# Math 753 • Session 2

If you’re just joining us, check out the background to this whole experiment, as well as the Session 1 post.

# Summary

We’ll begin with some problem solving and estimation to warm up our brains (complements of MATHCOUNTS and Estimation 180). The majority of our activities in this session will focus on the following two course themes:

#2: Ratios and Proportional Relationships)

#5: Four Representations: Numerical, Graphical, Algebraic, Verbal

Additionally, we’ll begin digging into the CCSSM Standards for Mathematical Content (what I’ll refer to from now on as the “CCSSM Content Standards”).

# Resources

Slides

If you want ’em, get ’em here: PDF, Keynote

MATHCOUNTS

We got our wheels turning by working through problems from Warm-Up 2. Need the handbook? Get it here.

Estimation 180

I’ve really enjoyed working through every challenge in my fourth period class this year (we’re on Day 16 on the 16th day of school!). We don’t have enough sessions to do the same thing in Math 753, but I want the teachers to have a sense of the types of challenges we’re skipping over. I’ve provided a two-slide preview of the Day 1-10 and Day 11-20 challenges in the hopes that they’ll be drawn back to them later (either on their own or with their students).

Our challenges for Session 2: Day 13 and Day 14

CCSSM Content Standards

Our first real venture into the content standards for CCSSM. After briefly discussing the Four Big Ideas in Algebra conversation that started with Grant Wiggins’ 100th blog post, teachers will work on this:

The Running Game

I’m excited to bring the next pair of Running Game challenges to the class, partially because the challenges increase slightly in difficulty with each pair of days, but also (and primarily) because I have a shiny new handout.

Our scheduled challenges: Day 3 and Day 4

Visual Patterns

In the first session we explored several proportional relationships. (Check the Session 1 slides for specifics.) In this second session we’ll branch out to look at patterns involving a steady rate of increase with a slight shift away from simple multiples. For example, instead of 3, 6, 9, 12, etc., we might look at 4, 7, 10, 13, etc.

If that makes no sense, check out the Session 2 slides.

In last week’s session I introduced a half-baked task based on caloric content of beverages at the In N Out soda fountain. The task was mediocre, but the context (in my opinion) had some merit. With that in mind, I’ve revamped the task. The focus now is on making connections among multiple representations.

The slide deck contains a few potentially useful images, but the real goods are here:

Students will work in small groups (2 to 4, ideally) to cut out and then match the various representations contained in each packet of “ingredients.”

Graphing Stories

Water volume (by Esteban Diaz-Ibarra) and Distance from center of carousel (by Adam Poetzel).

Compliments of course to Dan Meyer and BuzzMath for the excellent resource.

Grant Wiggins (author of Understanding by Design) recently started a conversation, in his 100th blog post, no less, about the big ideas in algebra. The key passage:

Here is a thought experiment: can you identify 4 big ideas in algebra, ideas that not only provide a powerful set of intellectual priorities for the course but that have rich connections to other fields? Doubt it. Because algebra courses, as designed, have no big ideas, as taught, just a list of topics. Look at any textbook: each chapter is just a new tool. There is no throughline to the course nor are their priority ideas that recur and go deeper, by design. In fact, no problems ever require work from many chapters simultaneously, just learning and being quizzed on each topic – a telling sign.

Your task (if you’re in Math 753, or following along at home):

1. Read the post and all of the comments. (Get a beverage and a snack ready; there are quite a few.)
2. Spend at least 24 hours with the ideas jostling around in your brain.
3. Add your own voice to the conversation by posting a comment, either on Wiggins blog, or here.
4. Things to discuss might include (a) your own list of 4 big ideas, (b) ways in which your list is being reshaped as a result of our class and the discussion started by Grant Wiggins, (c) questions you’ve always had about the big ideas in algebra, (d) questions you never knew you had until now, and (e) anything else that comes to mind as a result of the reading assignment.

Bonus task (this kind of bonus, not the “points” kind):

• Never used Twitter? Get your toes wet by exploring Grant Wiggins’ timeline. Keep your eyes out for new threads and clarifying comments in the “big ideas in algebra” conversation.
• Don’t worry if you get distracted and fall down a few unrelated rabbit holes. Part of the beauty in the conversations on Twitter is that you can find millions of different topics, discussed at varying levels of intensity, and they’re often just a click or two away.

1. While reading Grant Wiggins I could not help but smile and agree with so much of what he was saying. I had the experience of going through Algebra courses here in the US and in El Salvador. I had to take algebra twice not because I did not show proficiency the first time, but because the US would not honor my Algebra course from El Salvador which added to my frustration with the subject. I have always questioned why Algebra seemed so abstract and pointless. I could not identify the big general ideas of the course. I think that if you would have asked my 14 yr old self what Algebra taught; I would have responded, “how to isolate X.” Which I now understand is not the point. So why is Algebra such a pointless subject?

I agree will what Wiggins had to say, it is simply taught out of context. Now my questions are many. So really, What are the big ideas in Algebra? What does Arithmetic do, that Algebra can’t and vice-versa. Should Algebra be taught as a focus of patterns and generalizations? After reading the blog I’ve decided that one of Algebra’s big ideas should be Real World Application.

I could not help but wonder the following: