Wednesday, September 19, 2012

Locker Problem Reflections Period 1 & 2

Students in periods 1,2,7, & 9 used created models as a problem solving technique to solve the complex locker problem.  The directions and parameters for the problem can be found here. The following are reflections written by the students after they managed to solve the problem and understand its patterns.

Reflection of Locker Problems
By: MC, VC, CC

Our group made a model of the locker problem and we determined, using our model, (the chalupa2 method), that every square number is open because it has an odd number of factors. Sometimes, we made mistakes. Some of our mistakes were misplacing things. This shook us off course and it just took it longer to figure out the answer. We thought of the method we used in our heads and we modified it on paper. The chalupa2 method is using a 30 by 30 grid and filling out each of the boxes with symbols of open and or closed lockers. We learned that this model took a long time and that we could have done it another way. Our teacher, Mr.Lattanzi, showed us that we didn’t have to fill out the whole model to figure out the answer. Even though it took a long time to fill out, it helped us a lot because we could see what we were thinking in our head. Using this model we could see a pattern. This pattern was critical to this problem. With the pattern we could figure out the answer 10 times faster than usual. This experience helped a lot because if we were in a situation like this problem we could use the same method to figure out the answer easily.
As you can see, we had struggles with this problem. Combining our brains together helped out a lot. Our model amazed us with its success. Now, if we ever get stuck in this situation again, we can use many methods we used for this problem to help. (This model is not a patented model. People can use this to figure out problems similar to this but keep in mind that we made it.)

Locker Problem

While doing our locker project, we learned a lot.  JT AR, and I (BE) first created a model that didn’t quite work the way we wanted it to. In the model, we listed all the lockers from 1 to 30 and listed all the factors for each locker. Soon we noticed that this model was disorganized. Then when our class shared some of our models, we thought another group’s idea was more organized and well-developed. That model showed us the pattern clearly between the students that were opening and closing the lockers. It included writing out the numbers 1-30 twice (once down the y-axis and the other across the x-axis) to show both the students and the lockers so we could figure out the pattern for the 1,000 students and lockers. As our project came to an end, we color coded the graph paper that we did our project on. The project helped us learn to work better with a group and taught us about divisible numbers, factors, and products. We learned the importance of a model and finding patterns when you have large numbers because it makes it simpler to figure out the problem. It is also an organized way to see all the work you did and learned from it too figure out other problems that are similar. Overall, we found out that all of the square numbers had an odd number of factors which keeps them open at the end. We learned a lot during this locker experience.

    We were assigned to do a locker problem and make a model to show our work. The locker problem is where we have to find out which lockers are open or closed at the end. We also had to find out which student touched which locker. We started off by labeling lockers and students with numbers in a 30 by 26 grid formation. Next, we started filling out the graph by putting an O and highlighting it orange for the locker being open and a C which was highlighted blue if the locker was closed. After that, we determined which student touched each locker and we searched for important patterns. Modeling is important because it helps show what we are thinking in our head, and it helps us find patterns.
The challenge started when we had to figure out how to setup and label the graph. That was a problem because if we counted wrong then we wouldn’t see the pattern. One mistake we made was we counted wrong and ended up with lots of problems. We eventually found out that all the lockers with their number being a square number (1, 4, 9, 16, 25 etc.) were opened and all the other numbered lockers were closed. What we would have done differently is we would have paid more attention to the number of lockers and students and the type of number they were. We learned that working together is better than working alone because we can get more work done and use our time wisely.

Written by: TT, EW, CB, KC

by: AL, CB, AS, HK

In the beginning, we read the locker problem. Then, we made a small chart of thirty lockers out of a thousand to help us solve it. Our goal was to see which lockers would be closed or open after the one thousandth locker and who touched which locker. Modeling was an important part because it helped us visualize the problem before we solved it.  The challenges we had in this problem was figuring out the pattern with the square numbers. An occasional mistake we made was getting open and closed lockers confused.  If we had the chance to do it again we would have done the color coding and labeling differently. This experience would help us when using combinations and problem solving. Patterns are an important part because they would help us if we had to figure out bigger numbers that weren’t on our chart. As a group, we enjoyed drawing the model and figuring out the problem which helped us learn when we have a big number problem to find the pattern.

Locker Reflection  - BS, LH, NK

Our group did a project about who opened what locker. We decided that we couldn't do all the math in our head so we made a chart on graph paper. We went across and down making lines 1-30. Person 1 opened all the lockers. Person 2 closed every other locker. Person 3 changed every 3rd locker, so say that 3 was closed and 6 was open. person 3 would open 3 and close 6 but leave 1,2,4, and 5 the same way they had found it. So person 4 changed every 4th locker, or every multiple of 4 because they were the 4th person, so the number of the person, the multiple of the locker they change. In our chart, we put c’s for closed and o’s for open. Lots of times we mixed up the letters and realized that the whole thing was wrong. We had to start over. On diagonal all of the lockers were changed. We looked at the real pattern and found that on diagonal 1,4,9,16, and 25 were open. Do you know why they were open? Because they are all square numbers! One of the mistakes we made is when we finished, we traced it with marker and realized it was wrong, so next time we should check our work more carefully. This project helped us realize  that we should organize our thoughts better by using graphs instead  trying to figure it out in our heads. We have seen that car companies use models of cars that they want to sell before making the real version. They can see how the cars would look before creating it. A pattern is important because you can see how everything is related to each other and it makes it easier to solve problems with bigger numbers. There were definitely challenges involved in the project. One of the challenges was that in the beginning we couldn't find what kind of model to use to figure out the problem. Another challenge is that also in the beginning, some of us didn't know how to solve the problem, but then we all helped each other and came up with a solution. In the end, the locker problem was a fun, hard working project and we enjoyed trying to figure it out.

Tuesday, September 18, 2012

U-Turn Method to Find All Factors

Hi Guys, Remember this from class?  We talked about why this method is useful and how it keeps us organized, but one of the great things about this method is that if you are stuck or can't think of a factor pair quickly, you can skip it and come back later using the other factors you found as clues.

Here's the screencast.