Last week, I did lesson 3.1 of the Mathematics Vision Project (MVP) Math 1 Module 3. This week, I’m doing lesson 3.2 and I am both excited and apprehensive. In this post, I will explain my excitement and apprehension, as well as give a summary of how I’m planning to structure my lessons this week.

I’m excited because I think that the contexts used in this lesson provide a low entry-point, so I anticipate most students being able to feel like they immediately understand (at least part of) what’s happening.

The context is that some kids are rafting down a river. One kid measures the depth of the water:

Another kid measures the total distance they’ve traveled:

I’m apprehensive because there is a LOT of vocabulary used to describe the features of these functions that my students are either only somewhat comfortable with, or straight-up have never even been taught. Part of this is because of instructional decisions that I made earlier in the year.

I found module 2 to be incredibly challenging to teach, because it assumed that students had mastered middle school content standards that frankly many of my students have never been exposed to, much less mastered. I found that a lot of the linear contexts were not well suited to developing proportional reasoning for students who have never been asked to reason proportionally before.

Critiquing module 2 really needs to be a blog post in and of itself, but suffice it to say that I never really solidified “domain” or “intercept” or some other vocabulary terms that are necessary for lesson 3.2 and are supposed to be mastered by the end of module 2.

When planning for 3.2, I had about 30 seconds in which I considered front-loading vocabulary so that I could ask students the content questions and preserve the wording of the questions used in the original MVP materials.

**But then I came to my senses and remembered that vocabulary words are meaningless if students don’t have a concept they’re already thinking about that they’re ready to attach the vocabulary word to.**

So, rather than telling students to “interpret/describe the key features (increasing, decreasing, domain, range, maximum, minimum, intercepts) of the relationship”, I’m asking the following questions:

**When**is the depth increasing?**When**is the depth decreasing?**How long**was Alonzo measuring the depth for? When did he start measuring? When did he stop measuring?- What is the
**range**of river depths that Alonzo measured? - What is the
**minimum**depth of the river? - What is the
**maximum**depth of the river?

By focusing on the word “when” in questions 1 and 2, I’m hoping to draw students’ attention to the *x*-axis when describing intervals of increase and decrease (they also saw this in a Warm Up last week).

I’m hoping that students’ answers to questions 3 and 4 will help lead to a more formalized definition of domain and range.

I’m planning to spend about a week on this lesson. Here’s the preliminary breakdown:

**Monday**

Introduce the context, notice/wonder about the table, begin working on the questions in random groups at #VNPS.

I highly doubt that we’ll have time to debrief on this day, but I’m hoping that kids will be able to make decent progress. Thus, I’m planning to have them copy their work from the whiteboards onto paper at the end of class so that they have a record of it the next day.

**Tuesday**

Ideally, if students were mostly able to finish answering the questions on Monday, I’ll give them some time at the beginning of the period to make posters displaying their work. The reason I’d like the work on posters rather than whiteboards is so that they’ll have a (large) record saved for later in the week when we’re discussing the analysis questions involving both the table and the graph contexts.

Once their posters are made, we’ll discuss the answers as a class. This is where I’m hoping to motivate the words **domain** and **range** (and maybe **interval??**).

A note about whole-class debriefs: depending on the class, these have sometimes been **incredibly **painful, with me feeling like I’m pulling teeth trying to get kids to listen to and engage with each other. I think they might focus a little more if they have something to **DO** when other groups are presenting their ideas, so I’m going to have students fill out the following note organizer:

I’ve never used this structure before, so we’ll see how it goes!

**Wednesday**

I’m currently planning for us to spend some time noticing and wondering about the graph, and then have kids start working on the interpretation questions at #VNPS. Alternatively, depending on how Tuesday’s debrief goes, I might want to spend some time on Wednesday solidifying vocabulary words.

**Thursday**

At this point, I feel like it’s hard to predict because it’s so dependent on how Tuesday and Wednesday shake-out, but I’m anticipating some combination of debriefing the graph questions and/or solidifying vocabulary.

**Friday**

Most likely this will be spent working on the follow-up analysis questions at the end of the lesson. By this point, I should be able to use the vocabulary and wording in the original MVP materials.

ALSO, I’m finally going to take a few minutes of class time to do something that I’ve been meaning to do forever: The Mathematicians Project. This is an awesome idea that the inimitable Annie Perkins had to help students see themselves as mathematicians by learning about mathematicians other than old white dudes.

I wanted to do the Mathematicians Project earlier this year, but felt a little too overwhelmed with being at a new school and implementing a new curriculum. But then I’ve watched in horror as we deal with the consequences of having blatant racists run the country, and I decided that it really was time to start the Mathematicians Project (among many other things!).

Since I’m starting the project at the beginning of Black History Month, I’m going to begin by focusing on Black mathematicians, and this Friday we’ll talk about Katherine Johnson (played by Taraji P. Henson in Hidden Figures).

I plan to continue the project for the rest of the year, and definitely want to highlight Latinx (particularly Central American), Arab (particularly Yemeni), Chinese, and Filipino mathematicians, because those are the primary demographics of my students.

Here’s my blurb on Katherine Johnson:

Word Doc: The Mathematician’s Project

PDF: The Mathematician’s Project

And here are the materials I have so far for lesson 3.2:

Word Doc: 1.29 MVP 3.2 Floating Down the River

On the Monday at the end of period could you take a photo of each board & print it up for the. To have the next day? Saves them copying all their work to paper which sounds time consuming. Just a thought.

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Yeah, I’ve tried that. Some of my “boards” are actually windows, and they don’t photograph well. I’ve had students copy down their work before, and it actually doesn’t take too much time (just a couple of minutes). This is my first year doing VNPS on a regular basis, and I haven’t quite figured out a perfect system to save work from one day to the next.

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