Guess My Rule w/ Probability and Venn Diagrams

I’m on my second time teaching through our district’s intro level Probability and Statistics course. The first probability standard is very basic information, like:

• writing out the sample space for a scenario
• all probabilities in a scenario must total 100%
• probabilities are between 0% and 100%
• creating Venn diagrams for scenarios
• calculating probability of simple events and their complements

Pretty quickly, it gets boring just doing practice problems or even Desmos activities for this basic information. We’ve done some textbook style practice (which I’ve converted to Desmos for covid reasons and will probably keep even post covid crisis) and the Desmos Intro to Probability and Last Taco activities. We played BLOCKO to introduce the sample space idea and talk about why probability might be useful. I was searching for another fun activity to do to kind of drive these ideas home, and maybe get more practice with Venn Diagrams…and I remembered Sarah Carter’s Guess My Rule activity that she has used to develop groupwork norms in her classes. Putting the cards in and out of the circles made me think Venn Diagrams, so I thought I could adapt the cards and rules to my purposes!

(side note, we are still being very covid cautious, all my students are masked, and they were able to stay fairly distanced in this activity. Research shows that covid is NOT spread through surfaces so I felt good about them both touching the cards and paper, and my class is also only 8 students so I felt good about our risk level and our ability to spread out in the classroom)

For the first part of the game, I essentially took Sarah’s original activity instructions that she’d adapted from a book and adjusted them for two rules instead of one, so they would be placing the cards in a traditional Venn Diagram (or technically, Euler diagram because they’re including the “outside of the diagram” option). I challenged students to play two rounds each where they drew two rules and didn’t show their partner, and their partner handed them cards to place in the diagram. We played a practice round on the board first where I taped the cards to the diagram on the board and had the whole class guess. I think that was important to them understanding the rules.

Then I set them free to playing. Unfortunately, I don’t have any pictures because we had an odd number of students in class that day so I ended up pairing up with one student! This helped my students really understand all the different areas of a Venn Diagram by truly using their logical thinking skills to decide where each card needed to go, and to hypothesize about the rules based on what was in the diagram. A few students I could tell were struggling with the Venn Diagram concept – one student needed all 36 cards in the diagram before she could guess the rules! Most of my students were getting really competitive, though, and would yell across the room “Miss Mastalio he’s too good at this! How am I supposed to win!” when their partner guessed after 3 cards. I had students who haven’t done an assignment in weeks getting super invested in this game!

When I do this again, I might put more rules in about only being able to make one guess per card added to make it a little tougher. Another complaint I got was that by their last round, they’d memorized all the rules in the rule deck so guessing was easier, so I might brainstorm some new rules to add to the deck before doing this again. The small set works for Sarah’s groupwork game, but I do think it makes this one a bit less impactful.

As you see in the instructions, after the final game I had them place ALL 36 cards in the diagrams based on the last two rules they’d drawn, and then calculate P(A), P(B), P(A^C), and P(B^C) based on their rules. This was a good refresher of the probability notation we’ve been working on and what a complement was.

After that, I put some challenges on the back of their diagram sheet. These were optional, but almost all my groups chose to do at least one of them. I told them they could get creative with their rules and they certainly did!

I don’t know why “only shapes” amused me so much as a rule!

“flat sided shapes” is so creative!

Several of my students really benefited from physically placing items in a Venn diagram and I think they’ll be more prepared to do so on paper moving forward. This also made them think more critically about probability instead of just “take this number and divide it by this number” which I think will help them as we move into more complicated probability rules.

If you would like the instruction slides / worksheet I used, go here. For the worksheet, I just printed slides 3 and 5 front to back. You can find the files for the cards and rules in Sarah’s post, and I’ll try to come back to this post and add my additional rule cards when I get around to doing that! (or, I’ll probably just add them to that Google Slide deck)

Anscombe’s Quartet Desmos Activity

Well, I last wrote a post on August 18 – almost 8 months ago. I’m not interested in explaining why or apologizing or anything – anyone who has been teaching this year already knows why.

