One of my many favorite problems to pose to my class is the Locker Problem. There are many versions of it on line, and you can also find some tech tools for use in the class. I pose the problem to my students and then give them a few minutes to accomplish steps one and two of the 4 step problem solving approach. After a little while we talk about what strategies the students have chosen. Draw a picture always comes up and through discussion we determine we don't want to draw 1000 lockers so we whittle it down to trying a simpler problem and looking for a pattern. After a little more time to work on the problem we talk about some other ways we can solve the problem and all of a sudden the students start getting creative! Some students use a deck of cards to represent lockers, some use puzzle pieces, some use pairs of scissors and some actually go to our 6th grade locker bay with colored post it notes. Eventually they begin to see a pattern emerge. I have the students present their work to the class and we review the pattern if necessary using the interactive hundreds chart on the Smartboard.
Here's the problem from CMP:
There are 1,000 lockers in the long hall of
Westfalls High. In preparation for the beginning of school, the janitor
cleans the lockers and paints fresh numbers on the locker doors. The
lockers are numbered from 1 to 1,000. When the 1,000 Westfalls High
students return from summer vacation, they decide to celebrate the
beginning of the school year by working off some energy.
- Student 1 opens every locker.
- Student 2 either opens or closes every other locker.
- Student 3 opens or closes every third locker. And so on, ...
I like all of the different ways your students chose to represent what was going on with the locker problem. I've started this problem by having 10 students come up and I have the locker number and and open side and closed side of a paper. We model what happens with the first 5 students
ReplyDeleteI like how you give the students the freedom to really explore the problem using different manipulatives and drawings of their choice. Isn't it amazing how creative kids can be given the opportunity? This is a great introduction to powers and perfect squares.
ReplyDeleteI've never seen this problem before, but I love it! what a great activity for a first lesson with a new class, to get them interacting, problem solving and generally in the right mindset for the rest of the year.
ReplyDeleteThis is a great problem and really helps the kids understand pattern identification. How far do you find they have to go before they recognize the pattern?
ReplyDeleteI have 6th graders working on this problem, and we have already solved a few problems that follow the same pattern. When they have gone through the first 5 rounds they generally recognize the pattern.
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