Edit – March 13, 2014 – The original YouTube video I reference below has been removed. It’s better to section this one into pieces anyhow, and I have done that for you in higher resolution at the links in the February 25, 2012 update. Those links should be working. There’s also a less cluttered version of this entire task here: Basketball Free Throws
February 25, 2012 Update
Based on session feedback, I have broken the video into four parts, so you don’t have to keep hitting “Pause” and risk showing too much too soon. There was also the slight problem of the title of the YouTube video kind of giving away what was about to happen to poor Darius.
This idea is another I picked up at ISTE2011 in Philadelphia in a session on technology in math with Frank Sobierajski. Frank mentioned using the 2005 Conference USA championship between Memphis and Louisville in a math class. He didn’t flesh it out, but I immediately knew how I would use it. I remember the game vividly. As a basketball fan and a math fan, this one really speaks to me.
Before we get to it, consider the following question. One like it could be found in any of our Math 30 Pure textbooks.
A basketball player is successful on 72% of his free throw attempts. What is the probability that he makes at least two of his next three free throws?
The question is fine. We’ve all given similar practice questions to kids. But in this format, it is nothing more than practice on binomial probabilities. It evokes none of the emotion of sport. Is the player under pressure to make these shots, or is he just messing around in the gym? Does it matter?
This same question could be given before the students know anything about the binomial probability distribution, making it a rich learning through problem solving experience. In the textbook format above, though, students would not be remotely compelled to struggle with it long enough to get a solution. But if you present it in the format I describe below, I contend that students will be hooked. They will want to know if he can make at least 2 of 3 shots, and will invent binomial probability on their own. Try it.
In the frame of the 7 steps of learning through problem solving, here is how I would use it before students have been taught anything about binomial probabilities.
- Play the first 0:17 of this video. Consider downloading it first, and changing the title, because the title kind of gives away what is going to happen. Pause, and make sure the students understand the context and the magnitude of the situation. This is a conference championship game. The winner will go into the NCAA tournament of 64, and the loser’s season will end. There are 6 seconds left. Memphis, in blue, has the ball and are trailing by 2. Once students understand the context, play the video up to the point where Darius Washington steps up to the line for his first free throw, and the announcer says, “For the season – 72%”. Make sure to pause it before he shoots the first shot. Make sure students understand what is going on here. Some don’t know basketball rules. Make sure they understand that he will get three shots, and each shot is worth one point.
- Ask the students what they wonder about. I suspect they will wonder who won.
- Have students make a prediction. Let the discussion go on and I’m confident they will talk about the three possible outcomes (If he makes 3, Memphis wins. If he makes 2, they go to overtime. If he makes 0 or 1, Louisville wins).
- Ask them if they require further information. I would make sure they heard the relevant parts of the video, which are the facts that Darius Washington is a 72% free throw shooter on the year, and that he is 2/3 in the game.
- Let students work on the math. Who wins? What are the probabilities of each of the outcomes?
- Play the video to 1:40, so students can see him make the first shot. Repeat steps 3-5. Does Memphis have a better chance of winning now? Play the video to 2:00, so students can see him miss shot #2. Repeat steps 3-5. Play the rest of the video.
- Share student solutions. How did the predictions (and math) change after each shot? Why did the math not match the outcome?
Based on Season 72%
Before first shot: Memphis win = 37.3%, Tie = 43.5%, Louisville win = 19.2%
After first shot: Memphis win = 51.8%, Tie = 40.3%, Louisville win = 7.9%
After second shot: Memphis win = 0%, Tie = 72%, Louisville win = 28%
Before first shot: Memphis win = 29.6%, Tie = 44.4%, Louisville win = 26.0%
After first shot: Memphis win = 44.4%, Tie = 44.4%, Louisville win = 11.2%