# Summary

Another big evening of sharing resources and challenges created by the teachers, plus further exploration of Dave Youngs’ Fascinating Triangle mathematical microworld.

# Resources

Slides

Two flavors: PDF, Keynote

MATHCOUNTS

Workout 2. Official handbook is here. This evening we’ll spend a little more time than we usually do working on problems and sharing solutions.

Estimation 180

Days 51-60, here we come! In particular, we’ll look at Day 51 (soda capacity) and Day 52 (glass vase capacity). The rest of the challenges from Days 51-60 are here:

Just like last week, after completing these two official challenges, teachers will share the estimation challenges they created for homework.

Course Themes

Arithmetic to algebra (#1) and four representations (#5).

The Fascinating Triangle

Here’s the game plan for today:

Visual Patterns

A third week of sharing our own Visual Patterns, followed by a journey into two (basic) quadratic patterns (which we didn’t actually have time for last week):

Big Ideas in Algebra

Last week we ran out of time (again) and didn’t have an opportunity to discuss the Session 3 reading assignment, or the various comments teachers in the class left on the Session 3 post. We’ll carve out some time for that discussion in Session 6.

# Assignments

We take a break from reading and “create your own” assignments to focus nearly all of our attention on the Fascinating Triangle. In addition to spending another hour or two delving into one or more extensions, teachers will write a 1-2 reflection on the exploration process, plus “appendices” with “scratch work selections” of their explorations and findings.

# Summary

While proportional reasoning will factor into some of what we do in the future, we’re shifting ahead to one of the second themes of the course: arithmetic to algebra. Aside from a few of the usual activities (Estimation 180, Visual Patterns, Graphing Stories, etc.) and a few rounds of sharing our own creations in those categories, the major new piece tonight is an AIMS activity written (by Dave Youngs) called The Fascinating Triangle.

# Resources

Slides

Two flavors: PDF, Keynote

MATHCOUNTS

Warm-Up 4. Official handbook is here.

Estimation 180

Onward to Days 41-50! I couldn’t resist the Giant Wheel (Day 41) or Little Man Stadel standing in front of a giant tire (Day 46). Here’s a look at the rest of the challenges from 41-50:

After completing two of Mr. Stadel’s challenges, teachers will share the estimation challenges they created for homework.

Course Themes

Arithmetic to algebra (#1) and four representations (#5).

(Turns out I wasn’t a liar!)

The Fascinating Triangle

Three years ago when I first taught this class (when I had even less of a clue as to what I was doing than I do now), I taught half of the content and Dave Youngs taught the other half. During his portion he developed the idea of algebra as generalized arithmetic with the use of a series of activities/explorations. The Fascinating Triangle was one of those activities, and there are more patterns and connections in this little problem than I thought possible.

I love the “topic” listed on the teacher resource page:

Graphing Stories

As with today’s Estimation 180 challenges, we’ll explore two “official” challenges (Elevation, since nothing beats watching kids endure intense dizziness for the sake of mathematics; Distance from Camera, for the wonderful and stark contrast with Distance from Center of Carousel). Afterwards, teachers will share and discuss their creations in small groups.

Visual Patterns

A second week of sharing our own Visual Patterns, followed by a journey into two (basic) quadratic patterns:

In the weeks ahead, as we transition to course goal #3 (Expressions and Equations) we’ll begin watering the seeds planted by all of these visual patterns to simplify/expand/factor expressions, identify equivalent expressions, and solve equations.

Big Ideas in Algebra

We ran out of time last week and didn’t have an opportunity to discuss the Session 3 reading assignment, or the various comments teachers in the class left on the Session 3 post. We’ll carve out some time for that discussion in Session 5.

Calling it a “reading assignment” isn’t entirely accurate. However, you’ll do some reading to get started, and I imagine some of the “missions” will involve reading as well.

Whatever it should be called, the assignment is this:

Step 1
Go to http://exploremtbos.wordpress.com/

Step 2

Step 3
Get excited!

Estimation 180 (#2)

Another round of create-your-own (one or two) estimation challenges. Again, they may be inspired by what we’ve done in class, or what you see over at Estimation 180, but they must be your own invention. A few more details:

• Take a photo of something that can be estimated
• Use presentation software (Apple Keynote, Google Presentation, or Microsoft PowerPoint) to create a “question” slide and an “answer” slide
• Make sure the answer is not revealed in the “question” slide
• Share your slides with me via email no later than 11:59 pm on Monday, September 23

Visual Patterns (#3)

Do it again! That is, create one or two more 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.

# Math 753 • Session 4

Personal challenge for this post: Brevity. You’ll know by the end if I achieved my goal. 🙂

# Summary

A few of our “usual” activities,  annotating graphing stories, expansion of the “create your own” theme into new territory, and a fresh attempt at a proportional graphing challenge.

# Resources

Slides

Two flavors: PDF, Keynote

MATHCOUNTS

Warm-Up 3. Official handbook is here.

Estimation 180

I was tempted to do some diaper estimation (this is a regular part of my life at home these days), but I opted instead for Red Vines (Day 36 and Day 37). Here’s a look at what we’re skipping:

Course Themes

Ratios and proportional reasoning (#2) and four representations (#5).

I think I won’t be a liar if I promise that we’re moving into new territory next week (probably “arithmetic to algebra”).

Graphing Stories

I’m moving this section of the class forward in the evening so we’re sure to have enough time to discuss. (In recent sessions I’ve run short on time and had to cancel this activity.)

In addition to reviewing the first four graphing stories, we’ll annotate solution graphs using ThingLink (HT: John Stevens). Here’s a sample created (i.e., annotated) by yours truly (image credit goes to Dan Meyer, video credit to Adam Poetzel).

More details on this assignment below.

Desmos Proportional Graphing Challenge v2.0

Heading into a class or a workshop, my excitement level for a particular activity is often directly proportional to the amount of time I spent creating/preparing/tweaking. In line with that model, I was very excited to see how the first version of the Proportional Graphing Challenge would play out.

In a nutshell: It was terrible.

I’ll share my thoughts on how any why things went wrong sometime in the future, but for now I have a second approach that (I hope) deals with some of the weaknesses of v1.0.

One major shift: No more browser-tab juggling. Instead, students will have paper copies of the challenges as they use Desmos to match various graphs.

Here are the handouts: One, TwoThree

Visual Patterns

Last session I assigned our first “Create Your Own” visual pattern. I’m excited to see what everyone brings to class. We’ll do a pair/trade/solve/discuss model for one, two, or three rounds, as time allows.

I’m hopeful that this mixing of ideas will lead to even more creative patterns in future sessions.

Big Ideas in Algebra

Last session’s reading assignment included a handful of blog post responses to the previous week’s reading assignment (Grant Wiggins’ “bashing algebra” post). No new reading assignment for this week, but we’ll carve out a space to discuss how last week’s reading is shaping our own “big ideas” list.

Proportion Play

I originally thought we wouldn’t work through every Running Game challenge as last week’s solving session culminated in a great look at a variety of solution approaches to the second half of the Day 5 Challenge.

However, after trying the Day 7 Challenge with my own students, I’m convinced that there is still some untouched, discussion-rich territory to explore in the upcoming challenges. We may still jump ahead to one of the super challenges in the next couple of weeks, but for now I’m curious to see how teachers attack Day 7 and Day 8.

Nothing official this week. However, I invite you to explore one of the blogs you’ve come across in recent weeks if you find yourself with 30 minutes to spare one day this week. Or try one of these amazing blogs:

Estimation 180 (#1)

Create one or two of your own estimation challenges. They may be inspired by what we’ve done in class, or what you see over at Estimation 180, but they must be your own invention. A few more details:

• Take a photo of something that can be estimated
• Use presentation software (Apple Keynote, Google Presentation, or Microsoft PowerPoint) to create a “question” slide and an “answer” slide
• Make sure the answer is not revealed in the “question” slide
• Share your slides with me via email no later than 11:59 pm on Monday, September 23

Annotate a Graphing Story (#1, #2)

The first annotation should be completed in class. The steps for each annotation are the same.

Something to do once:

Things to do each time:

• Select a graphing story from here
• Watch one of the videos
• Carefully sketch your solution by hand (consider using pens, colored pencils, and/or markers)
• Take a photo with a smartphone