I just came back from the Teaching Math through Problem Solving 2 Conference which featured keynote presenters Jon Orr and Kyle Pearce (which was awesome!), and I am feeling newly inspired to do new and exciting things in my classroom in September, including spiralling a course for the first time (but more on that later).

This past semester I was happy to be teaching Grade 12 Data Management (MDM4U) for the second time. I focused as much as I could on using rich math tasks to help my students become critical thinkers. One of the best things I stumbled upon was Bob Lochel’s blog. While there are many resources out there for Grade 9 and 10 math concepts, it was harder for me to find good posts about higher-level discrete math, statistics and probability, and it was a data management teacher’s dream to find a stats teacher with blog posts for days!

This 3-act task comes from the Amazing Race problem in this post by Bob Lochel – scroll to the heading “Statistical tales of the improbable”. This lesson focuses on the hypergeometric distribution. My students had already finished a unit on probability, and in previous lessons learned about the binomial and geometric distributions. Students should have some prior knowledge of probability and a good foundation on counting techniques (combinations in particular).

Here’s how this problem would look if it was in the textbook:

How many of your students have tuned out?

Now here’s the 3-act version:

### ACT 1

First, I played this video up until about 1:14 and had students write down: what do you notice? What do you wonder?

Here’s what one of my students came up with:

I wrote down some of my class’s ideas on the board:

### ACT 2

Next, I revealed some information to confirm what my students saw and heard in the video, and posed a challenge for them to solve:

My students had seen questions like this before in the Probability unit, but if you’re spiralling, all you really need is an understanding of combinations and some basic probability to be able to solve the problem. For those who finished quickly, you can offer follow-up questions:

- If a team unrolls 6 bales, what is the probability of finding
**exactly 2**clues? - If a team unrolls 6 bales, what’s the probability of them finding
**at least one**clue?

I then had students make a probability distribution table and graph:

Students then answered some questions about the problem they had just solved. You can do this as a handout, but my school does not use handouts so I displayed it on the board:

We took this up together and I classified these characteristics as defining features of the Hypergeometric Distribution. We talked about the importance of the trials being *dependent*, which was different from other distributions we had seen (binomial, geometric, uniform). Next, I challenged students to use the variables we defined to come up with a general probability formula P(X=x) for the Hypergeometric Distribution.

**ACT 3**

I didn’t have an Act 3 for this problem at the time, but if I were to do it again, I would print off 270 game cards which include 20 clues and 250 blanks and have a student draw 6 cards without replacement.

To wrap up my class, I had students check out this simulation:

Data Management is one of my favourite courses and I was a bit disappointed to find out I won’t be teaching it again next year, but I’m excited for new challenges. I will be teaching Grade 10 applied math (MFM2P) for the first time, and I will be spiralling! Will post more about it as I go!

Thanks again to Bob Lochel for the idea and problem for this post!

Oh and here’s my friend Julia (@MsFolino) and I at the conference with Jon Orr and Kyle Pearce!

EDIT: Meg Craig has corrected me on the rules of the Amazing Race and also suggested an idea for an extension to the problem, which I made into a Would You Rather math warm up: