Techstravaganza Resources

Desmos and Statistics! Resources from the AP Statistics Reading “Techstravaganza” – June 2019 in Kansas City, Bob Lochel and Leigh Nataro


PCTM 2019

I am proud to be the program chair for the 2019 PCTM Conference in August, with my good friend Sue Negro.

The preliminary lineup of speakers appears in the file below. With Keynotes by Dan Meyer and Robert Berry, a Desmos pre-conference the day before, and our first ever trivia night, it’s going to be a great 2 days in Harrisburg!

Register today and get all the details:

Golfing with Linear Equations

For the first time in many years, I am teaching a College Prep Algebra 1 class with a fantastic group of 9th graders. Nearing the end of our linear functions unit, my colleagues and I discussed a desire to have some sort of culminating activity. And while I have used drawing projects often in some courses, in algebra 1 such tasks have often left me feeling unfulfilled. Too many horizontal and vertical lines for my liking I suppose.

I recalled reading about a potential golf-related task on twitter. To be honest, I don’t recall whose exact post provided the inspiration here (note – I am thinking it was Robert Kaplinsky or John Stevens, but I may be wrong. If anyone locates a source, I’ll edit this and provide ample credit), but it felt like a game-related task could provide by the strategy and fun elements which tend to be missed by drawing tasks.


The goal – write equations of lines which connect the “tee” to the “hole”. Use domain and/or range restrictions to connect your “shots”. Try to reach each hole in a minimal number of shots. Leaving the course (the green area) or hitting “water” are forbidden. All vertical or horizontal likes incur a one-stroke penalty.

On the day before the task, the class worked through a practice hole. Besides understanding the math task, there are also a few Desmos items for students to understand:

  • Syntax for domain / range restrictions
  • Placing items into folders
  • Turning folders on /off

practice hole

golfFor the actual task, a shared a link to a Desmos file with 5 golf holes. I tried to build tasks which increased in their difficulty. In practice, the task took an entire class period (75 minutes), and students worked in pairs to discuss, plan, and complete the holes. All students then uploaded their graphs to Canvas for my review, and filled out a “scorecard” which included “par” for each hole.  It became quite competitive and fun!



In the end, there is not too much I would change here. Perhaps add some more complex holes. I’d also like to provide opportunity for students to design and share their own golf holes, and study the “engine” which built mine.  I hope your class has fun with it! Please share your suggestions, questions and adaptations.

What’s Going On in This Graph

Today the New York Times Learning Network dropped the first “What’s Going On in This Graph?” (WGOITG) of the new school year. This feature started last year as a monthly piece, but now expands to a weekly release. In WGOITG, an infographic from a previous NYT article is shown with the title, and perhaps some other salient details, stripped away – like this week’s graph…


Challenge your students to list some things they notice and wonder about the graph, and visit the NYT August post to discover how teachers use WGOITG in their classrooms. Here are some ideas I have used before with my 9th graders:

  • Have groups work in pairs to write a title and lede (brief introduction) to accompany the graph.
  • Ask tables to develop a short list of bullet points facts which are supported by the graph, and share out on note cards.
  • Have students consider how color, sizing, scaling are used in effective ways to support the story (note how the size of the arrows play a role in the graph shown here). This is a wonderful opportunity to think of statistics beyond traditional graphs and measures.

Invite your students to join in the moderated conversation, which drops on Thursday. Have your own favorite way to use WGOITG? Share it in the comments!



TMC Desmos Day – Stats Session

Today I am in Cleveland for 2018 Twitter Math Camp! It’s the Desmos Pre-Conference Day, and I am facilitating a session on using Desmos in Statistics classes. Below are many of the links and resources I plan to use – even if you are not in Cleveland with us, feel free to borrow from these resources.

Baseball Data Set

Comparing Data Sets and Summary Statistics

Regression Facts (Mean/mean point and slope)

Teaching the meaning of r-squared

“Release the Hounds” – my first attempt at random sampling

Participate as a student, Steal and Share

“Backpack Weights” – thinking about scatterplots (AP Stats)

Participate as a student, Steal and Share

Assembling the Model Solution

I use College Board released AP items often in my Statistics course. The problems are aligned to clearly-stated goals, and the solutions provide insight not only into the grading of AP questions but also allow students to study well-articulated explanations. You can visit the College Board Statistics website and explore. Jason Molesky’s website provides helpful guidance on using FRAPPY’s (Free-Response AP Practice…Yay!) as a formative assessment tool in AP Stats.

