New here? Check out the background to this series before you dive in.

Summary

Once again we’ll get things rolling with some MATHCOUNTS problem solving and Estimation 180… er, well… estimation.

For at least one more week the primary focus will be on the following two course themes:

#2: Ratios and Proportional Relationships

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

We’ll also continue the “Four Big Ideas in Algebra” conversation.

Resources

Slides

Two flavors: PDF, Keynote

MATHCOUNTS

After two weeks of Warm-Ups we’re ready for our first Workout. Still need a copy of the handbook? It’s right here, it’s awesome, and it’s free.

Estimation 180

Nothing says mathematical reasoning like a couple rolls of toilet paper. In Session 3 we’ll work on Day 28 and Day 29 on the site. Here’s a look at the rest of what Days 21-30 have to offer:

Four Big Ideas in Algebra

We’ll spend a few minutes discussing our reactions to the Session 2 reading assignment (a Grant Wiggins blog post), including any affirmation, surprises, disagreement, new insights, or new questions that came up in the course of reading the post and its comments, and writing a comment of our own.

For now, we’ll leave the larger “Four Big Ideas” conversation alone until a later session.

The Running Game

I’ve tweaked the new handout a bit based on a comment from the class in the Session 2 Feedback Form. Here’s the latest and greatest version.

Our scheduled challenges: Day 5 and Day 6

Visual Patterns

No time for a new style of visual patterns (we’ll continue pressing forward in a week or two). For now I want to camp on linear growth a bit longer. Instead of giving a few new challenges from the website (or of my own invention), I have a “create your own” assignment for each member of the class. Details below.

Automatic Change Dispenser

On my way through the checkout at a local supermarket, I saw this:

I think the MTBoS is sharpening (or further twisting?) my brain, because I instantly wondered…

What’s the total value of those coins?

So I asked this on Twitter:

I've always wondered… What's the total value of these coins? What's your estimate? (cc: @mr_stadel) pic.twitter.com/rMpAXShV4T

— Michael Fenton (@mjfenton) September 7, 2013

I’ll add a full length blog post about how my thoughts grew from “Hey, this is a cool estimation task” to “Whoa, this could be a pretty sweet three act task if I don’t blow the presentation (like I usually do).” For now, check out the resources I’ve posted for this task over at 101qs.

Desmos Proportion Graphing Challenges

Earlier this year Dan Anderson, Justin Lanier, and I launched a website called Daily Desmos. Each day we (or someone else from our awesome and growing authoring team) creates one basic (er, well, not so basic) and one advanced graphing challenge. They’re fun to make and fun to solve.

(For more background, go here. For details about what’s next for Daily Desmos, go here and here.)

We recently had several discussions about how to make Desmos more useful to classroom teachers. One idea: Create a series of related challenges, intentional in sequence, progressing from simple to more challenging, and in doing so provide students with a sandbox for developing their graphing skills in an enjoyable, dynamic, exploratory (yet still somewhat structured) environment. (Sorry about that last sentence; it got a bit out of control.)

At any rate, because one of the major themes in Math 753 is proportional reasoning, and because we’ve been discussing creating a sequence of linear graphing challenges, I created a sequence of proportional graphing challenges (some might use the term direct variation). I’m waiting for feedback on the quality (or lackthereof) of this sequence. Once we’re happy with the quality and format, we’ll turn our attention to a linear sequence, then (probably) quadratic, and so on.

Graphing Stories

Since we ran short on time in the first two sessions, I want to revisit the first four stories in Session 3. Soon we’ll continue moving forward, and soon after that we’ll have an assignment where each of us (myself included) has to create our own 15 second graphing story (or two).

Reading Assignment

We’ll continue with our “Big Ideas in Algebra” discussion by reading a few responses to Grant Wiggins’ original post. Read the following (including all comments):

• Four Big Ideas in Algebra (by Patrick Honner, @mrhonner)
• Pretty Big Ideas (by Chris Lusto, aka @lustomatical)
• Pretty Big Ideas for Intermediate (Highschoolish) Mathematics (by Kate Nowak, aka @k8nowak)
• Grant Wiggins’ response to Patrick’s post

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

1. Read the four posts above, including all of the comments.
2. Spend at least 24 hours with the ideas bouncing around your brain.
3. Add your own voice to the conversation by posting a thoughtful comment, either on one of the blogs above, or on this post.
4. Things to discuss might include (a) your latest list of four big ideas in algebra, (b) ways in which your list is being reshaped as a result of reading several more perspectives, (c) new questions or confusion you have about the big ideas in algebra, (d) new clarity you have about anything related to this discussion, and (e) anything else that comes to mind as a result of the reading assignment.

Visual Patterns Assignment #1

Create one or two of your own visual patterns. They may be inspired by what we’ve done in class, or what you see over at Visual Patterns, but they must be your own invention. A few more details:

• Create a visual for Step 1, Step 2, and Step 3. (you may include Step 4 if you find it helpful or necessary.)
• Create each step by carefully drawing, using a computer, or taking photographs of patterns you see or build in the physical world. (I would love to see the latter.)
• Put Steps 1-3 (or 1-4) on a single sheet of paper (physical, digital, or both). Bring at least four physical copies of your visual pattern to class next week.
• Ideally, your pattern will fit the linear growth theme we’ve explored in the first few sessions.

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.

Soda Fountain Task, v2.0

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:

• Handout (one per student)
• Soda Fountain “Ingredients” (one packet per group)

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.

Reading Assignment

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.

For background, this.

Summary

Introductions, establishing course routines, discussing course themes, first round of recurring tasks/problems, proportional reasoning, graphing as storytelling, MTBoS shout-out.

Resources

Slide Deck

In recent workshops and classes I’ve been experimenting will pulling more and more of the resources I’ll using during a given session into a Keynote slide deck. It’s pretty easy to navigate around the Internet, but it’s even easier to progress through a set of slides. Also, preparing the slide deck in this semi-comprehensive way forces me to think more thoroughly through transitions from one activity to another and connections between our tasks each evening.

At any rate, the latest effort in this experiment is here, in two formats: PDF, Keynote

Math Counts

We’ll use MathCounts as a resource for our problem solving sets this semester. General information on this national middle school mathematics competition is here. Direct access to this year’s handbook (which contains over 300 problems) is here. (Note: I pulled our first problem solving set from the 2012-2013 handbook, but the new handbook is now available, along with a fresh site redesign.)

Estimation 180

For extended commentary on why I think Estimation 180 is awesome, check out my guest post over at Andrew Stadel’s Estimation 180 site. (For further evidence of my love for Estimation 180—imitation, sincerity, flattery, etc.—check out The Running Game and Proportion Play (details below).

Common Core State Standards for Mathematics (CCSSM)

We’ll dig into the common core standards more next session.

The Running Game

A series of bite-sized proportional reasoning challenges, with some new additions since we talked last week. More details coming later, but I think I’m done with “Running Game” challenges. In the near future I hope to add a second set of challenges, “Partial Produce.”

And I almost forgot! I have a new draft for the Running Game handout.

Visual Patterns

I love Fawn Nguyen’s Visual Patterns website. Her blog and Twitter are worth your time as well.

First, to bring Visual Patterns into my classroom, I’ve created a series of introductory challenges. They begin with simply proportional patterns, move into linear, then quadratic, advanced quadratic, and finally oblong and triangular numbers. I’m finding that with this set of sequenced training patterns in hand I can lead students of varying experience, age, and ability into the world of visual patterns. My ultimate goal is to turn students loose on the full set of challenges available on Visual Patterns, and with a few carefully chosen (or newly created) patterns I can do just that.

Second, I’ve tweaked Fawn’s excellent handout to provide students with more room to draw, sketch, etc., and I’ve added a fifth task (working backward from a given number of items to find an unknown step number). My handout is here in three formats: PDF, Pages, Word

(The file was made using Apple’s Pages, so I make no promises that the Word file preserved the formatting perfectly.)

In N Out Soda Fountain Task

In class we worked through an early version of this task, based on this photo taken a few days ago at an In N Out soda fountain. I know there’s a worthwhile task on proportional reasoning in there, and you can see my rough thoughts by looking through the slide deck. I expect I’ll revise this task later in the course (based in part on comments and brainstorming from our first session) and bring a new version back for further discussion.

