It’s been a great week in my probability and statistics classes. I’m not sure why I’m pleasantly surprised. This time of year it’s absolutely essential that we engage kids in meaningful mathematics and when we do, they respond well.
Tuesday, after assessing expected value, we moved to tree diagrams and conditional probability.
Wednesday, I used Nrich’s In a Box problem to create some discussion about dependent and independent events.
I started with a bag with unifix cubes and had them do some experimenting to see if the game was fair. What I love about this problem is that the initial answers that the kids come up with are usually completely wrong. It really allows the teacher to identify the misconceptions. Additionally, this problem is so easy to extend. Simply have the students come up with a scenario of ribbons that creates a fair game. Most will come up with something like 2 red and 2 blue. Have them test their theory, find out it’s wrong and then test another. Even when they find the magic combination that creates a fair game, there is still the task of generalizing the results that’s challenging.
Thursday, I totally stole Andrew Stadel’s 4! lesson. What a great intro to the idea of factorial. Last trimester I used IMP’s ice cream bowls and cones, which I still might refer to. I felt like having a few students up in front at the beginning got everyone on the same page at the same time. It was completely awesome to see the different methods for solving this. I love the repeated reasoning here:
Plus, opportunities to use animal counters in HS math are scarce.
What’s the most pleasing about this week is that I think that this group’s conceptual foundation of these concepts is more solid than it has been in any previous year. We still have practice to do, but I feel like they have made a good connection to what their answers represent. In the past, my formula driven instruction didn’t bode well for retention of the concepts. I’m more hopeful this time around.