For example, 4 has three factors: 1, 2, and 4 The lockers which are touched the most are those lockers whose number has the most factors. Locker 3 is opened by the 1st person, left alone by the 2nd and then closed by the 3rd. Now note that the square numbers are the only numbers with an odd number of factors all other numbers have factors which come in pairs.
Which lockers were touched by only three students? This task provides students with an excellent opportunity to engage in MP7, Look for and make use of structure if they see early on that there is a relationship with factors and multiples or MP8, Look for and express regularity in repeated reasoning if they start to see and describe the pattern as they imagine students opening and closing the lockers.
Now consider the factors of 16 which are 1, 2, 4, 8, and On this student work, for exampleyou'll see two additional "hints" both of which came by way to student questions: "Can we do this with real lockers?
Lets use a table. I say that when everyone is seated with their group, I'll explain the task.
Asking students to try a larger number of lockers say 50 or and repeating the game can also help students look for a pattern since going through all the rounds of the game becomes less and less feasible as the number of lockers increases.
Notice that if the locker number, 24, is divisible by the person number, then the state changes: The number 24 has 8 factors, that is, 8 numbers that divide evenly into it.