But, I finally created something new that I’m proud of and would like to share!

I’m teaching a course called Probability and Statistics, which is our district’s intro version to this material. It covers:

• data collection (sampling methods and study types)
• one variable data visualization (dotplots, histograms, boxplots, measures of center and spread)
• two variable data visualization (scatterplots, regression, residuals)
• basic probability rules (what is probability, addition, subtraction)
• counting principles (permutations, combinations, binomial probability, geometric probability)

We’re working on the two variable data visualization right now, and my students first semester kind of struggled with the concept of whether the least-squares regression model was a “good fit” for the data or not. Basically, I wanted to focus more on residuals – what they are, what we want them to look like, and why it’s important to check them. Anscombe’s Quartet immediately came to mind as a good way to do that, but I didn’t just want to be like “well, here’s these four datasets that all have the same regression equation but look how different they look!” I wanted to do a slow reveal sort of deal, where they really got to play with the data before seeing it, and learn the lesson of why residuals are important.

I also was kind of ready to challenge my Desmos computation layer skills, since I’ve been casually watching most of the #DesmosLive videos this year. Before this, I had done a little bit of auto checking answers and putting sentence starters in text boxes with computation layer, and made an interactive slider for my conferences reflection activity, but not much more. This took a lot of googling and patience to make it look how I wanted it!

Here’s an overview if you’re teaching this activity. I walked through it with my class kind of slide by slide, since I know my students are not practiced in reading and processing long text directions on their own, but they still did all of the noticing/wondering on their own and the class level discussion was good. If you have students that are more self-sufficient in their abilities to read through directions independently, this could easily be assigned as homework or an independent in-class activity. I made certain answers “share with class” so they would still see some classmate responses as they worked through it.

Students already knew how to: make a scatterplot in Desmos, describe the association visually (strong/weak, positive/negative, linear/exponential/quadratic), and find/interpret r (correlation coefficient). We’d also talked about “lines of best fit” and how to read the regression equation off of Desmos’ output.

The Anscombe’s Quartet Desmos Activity

(the info below is also in the Desmos “Teacher Moves” for the activity)

Slides 1-2 are a typical notice/wonder structure. Note that we had already created scatterplots before doing this and described the visual association, which gives them more things to notice or wonder here.

Slide 3 refreshes their memory on the correlation coefficient and asks them to predict which dataset the regression equation belongs to – note that they HAVE to put responses for both items here or later on the activity will withhold certain information

Slide 4 has them test their prediction, and slide 5 asks if they were correct (obviously, spoiler alert for Anscombe’s Quartet here…they’re all gonna be correct). They must also submit a response on slide 5 before the activity gives them the info to move on.

slide 6 asks them to test a different dataset, at which point they should probably get suspicious…and slide 7 asks them what they’re noticing or wondering at this point. This would be a good point to pace your activity to if students are working independently, maybe snapshot some responses while students are working, and have a discussion at this point before going on.

slide 8 reveals some information, but only if students have submitted all responses they were asked to up until this point!

on slide 9, they get to look at all 4 scatterplots and think about which ones would be well fit by the linear model with this information added. My students said 1,3, and maybe 4 at this point, so the only one they really eliminated was 2, but they were ready to get more information because they sensed that only one was really a good fit.

slide 10 introduces residuals (you could do this activity after already introducing them, but this also explains it from scratch). Once again, some information is withheld until the student correctly calculates this information.

finally, they get to see the residual plots and decide once and for all for which datasets the equation is a good fit on slide 11.

slide 12 asks them to summarize what they learned. One of my students said “don’t judge a book by its cover” which I loved.

And then slides 13-14 are a wild extension activity involving the “Datasaurus Dozen” which is a similar collection of datasets where all the summary statistics match but they look really different – students are challenged to make their own dataset that also fits in the collection. I had a lot of fun doing this myself, but my students were all too overwhelmed to attempt it, which is fine. It would be a great challenge for AP students or that one really motivated student in your intro class, and maybe to pair up students for.

Let me know if you use this activity and if you’d change anything from how I set it up!