# 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**

**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.

# Reading Assignment

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**

Sign up

**Step 3**

Get excited!

# “Create Your Own” Assignments

**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.