About this time, we were asked to take a problem and present it to our class and report on the results. The problem I had chosen was called The Locker Problem best explained in the linked video by Nuno1014's Youtube channel (careful the answers are revealed in the video). I use a snippet of the video in the lesson I created, I love how this person approaches the explanation and models the concept in this 9+ minute video.
Anyway, as a first draft students were having a very challenging time accessing the problem, but I saw a student trying a process of elimination with the locker doors and the students changing the state of each door. The array the student was making were reminiscent of a multiplication table, which we had plenty of in our math class. So I gave each student a 20 by 20 multiplication array, and I asked if the lockers numbers run around the top and the student numbers run along the side, how might that help them access the problem?
The change in the room was palpable as many struggling learners were able to access the problem, this tool allowed the students to go from hating math and this problem to a shouting with joy. When we give students a task that is challenging, but give them tools to help access the problem we create better, confident mathematicians.
From this point, The Locker Problem has taken on many different formulations and iterations. Most recently, we had the opportunity to start off the 2018-19 school year in an 8th grade math class with this problem. The problem creates the opportunity for exponents to come about in a natural conversation. The beginning of the lesson is shown in the slide deck below:
The power of this approach is that the problem experience immediately provides a shelf for the students to put the learning about exponents on, and it also gives context for using language about a concrete object to make more sense of the problem. When we move on to discussing exponent rules, factors, rational and irrational numbers, and other content students are able to articulate their ideas with The Locker Problem acting as their backdrop.
Resources are here:
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