Cheers to Better Deals – The Inequality Story

downloadAlthough I have attempted to teach this topic in many ways at a variety of levels, I always find it interesting to see how learners attempt to grapple with the concept and understanding. Learners who struggle with understanding linear graphs typically have an even more difficult, and when you add-on this is the first time the learners have literally ever met the material I am at the source of the stream that I  see in higher education. The topic is linear inequalities, the grade level is sixth grade, and I am attempting to teach these young minds this topic in 50 minutes, or less, and it is their first time (Does anyone else hear the Mission Impossible theme song here?) Well, I accepted the mission, I would attempt this process, twice actually, as I would teach this lesson back-to-back in two different group of 6th grade learners. As you are aware, I am a huge fan of 3 Act math lessons, with one of my favorite resources coming from La Cucina Matematica, where they shared Estimation 180 and found this amazing 3 Act lesson. As with any lesson, I have to adapt it a little to make it match my teaching style, and went in feeling ready to give it a tackle. In my career, this is the first time I have attempted to teach this lesson with a 3 Act component, and it is the first time I felt compelled to not give any instruction, but let the students conversation and discovery lead the way. One of the big pieces I was looking forward to was having students see their responses projected in front of them with Desmos, using their group responses to guide the inquiry. One note on this topic, I would prefer to have assigned each student their own opportunity to play on Desmos and then share out whole class, but I would need some additional front loading days to teach students how to interact and use Desmos, which I am unfortunate in that I didn’t have that opportunity, so we did that part whole class. My lesson followed this the PPT I made here or you can see below, which went off overall pretty well.

Immediately, I must say that the kids in the first class thought that Woody had cussed in the first act, so the second time I gave the lesson I had to front load that the bleep was covering up the answer to a question we were looking to answer. Another thing I picked up on right away, is that students struggled with figuring out what the humor was, they needed the mathematical background to understand what the reason for the humor was, which is an avenue to pursue with them later. The way that the various groups interacted, the way in which the conversations went within each group depended a lot on what they noticed from the clip. I was surprised by the number of kids who actually knew the show, a big thanks to reruns and older parents, as those students were more interested in the problem since they had more background knowledge of the show. The beautiful thing about this lesson, is that the discussion and interactions gave the students the opportunity to discuss and find the break even point, with about half the students understanding why the deal was better or worse. Quantitatively speaking more than 90% of the learners were able to understand that $25 per week was the break even point, and they were able to understand that certain values like $30 a week was greater than while $20 a week was less than the value of the original deal. We started to talk about how $24.99 per week was still less than the original $100 a month raise, while $25.01 per week was greater than the original $100 a month raise; however, there were only about six kids per class that were able to articulate this point and why in their exit slips. The next steps in this lesson would be to flush out the idea mentioned above, that any value greater that then $25 per week is a better deal (more money) for Woody, while any deal of $24.99 per week or less is a worse deal (less money) for Woody. The discreteness of money helps make this more concrete which was one reason I thought it might be very valuable for these learners, not to mention money is something they are familiar with. Overall, I would say the lesson went well and promoted a lot of great discussions among the students, it removed any prior need for mathematical knowledge so all kids had an entry-level assessment into the game, and the students discussing the break even point was a huge win. The use of Desmos really helped visualize it for students, and will give them some place to start building on. I feel confident this was by far the best attempt at securing an understanding of this difficult concept and I imagine that with follow-up and repeated visits this topic will be mastered by most of these young learners.