I’m excited about lesson 1.4, because I think it will be fairly accessible for most students, yet there’s a lot of rich discussion that can come out of it. The MVP teacher’s notes say to focus on the common difference between consecutive terms, and where we see that common difference in each representation (table, graph, explicit function, recursive function).
In my sheltered classes, I’m going to ask a student to show us what push-ups are, to make sure we’re all on the same page about the context here. I can already think of a few hyperactive kids who I’m sure will be happy to volunteer!
After reading through the scenario as a class, I want to give some time for students to notice and wonder. We’ll do this individually first, then in pairs, and then as a class.
This will serve as the launch for the lesson, and then I’ll have students work in groups at Vertical Non-Permanent Surfaces (#VNPS).
Where we go from there will be entirely dependent on what the students produce. The MVP teacher’s notes recommend sequencing student responses during the whole-class discussion as follows: table, graph, recursive equation, explicit equation – emphasizing with each where we can see the common difference.
I haven’t formally discussed function notation with my classes yet, so I’m planning to introduce that (for both explicit and recursive functions) at the end of this lesson.
This lesson is starting on a Monday, and depending on how things go, the final wrap-up with function notation may take place on either Tuesday or Wednesday. If we’re able to finish up this lesson by the end of Tuesday, then I’m going to use Wednesday’s short period to do another Illustrative Mathematics lesson to review operations with signed numbers – something I’ve seen my kids struggling with a LOT.
Either way, I plan to start lesson 1.5 on Thursday.
Lesson 1.5 has kind of terrified me as a teacher of sheltered classes for English learners. This is the original problem context:
There’s so much text! And it’s so culturally dependent! After talking this over with my Math 1 co-lead as well as the ELL department chair, I have decided to rework the context to make it easier for my English learners to access.
I would love feedback on what I have made! I initially wanted to do something more tangible and concrete, but I also didn’t want the common ratio to be 2, since that’s what the kids saw with the last geometric sequence in lesson 1.3.
I don’t think a lot of kids know about chain emails, but they are on social media. I originally wanted to make the context based on Instagram, but to be honest I’m not on Instagram, and I was worried that I’d write it in a way that doesn’t make sense based on how the app works. I decided to use twitter because I think most kids are familiar with it and I understand how twitter works.
That being said, if you can think of a different, non-internet-based context for a geometric sequence, please let me know! I’m definitely not wedded to my version here.
This is what I came up with, keeping the numbers the same as in the original MVP lesson:
Again, I’m planning to launch with #noticewonder (individually, in pairs, then as a class). I think I’m going to make a tree diagram to help explain the context in my sheltered classes. My goal will be to NOT use it, or maybe if a kid draws something similar to have them explain their tree diagram and how it represents the problem.
I don’t want to prescribe student thinking on this problem, but I also want something in my back pocket in case my kiddos are totally confused by this context.
Once they (hopefully) understand the context, it will be off to work in groups at #VNPS!