Mathalicious: Three Shots
This is another incredible lesson available at Mathalicious (this one is free). The lesson starts with a video of a real life basketball scenario in which Memphis is trailing by 2 points and has 3 free throws at the end of regulation. We scaffolded students through probability calculations as we slowly revealed the outcome of each free throw. This lesson has some great connections to Chapter 5 (independent events, conditional probability), but our focus was on developing the conceptual understanding of the binomial formula. In Lesson 5.3 students will be learning the binomial formula, but instead of simply giving them the formula, this lesson helps students to understand the components of the binomial formula. The best context for discussing the binomial formula is when calculating the probability of overtime.
So what does the 3 represent? It is the number of ways of making 2 and missing 1. This can also be calculated using a combination (3 choose 2). Discussing this idea with students is vital if they are to understand the binomial formula.
In the student handout, there is a big mental switch that has to happen on the back side of the sheet. Instead of thinking from the perspective of Memphis (the team losing), we now switch to thinking from the perspective of Louisville (the team in the lead). We told our students that we became the Louisville coach and we are trying to decide whether we should tell our team to foul or let the player shoot the 3-pointer. Question #6 on the handout is very challenging and is a good way to differentiate for your more advanced students, but shouldn’t be required of all students.