For now, have a look at the slide deck to review what we explored.

Desmos

It’s free, it’s amazing. Did I mention it’s amazing? Oh, and it keeps getter better.

• Head over to the Main page
• Click through to the calculator
• Create a free account (you might want a Google Account while you’re at it)
• Experiment and explore!
• Not sure where to begin? Just start by clicking on everything you see.
• If you’d prefer a more structured introduction, download Quick Start Guide or the full length User Guide

Graphing Stories

Our fifth theme for the course (if you take my list in the slide deck over FPU’s list in the course catalog) will be exploring algebra through (and making connections between) four representations:

• Numerical
• Graphical
• Algebraic
• Verbal

We’ll explore graphs as data rich, contextualized storytellers, and Graphing Stories will serve us well in that effort.

Reason and Wonder

If you’re reading this, you’ve already made your way to my blog. Have a look around!

Reading Assignment

Nothing this week.

In 2010 I team taught a class in the grad math/science program at Fresno Pacific University. My teaching partner (Dave Youngs) was more a mentor than a colleague at that point, as I had only recently finished my journey through the masters in education program at FPU. I benefitted greatly from the opportunity to work side by side with someone who knew the ropes, and I enjoyed that sort of partnership (first with Dave, and later with another mentor, Richard Thiessen) for three or four semesters. Afterwards, I tried my hand flying solo through a couple of courses.

When my wife and I had twins in November 2012, I took a break from the adjunct instructor gig. The girls are almost a year old now (and diapers are expensive!) so with my wife’s full blessing and encouragement I’m back in the classroom. This semester I’m teaching Math 753, Concepts in Algebra, to a small (but amazing) group of teachers whose positions range second grade to middle school. Our first session was this past Wednesday (August 28).

This is actually the same course I taught in my first semester as an adjunct instructor, working side by side with Dave, but I feel like it’s brand new for two reasons. (1) I’m no longer team teaching. All of Dave’s expertise is now an email or phone call away, rather than right there in the room while I’m teaching. (2) In the three years since I first taught this course, my philosophy and practice (as a teacher of adults, as well as a middle and high school teacher of mathematics) have shifted more than a little bit.

Why Post on the Blog?

“Great Mike, thanks for sharing. Um… why are you sharing this?”

After each class session I’ll post a brief summary or reflection, a small collection of links to resources used or discussed in the class, and—more often than not—a reading assignment (in the form of links to articles and/or blog posts). My purpose for posting these sessions (and hence this background) is threefold.

1. I want the participants in the class to dip their toes into the mathtwitterblogosphere. I could easily share resources with my students another way (Moodle, Dropbox, Edmodo, Piazza, etc.) but by posting them here, I’m hoping to use my blog to draw them into reading more widely and exploring more deeply the strange and amazing community that I discovered back in March.
2. By making the course goings-on somewhat public, I’m motivated to design a better course than I might if everything we did in Math 753 remained hidden in our own little corner of the world. It’s not that I would just phone it in, but in sharing publicly I’m putting a bit more pressure on myself to create an even more meaningful course.
3. In the off chance that someone not in the class is interested in exploring what we explore… Well, have at it. 🙂

Links

These will all be dead links until the actual sessions have occurred (and the post-session writeup post has been written and posted), but eventually easy access to each session post will be found below.

Session 1 (August 28, 2013)

Session 2 (September 4, 2013)

Session 3 (September 11, 2013)

Session 4 (September 18, 2013)

Session 5 (September 25, 2013)

Session 6 (October 2, 2013)

Session 7 (October 9, 2013)

Session 8 (October 16, 2013)

Session 9 (October 23, 2013)

Session 10 (October 30, 2013)

Session 11 (November 6, 2013)

Session 12 (November 13, 2013)

Session 13 (November 20, 2013)

Session 14 (November 27, 2013)

Session 15 (December 4, 2013)

Session 16 (December 11, 2013)

Comments

I’ll close the comments for this post, but leave them open for the individual sessions (partially because I will share the course description/goals in the Session 1 post). If you have thoughts on how to make this experiment more useful to anyone involved, please share them. If you have recommendations for our reading assignments (articles, blog posts, books, Twitter chats, etc.), let me know. In the session posts, of course. 🙂