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(AC), and P(BC) 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!
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)
Mastalio. Math. Mavericks. 