Set it up!
Problem Statement:
After playing a few games of set we decided to investigate the game a little further. My group and I decided to look into "what would happen if set was four instead? Would you need to add another shape pattern or color?"
Process Description:
At first my group and I just laid out all of the cards and looked at them. We noticed that to make a set of three you have to have a certain amount of cards in each category. We then tried to make sets of four by looking at all of the cards, this was really hard and we were all unable to find any. But why? We started coming up with ideas on how to fix this problem.
Solution:
We figured out that to play this game with a set of four you would have to add another shape, color, and pattern. It works out this way because each set is made from cards that are either all the same in a category or all different. To make this work I think you would have to add at least 36 cards because for every shape you would have to add a card in every color and pattern, etc.
Reflection:
Playing set with my friends was a lot of fun. I learned a lot about patterns and also multiples. I think that I deserve an A on this because I worked creatively and thought really hard on how we could solve our question. I think that with these free think i used "model with mathematics" because at first it just seemed like we were playing a fun game but while solving our problem we had to think out of the box and use our math skills to help us out.
After playing a few games of set we decided to investigate the game a little further. My group and I decided to look into "what would happen if set was four instead? Would you need to add another shape pattern or color?"
Process Description:
At first my group and I just laid out all of the cards and looked at them. We noticed that to make a set of three you have to have a certain amount of cards in each category. We then tried to make sets of four by looking at all of the cards, this was really hard and we were all unable to find any. But why? We started coming up with ideas on how to fix this problem.
Solution:
We figured out that to play this game with a set of four you would have to add another shape, color, and pattern. It works out this way because each set is made from cards that are either all the same in a category or all different. To make this work I think you would have to add at least 36 cards because for every shape you would have to add a card in every color and pattern, etc.
Reflection:
Playing set with my friends was a lot of fun. I learned a lot about patterns and also multiples. I think that I deserve an A on this because I worked creatively and thought really hard on how we could solve our question. I think that with these free think i used "model with mathematics" because at first it just seemed like we were playing a fun game but while solving our problem we had to think out of the box and use our math skills to help us out.
Locker Problem
Problem Statement:
This problem was about HTHNC getting lockers. If student number 1 went by and opened every locker, then student number 2 comes by and closes every other locker, then student number 3 comes by and changes the state of every third locker, then student number 4 comes by and changes the state of every fourth locker, and so on. What would happen if 552 students went by? Which lockers would be open? Which lockers would be touched the most?
Process Description:
First we made a chart so we could see what was happening with the first few lockers, our chart looked like this:
This problem was about HTHNC getting lockers. If student number 1 went by and opened every locker, then student number 2 comes by and closes every other locker, then student number 3 comes by and changes the state of every third locker, then student number 4 comes by and changes the state of every fourth locker, and so on. What would happen if 552 students went by? Which lockers would be open? Which lockers would be touched the most?
Process Description:
First we made a chart so we could see what was happening with the first few lockers, our chart looked like this:
We started with student number 1 and wrote Os under each locker to represent how he opened every locker. Then on the second row we closed every other locker (put Xs) to represent student number 2. For person number 3 we changed the state of every third locker, and so on. It didn't take us long to figure out the pattern.
Solution:
After using our chart we noticed that all of the perfect squared lockers are open. So we decided to test this further just to make sure. So we went all the way up to 25 and it still proved to be correct. We also noticed that the order that the kids go in doesn't matter just as long as they all still go. All of the prime lockers were only touched twice, which showed us that the amount of times a locker was touched was based on its factors. The most any of the lockers were touched was 24 times. There are 23 perfect roots in between 0 and 552, so there would be 23 open lockers.
Reflection:
From doing this problem I learned a little more about factors and roots. I also used my chart making skills to work through the problem in a more organized and less confusing way. One mathematical practice that my group used was Make sense of problems and persevere in solving them. We used this because at first we had no idea how to even start solving the problem, but then we made sense of it and brainstormed on how we could solve it. I think that I deserve a 10/10 on the free think because I helped as much as I could on the brainstorming and I worked really hard on our poster.
Solution:
After using our chart we noticed that all of the perfect squared lockers are open. So we decided to test this further just to make sure. So we went all the way up to 25 and it still proved to be correct. We also noticed that the order that the kids go in doesn't matter just as long as they all still go. All of the prime lockers were only touched twice, which showed us that the amount of times a locker was touched was based on its factors. The most any of the lockers were touched was 24 times. There are 23 perfect roots in between 0 and 552, so there would be 23 open lockers.
Reflection:
From doing this problem I learned a little more about factors and roots. I also used my chart making skills to work through the problem in a more organized and less confusing way. One mathematical practice that my group used was Make sense of problems and persevere in solving them. We used this because at first we had no idea how to even start solving the problem, but then we made sense of it and brainstormed on how we could solve it. I think that I deserve a 10/10 on the free think because I helped as much as I could on the brainstorming and I worked really hard on our poster.
House Hunting Problem
Problem Statement:
Albert Einstein was the original author of this problem. The problem states that there are five houses on a street in five different colors (Blue, green, red, white, yellow). Each house is owned by a man of a different nationality (British, Danish, Swedish, German, Norwegian). Each owner drinks a different beverage (beer, coffee, milk, tea and water). Each owner Smokes a different kind of cigarette (Blue Master, Dunhill, Pall Mall, Prince and blend). Each owner has a different pet (cat, bird, dog, fish and horse). The problem gives you a list of hints but doesn't exactly tell you what goes where, and you have to solve for which house has the fish.
Process Description:
First my group decided that we would need to make a chart to organize all of the hints. We ended up having to make two charts because the hints didn't all fit the same way. We read through the hints many times and filled out the chart, if we didn't exactly know where something went would would try to narrow it down to at least two. This step helped us a lot because then we could use process of elimination to find out where it went exactly, eventually we solved the problem this way.
Here's an example of what our two charts looked like:
Albert Einstein was the original author of this problem. The problem states that there are five houses on a street in five different colors (Blue, green, red, white, yellow). Each house is owned by a man of a different nationality (British, Danish, Swedish, German, Norwegian). Each owner drinks a different beverage (beer, coffee, milk, tea and water). Each owner Smokes a different kind of cigarette (Blue Master, Dunhill, Pall Mall, Prince and blend). Each owner has a different pet (cat, bird, dog, fish and horse). The problem gives you a list of hints but doesn't exactly tell you what goes where, and you have to solve for which house has the fish.
Process Description:
First my group decided that we would need to make a chart to organize all of the hints. We ended up having to make two charts because the hints didn't all fit the same way. We read through the hints many times and filled out the chart, if we didn't exactly know where something went would would try to narrow it down to at least two. This step helped us a lot because then we could use process of elimination to find out where it went exactly, eventually we solved the problem this way.
Here's an example of what our two charts looked like:
Solution:
Our final answer was that the German keeps the fish. We know that our answer is correct because we went through all of the hints and made sure that they fit in correctly with our chart, since everything made sense and was correct we know that we found the answer.
Here is what one of our final charts looked like:
Our final answer was that the German keeps the fish. We know that our answer is correct because we went through all of the hints and made sure that they fit in correctly with our chart, since everything made sense and was correct we know that we found the answer.
Here is what one of our final charts looked like:
Reflection:
From doing this problem I learned how to organize my thoughts and make charts. I also learned how to work in a group and make sure that we all try or incorporate each others ideas. We made a lot of progress with our problem and I was a big help to the group, I came up with some of the ideas that helped us solve the problem. A big part of the problem is just keeping an for the clues and how they could fit together, this is another way that our group worked together. It was helpful to have so many eyes looking out and throwing out ideas. One of the biggest mathematical practices that we used was "Make sense of problems and persevere in solving them". We used this because at first our problem was really confusing and didn't make sense, but we made sense of the problem by creating the chart and organizing our thoughts and ideas. I think that I deserve a 10/10 on this free think friday problem.
From doing this problem I learned how to organize my thoughts and make charts. I also learned how to work in a group and make sure that we all try or incorporate each others ideas. We made a lot of progress with our problem and I was a big help to the group, I came up with some of the ideas that helped us solve the problem. A big part of the problem is just keeping an for the clues and how they could fit together, this is another way that our group worked together. It was helpful to have so many eyes looking out and throwing out ideas. One of the biggest mathematical practices that we used was "Make sense of problems and persevere in solving them". We used this because at first our problem was really confusing and didn't make sense, but we made sense of the problem by creating the chart and organizing our thoughts and ideas. I think that I deserve a 10/10 on this free think friday problem.