Each free-response solution begins with the “model solution” – the ideal explanation a student would provide for full question credit. It is not unusual for Statistics students to struggle with clear communication, and having students read and dissect the model solution can be helpful in strengthening statistical arguments. A few times this year, I have used the model solution as a formative assessment tool with an activity I call “Assembling the Model Solution”.

Here’s how it works – start with an AP Free-Response question with a narrative aspect. Today, I chose a problem which requires students to interpret a P-value, from 2009:


The model solution contains a number of non-negotiable elements: a conditional probability, a reference to smple results, and the “extremeness” of results.


Next, I took the model solution as broke it into small, strategic “bites”. At the same time, I added some parallel distractors and a junk phrase or two.


Then, use a paper cutter and slice the Word document into phrase slices, and paper clip together. All students then received the problem and the slips of paper, with the challenge to assemble the model solution for part a of the problem.


The conversation were rich, and the teams mostly debated the salient aspects of the problem apprpriately. The biggest points of debate and incorrect solutions came from:

  • The difference between “sample” and “population” proportions.
  • The assumption of sameness in the treatments as the conditional aspect of P-value.

I have used this strategy a few times now, and continue to tweak how I provide the slips of paper. I’m also looking at digital options, but I like the social aspect of moving the slips of paper. The method is not ideal for everything in AP Stats, but there are a few areas in our curriculum where this fits in nicely:

  • Sampling and experimental design
  • Conclusions for inference procedures
  • Describing distribuitions.

You can download my file for this activity here.  Enjoy!

  • Credit to Jon Osters and the AP Stats glitterati who rightfully pointed out that my original post spelled “Yay!” incorrectly.

Today, Nothing Worked Well…and That’s OK

My 9th grade class has a quiz on statistics concepts tomorrow – standard deviation, interpreting graphs, outliers and the normal distribution. It’s a real cornucopia of stats ideas! To review, today’s class goal was to collect class-wide data using a fun applet, share using the collaboration space in OneNote, use a website to assess the data, and write our statistical summaries. A fun day filled with stats fairies and pixie dust! Here was the lineup:

  • shapesCollect data using Shapesplosion – an online game (think the old Perfection Game) developed by folks from Grinnell College. The plan was to play with, and without color. Aside: it’s OK if you disappear for a while to play with this site, it’s super-fun!
  • Share data using the collaboration space on OneNote.
  • Use the web apps to make graphs and produce statistical summaries.

This is what I had in mind….Here’s what really happened

  • Shapesplosion didn’t work – while I rehearsed the site on my laptop, it didn’t work for the kids. It was a Flash issue, and stopping to figure this out wasn’t in the cards. After a few minutes of hemming and hawing, I settled upon a far less fun data collection idea: Tell me a temperature you deem “cold” when you go outside, and one you deem “hot”. Not nearly as sexy as the time data I wanted…but hey, I needed a data set.  But at least we have data until…..
  • ArtOfStat was glitchy and wasn’t playing nice with copy/paste from OneNote. Kids are getting restless, we haven’t done much stats review, and I am definitely starting to lose my “big” class.

manuel.gifSo, what do you do when a lesson goes south, your objective is slowly slipping away and the kids smell chum in the water?


It’s not the kids’ fault when your plans go kaput. You may feel like some yelling is in order, but breathe, calm down, and be honest about what went wrong.

Student learning can’t be compromised because things go south. “There’s no time” is an easy out when we get rushed, but maintaining lesson fidelity is far more important than rushing to get to “stuff”.

Maintain clear expectations. Eventually all of my students were able to review some, and I had to alter my plan of attack. But stopping class, making sure we were all on the same page and understood the statistical expectations was necessary.

It won’t be the last time stuff goes wrong….roll with it…and laugh along with it.