Locker Task

I was working with 2 different MTH1W classes today, introducing the locker problem. It always impresses me the creativity that the students show as they approach the open questions.

Here is the question: There are 100 lockers and 100 people. The first person opens all the lockers. The 2nd person closes every second locker, the 3rd person changes (open/closed) every third locker, the 4th person changes every 4th locker (and so on). After 100 people have gone past, which lockers are open.

We had groups who drew the 100 lockers and went through each opening and closing them with various symbols ans colours. Some groups modelled the first 10 or 20 lockers and wrote the status of each locker after each person passed by the lockers. This method was easier to troubleshoot. One group used a different colour for each person, and then noticed that if there’s an even number of dots then the locker is closed, and if there’s an odd number the locker is open.

one group was very keen on proving that all prime number lockers were closed. Another group focused on the lockers, and which people touched them, and if it’s an odd number of people then the locker is open.

Others saw the pattern of 1,4,9,16 and could see that it’s perfect squares, and some people saw that in the end that we skipped over 2, skipped over 4, skipped over 6, skipped over 8, and they worked out the pattern from there.

We consolidated the ideas of square numbers, and how they have an odd number of factors since there is a number that is multiplied by itself.

It’s fun to watch students get better at persevering through a challenging problem. We’re off to a good start already!