Locker Problem

There are 100 lockers, and 100 people. Person 1 walks past and opens all the lockers. Person 2 walks past the lockers and closes every 2nd locker. Person 3 walks by and changes the stare (open/closed) of each 3rd locker. This continues and each person walks past changing lockers depending on their position, the 5th changes every 5th locker and the 10th changes every 10th locker etc.

At the end, we want to know which lockers are open.

Students worked so hard in groups to solve the problem. Representing the information was a challenge!

Many groups started to notice some patterns, and then they extended patterns to cover the 100 lockers.

People caught on to the fact that the open lockers will be the ones that are square numbers. This is because they have an odd number of factors. We also noticed that the numbers go up by 3,5,7,9,… and that the 2nd differences (the change in the differences) is 2 each time.

After our debrief and consolidation we took a minute to email families. Students filled in some blanks in an email template, and sent it to me as well as their family. We keep emailing over the course of the term to keep communication going, and to provide moments for reflection.