The Locker Problem
Imagine that you are at a school that still has student lockers. There are 1000 lockers all shut and unlocked, and 1000 students. Supposed the first student goes along the row and opens every locker. The second student then goes along and shuts ever other locker, starting at locker number 2. The third student changes the state of every third locker beginning with number 3 (if the locker is open, shuts it and if the locker is closed, opens it). The fourth student changes the state of every fourth locker beginning with locker 4. This goes on for all of the 1000 students at the school. Which lockers will be left open at the end of the 1000 students? Which will be closed?
How is math problem solving?
Math is problem solving because everything in math has a solution. There are more than one way to attain a solution, but eventually a solution is found. As a teacher it's important to give students the tools to solve problems and help them to explore math through looking for a solution in their own way.