SWBAT weigh possible outcomes associated with probability games that they create. SWBAT analyze decisions and strategies using probability concepts.

A quick peek behind the scenes of a few carnival games kicks off this real application of probability!

10 minutes

To roll out this event, I like to show the students a video clip. Thanks to YouTube and countless other websites there are a lot of probability videos at your disposal. If you are feeling really creative, go down to your local street fair this summer and take pictures of some of the games – this will add a personalized touch to the entry event of the lesson! After writing this, I never look at carnival games the same way again. I would venture the same will be true for your students. (Although they are still fun to play!)

I like using entry videos because they provide a unique element of authenticity to the lesson. Having an outside party deliver a project roll out or entry adds a new dimension, even if they say the exact same thing that you would have!

Below are two entry videos option.

Video option #1

Video clip option #2

After viewing these, I roll out the entry document describing the game designing task. As students brainstorm (MP1), they will likely refer to the videos. Allow them to make connections, however, I would steer them away from constructing elaborate ball-toss games like those shown in the video. Rather than saying “No, don’t do that” try to frame your responses with a mathematical context. For example, if a student wanted to build a game similar to the ball toss, then I would respond with the following questions:

- What variables will you have to consider?
- What elements of the game can you find a theoretical probability?
- What elements of the game will you struggle to account for?

In this particular game, and similar ones students will end up steering away from using it because it is difficult to mathematically account for all the unknowns. For example, is a softball all-star tossing the ball or is a 4 year old boy tossing it with sticky cotton candy all over his hand? These are GREAT mathematical conversations with your students that require them to make sense of problems and persevere in solving them!

Grouping Note (MP3): I group my students in like-ability pairs for this activity. I have found that this promotes collaboration and ensures that all students are actively involved in the entire process. Adding a third group member typically results in less production. In activities such as this, you will be VERY surprised by the quality of work that you get from students who do not normally thrive in a “traditional” setting! There is a lot of room for creativity, and the mathematics behind the probability calculations is not overwhelming.

15 minutes

This part of the lesson starts of with students constructing their *Knows/N2K’s . ***After** this is done like to provide my students with the project rubric to see if this answers any of their questions. Typically speaking, the rubric will allow the students to cross off approximately 40%-50% of their N2K’s. I don’t give the students the rubric right away because I feel it might cloud their creativity and I also like have students experience the sensation of a vague problem. Although it can sometimes be frustrating for students, this is more than compensated by how it promotes active questioning!

Most of the remaining N2K’s not addressed by the rubric will be content questions, requirements questions, and/or questions about the next steps in the problem so at this point a whole-class Know/N2K discussion is very appropriate. This helps everyone narrow their focus on the task at hand and clarifies any lingering questions. It is best to slow the students down and make sure that all of their bases are covered BEFORE they get so excited and start creating a game that won’t work, I can related to this, because it is exactly the type of student I was!

20 minutes

This last part of the lesson is where we brainstorm and approve game ideas.

Following brainstorming and idea approval, I initiate a "Critical Friends" session over the students proposed ideas. This helps them build on the framework of their idea, and helps ensure that it aligns to the rubric. Critical Friends is a classroom strategy that I use quite often, and it has also been attached as a video narrative. This process also helps the students recognize the tools that they have at their disposal (MP5).