this is the only solution because no one else can possibly own the fish due to other circumstances. As you can see in the hints, it is not possible for the swede to own fish because he owns the dogs. It is many circumstances like these that led us to our solution. We know that our solution is correct because we went back and re-checked all of the hints and they all still remain true, so our guess must be correct.
4. Self Assessment and Reflection
Through house hunting, I have learned perseverance. There were many times when me and my group mates wanted to just put down the pencils and quit. Even though we sometimes took a few brain breaks, we still managed to keep moving forward and once we all felt like we were actually getting somewhere, it became very easy for us to stay positive and motivated. We all suddenly got very involved and we all equally started to contribute to the problem. I also learned that taking breaks is not always a bad thing and it can re-motivate a group and help us to focus more effectively. I think that I deserve a 9/10. The only reason I don't think I deserve a ten is because I think I contributed to a lot of our group's distraction. I was present every time we had a free think friday session. I also was mentally present and asked many probing questions to help clarify my knowledge and to push my classmate's knowledge. I think we all contributed pretty evenly and used all of our strengths to out advantage. For example, Jessica is really strong and good at thinking outside of the box. She is a big picture thinker. Alura is very organized and helped us to keep all of our thoughts in order and she also took notes on everything we were saying. Jack was good at keeping us on track and not letting us get too distracted. I think I contributed my positive attitude and my " lets keep trying mentality."
I think the mathematical practice and expectation we used the most was look for and make use of structure. We basically tried the entire time to find a structure that would work well for this problem. Once we found the right structure (the graph in 2.) we became very successful very quickly. Structure and organization is what got us through this problem. We would not have been able to complete this problem without finding a structure and maintaining structure in our group itself.
After an extremely long process of elimination, we came to the conclusion that the German in the fourth green house who drank coffee and smoked prince cigarettes, owns the fish. Simply put, this is the only solution because no one else can possibly own the fish due to other circumstances. As you can see in the hints, it is not possible for the swede to own fish because he owns the dogs. It is many circumstances like these that led us to our solution. We know that our solution is correct because we went back and re-checked all of the hints and they all still remain true, so our guess must be correct.
4. Self Assessment and Reflection
Through house hunting, I have learned perseverance. There were many times when me and my group mates wanted to just put down the pencils and quit. Even though we sometimes took a few brain breaks, we still managed to keep moving forward and once we all felt like we were actually getting somewhere, it became very easy for us to stay positive and motivated. We all suddenly got very involved and we all equally started to contribute to the problem. I also learned that taking breaks is not always a bad thing and it can re-motivate a group and help us to focus more effectively. I think that I deserve a 9/10. The only reason I don't think I deserve a ten is because I think I contributed to a lot of our group's distraction. I was present every time we had a free think friday session. I also was mentally present and asked many probing questions to help clarify my knowledge and to push my classmate's knowledge. I think we all contributed pretty evenly and used all of our strengths to out advantage. For example, Jessica is really strong and good at thinking outside of the box. She is a big picture thinker. Alura is very organized and helped us to keep all of our thoughts in order and she also took notes on everything we were saying. Jack was good at keeping us on track and not letting us get too distracted. I think I contributed my positive attitude and my " lets keep trying mentality."
I think the mathematical practice and expectation we used the most was look for and make use of structure. We basically tried the entire time to find a structure that would work well for this problem. Once we found the right structure (the graph in 2.) we became very successful very quickly. Structure and organization is what got us through this problem. We would not have been able to complete this problem without finding a structure and maintaining structure in our group itself.