Teacher and coach

Here’s a brief description of how I used a bunch of great stuff I found online to create two video lessons for the probability unit in my math class (Common Core Math, Year 2).

**1. What did I want?**

I wanted my students to learn how to use probability tree diagrams to model and solve certain probability problems, specifically ones that were difficult or impossible to solve using the tools we had worked with so far (e.g., the Multiplication Rule, the Addition Rule, Venn diagrams, etc.). I also wanted them to gain an appreciation of how tree diagrams could be used to increase their conceptual understanding of certain problems, including more complicated probability problems such as, for example, the False positive paradox, which I thought might be a compelling segue into a more in-depth understanding of conditional probabilities. Plus, it would be good to have some enrichment type stuff for my more advanced students, and this seemed like a good possibility. Finally, I wanted my students to learn how to use the Multiplication Rule and the Addition Rule to determine if two events are independent just given numerical probabilities about the events.

If you’re thinking that this seems like a LOT of stuff to try to do in a single lesson, that’s exactly what I thought. But that was okay. I didn’t have to do all of this in a single lesson, and it’s always nice to have an idea of where you want a particular topic to go eventually, even if you don’t get there right away.

**2. Ask the internet**

I had nothing on tree diagrams, so I asked my buddy google for some suggestions. After a little bit of clicking and surfing I found the following:

http://www.mathsisfun.com/data/probability-tree-diagrams.html – this one (really good) web page by the folks at mathisfun.com eventually became a set of reading notes, a set of guided notes, a video, and a set of practice problems on tree diagrams (see below).

https://onlinecourses.science.psu.edu/stat200/node/32 – How to determine if two events are independent using numerical probabilities only.

http://www.unc.edu/~rls/s151-2010/class13.pdf – contains a really good explanation of a False Positive type problem using tree diagrams.

http://college.cengage.com/mathematics/larson/calculus_applied_life/1e/resources/app_c/1021662_App_C4.pdf – contains some really good worked-out examples of real-world type problems that use tree diagrams.

http://www.classzone.com/eservices/home/pdf/student/LA212EAD.pdf – contains some good practice problems on determining if events are independent using numerical probabilities only; also another great example of a False Positive type problem.

**3. Put it together**

I initially put together a set of detailed “reading notes” and practice problems on Tree Diagrams (which I basically took straight from the mathisfun.com page above) and tried it with my honors class. (Honors classes are great for trying out new stuff because they don’t get freaked out if everything’s not completely polished.) Based on some feedback from them, I turned the detailed/reading notes into a set of guided notes and then created a video based on the guided notes.

I did pretty much the same thing for what became my “Independence & Conditional Probability” topic, using the other resources above.

After the dust had settled I had created two new lessons and added them to my class website, each with a video, notes, and some practice problems:

6-6, Independence & Conditional Probability: Video, Notes/Practice

Total calendar time to create all this was probably about a week; total actual time spent was probably about 3 hours: 30 minutes to find the stuff I wanted online, 2 hours to create/format the notes and practice problems, and 30 minutes to record and upload the two videos.

Note that all of this new material is far from perfect; I already have several things that I want to add/modify (more practice problems, more examples for the notes, a few things I’d like to change in the videos, etc.). But the important thing is that a few weeks ago I had nothing at all on tree diagrams and now I have something, and while I did have some stuff on independence and conditional probability, now I have something better.

Which is why I call this the evolution of a video lesson. It’s never really finished, in the sense that I’m always tweaking it to make it better. The most important thing is to create something; then you have something to improve on.

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