# Month: September 2013

## First Period

Near the end of today’s AP Calculus lesson, I fired up a new web browser and intended to type desmos.com. We just discovered the product rule and were applying our newfound knowledge to this:

I accidentally ended up at google.com and saw this:

Well, we had to play. So we did. 🙂 And if you’ve already played a bit yourself, you’ll know it didn’t take long for us to get hooked.

It also didn’t take long for me to start wondering about how this could be turned into something mathematical. I mean, student engagement (with the game, at least) was instantaneous. Could I somehow leverage that into an engaging activity?

I think I can. In fact, I think I can turn this into something worth exploring in Algebra 1, Algebra 2, Precalculus, Statistics, and even Calculus. All I really need: more data.

## Second Period

During second period I work primarily on organizing/building/developing curriculum for our math department (all two of us!). I also oversee a few students’ independent study coursework (mostly in AP Statistics, plus a few in Honors Precalculus… highly capable students whose schedules didn’t work with the time we regularly offer the course).

I grabbed a few kids as they walked in the door and pointed them toward Google on their laptops. As they began playing, I started working on a data collection handout and formulating how I might turn this into an activity.

Here’s how it works:

1. Partner up
3. Play a few practice games
4. Once you’re familiar with the game, decide who will smash and who will record (of course, in fairness to your fellow man, you really ought to alternate these roles every few games)
5. Learn the attack styles (All Out Attack, Delayed Attack, and Over the Top). Details for all of these are on the handout (link above, image below, video far below).
6. Select an attack style, and attack!
7. While the smasher is smashing,the recorder will do his or her best to record the total number of candies that have spilled out after each of the 10 swings.
8. Ideally, students will play a game with each attack style (there’s room for one of each in the data table), and then trade roles.
9. (Since the numbers scroll/animate almost continuously—if you’re not terrible at the game—it’s pretty difficult to accurately record the number of candies for All Out Attack. I asked students to make their best estimate and most seemed able to handle it.

I then printed a few copies, and a few bits of data started rolling in.

## Third Period

A full lesson in Precalculus (third period) meant no room for messing around with Google’s birthday doodle. Too bad. Maybe next week (if the doodle is still accessible, which I believe it will be).

## Fourth Period

I carved out three minutes at the end of Algebra 1 (fourth period) to introduce the game to students, distribute copies of the handout, and invite students to play with a friend or family member at home. I have no idea if they’ll take me up on this. I imagine quite a few students will play this evening and tell me about their highest scores on Monday. And when I ask if they recorded any data… This.

## Fifth Period

We were supposed to work on corrections for our Chapter 2 Assessments. But we didn’t. We can do that Monday.

Today? Today was a day for data collection.

I thought students would need laptops since… you know… keyboard… space bar. As it turns out, Google’s one step (well, maybe more than one step) ahead of me. The game works on smartphones!

Me: “Okay kids, if you have a smartphone, tablet, or laptop, take it out. Go to Google.com. And in the name of mathematics, hit that piñata!

Students, without hesitation: “Okie dokie.” (Paraphrasing.)

## Lunch

I have no idea if this will be useless, but I made this video at lunch to introduce the problem. I was pushing to get it ready in time for my eighth period Precalculus class, so it’s pretty simple.

## Eighth Period

We wrapped up our lesson with about ten minutes left in class. I played the video (above), asked students to pair up, take out a device, and get cracking. They obliged.

Find a class, friend, spouse, neighbor, or stranger.

Play the game. Use all three attack styles, several times each

Record the data.

Send it to me. (There’s an awkward google form here, or you can just email me photos of the completed handout: mjfenton at gmail dot com.)

## What’s Next from Me?

If I even get a little bit of data, I’ll turn this into an activity or two for every class I can in the 7th through 12th grade sequence. I can already think of a few tasks for Algebra 1 through Calculus, but would love to hear your ideas if you have any. What should we do with all of this data? Drop a line in the comments and let me know.

# 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
• Add annotations to help tell the story of the graph
• Share your annotated image with me via email (copy any paste the URL into an email)
• Here’s the URL of my example: http://www.thinglink.com/scene/435893843829719042

Visual Patterns (#2)

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 3

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?

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).

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):

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

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.

# 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.