Problem Statement
In the Locker Lock-down problem, a school gets lockers for all 552 of its students. Each student then gets in line and walks past every single one, changing the open/closed position based on their respective number (2 opens every second locker, 3 every third etc.) Our goal was to find which lockers were open after the first 10 students went through, and which locker was touched the most.
Process Description
The process we used to find the answers to our questions was to find a way to plot each locker being open and closed somehow. I came up with the idea to use a spreadsheet (below) and mark each students touch pattern up to the tenth student. We marked a slash for each time the locker was touched and counted through the rows to see how many times a slash was marked for that row. Additionally, we color coded lockers that had only 1, 2, and 3 touches to get a better idea of what was happening. We made a surprising discovery in the fact that the number of lockers that only got touched buy one student were in the hundreds. We expected hardly any since there were so many people going through. The number of one touches would like change were we to add up every students touch path, but even up to 10 students that number is quite high.
Solution
Regarding the solutions to the main questions, we found that the answer to which lockers were left open is lockers 1, 4, and 9. The answer to the most touched is locker locker 360. During our search for the answers, we found another pattern with the lockers being that all of the prime number lockers were closed. We believe the reason for this is that since the prime numbers don't have any factors besides 1 and themselves, none of the other students were able to change their state. We find it interesting that the first student always managed to land a touch on the prime locker to close it. I think it would be interesting to add a question regarding how this prime pattern works with the locker problem.
Self-Assessment and Reflection
I believe I made a large contribution to our groups efforts to solve the problem. After brainstorming with my group mates I suggested the main idea on how to solve the problem using the check boxes on a spreadsheet and did the troubleshooting on how to set it up correctly. For my work I think I deserve an 9.5 out of 10 for being the one who did a majority of the work, including thinking of the spreadsheet, finding the most touched locker solution within, and creating the groups final poster.
The most relevant mathematical practice would likely be "model with mathematics." Without creating the spreadsheet model to search for our solutions, I am unsure of any other feasible way to finish the problem. Its a type of problem that needs to modeled to really understand whats happening and is difficult to explain with just words or math expressions.
After everyone finished their graphs, we all got together to discuss our own findings. For the most part everyone was able to find the solutions to the problems given. However, we did learn that there was another pattern similar to the prime pattern we found in which all of the perfect square lockers were always open. We weren't able to pin down an exact reason for how this worked but it was a great addition, and it leaves me curious to just how many different patterns may be hidden in this problem.
In the Locker Lock-down problem, a school gets lockers for all 552 of its students. Each student then gets in line and walks past every single one, changing the open/closed position based on their respective number (2 opens every second locker, 3 every third etc.) Our goal was to find which lockers were open after the first 10 students went through, and which locker was touched the most.
Process Description
The process we used to find the answers to our questions was to find a way to plot each locker being open and closed somehow. I came up with the idea to use a spreadsheet (below) and mark each students touch pattern up to the tenth student. We marked a slash for each time the locker was touched and counted through the rows to see how many times a slash was marked for that row. Additionally, we color coded lockers that had only 1, 2, and 3 touches to get a better idea of what was happening. We made a surprising discovery in the fact that the number of lockers that only got touched buy one student were in the hundreds. We expected hardly any since there were so many people going through. The number of one touches would like change were we to add up every students touch path, but even up to 10 students that number is quite high.
Solution
Regarding the solutions to the main questions, we found that the answer to which lockers were left open is lockers 1, 4, and 9. The answer to the most touched is locker locker 360. During our search for the answers, we found another pattern with the lockers being that all of the prime number lockers were closed. We believe the reason for this is that since the prime numbers don't have any factors besides 1 and themselves, none of the other students were able to change their state. We find it interesting that the first student always managed to land a touch on the prime locker to close it. I think it would be interesting to add a question regarding how this prime pattern works with the locker problem.
Self-Assessment and Reflection
I believe I made a large contribution to our groups efforts to solve the problem. After brainstorming with my group mates I suggested the main idea on how to solve the problem using the check boxes on a spreadsheet and did the troubleshooting on how to set it up correctly. For my work I think I deserve an 9.5 out of 10 for being the one who did a majority of the work, including thinking of the spreadsheet, finding the most touched locker solution within, and creating the groups final poster.
The most relevant mathematical practice would likely be "model with mathematics." Without creating the spreadsheet model to search for our solutions, I am unsure of any other feasible way to finish the problem. Its a type of problem that needs to modeled to really understand whats happening and is difficult to explain with just words or math expressions.
After everyone finished their graphs, we all got together to discuss our own findings. For the most part everyone was able to find the solutions to the problems given. However, we did learn that there was another pattern similar to the prime pattern we found in which all of the perfect square lockers were always open. We weren't able to pin down an exact reason for how this worked but it was a great addition, and it leaves me curious to just how many different patterns may be hidden in this problem.