Summer Lesson Planning: The Galton Board

Well, I’ve started planning some activities/interesting questions to add to my AP Stats curriculum.  I’ve noticed that my teaching lacks the ability to have my students see the normal distribution happen naturally.  Every year, I’m forced to have my students take my word that the normal distribution is…well…really real.

So, seeing that I’ve had some time to develop some lesson ideas (which is code for I get to watch The Price is Right)…and I remember seeing this:

Note: I’m going to come up with some binomial distribution lesson from this video too

I’ve taught workshops for teachers that involve probability, the normal distribution and the mention of galton boards (go ahead and click it…I made the hyperlink).  But the mention of the galton board was just that…a mention.  I wanted to have my students experience it!

I scoured the internet for an inexpensive (it is the summer afterall) galton board.  No such luck.  I tried to find a video on the internet that I could pull data from.  Even less luck.  So I made my own videos.

This is meant to be a ten minute #threeactmath inspired (gotta love Dan Meyer) activity.

It starts with:

Then, after some class discussion, they’ll find out there a total of 500 balls dropped.  Their job is to predict what will happen.

2.2 The Normal Distribution_3

The hope is to start making connections between the shape of the distribution and probability.  There are more ways to a middle slot than an end slot; meaning that there should be more in the middle.  The distribution should be symmetric (and we’ll discuss what would make it not symmetric).  Basically, building the idea of unimodal and symmetric for a normal distribution.

Then they’ll finally see the answer:

More than likely, my students won’t be correct in their guesses, but the conversation is really the important part.  I’m hoping to bring this back when we talk about binomial distributions/probability as well.  The more I write about this, the more I realize there’s some really rich discussion can come from this.

Please feel free to comment and discuss any thoughts you have.

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Summer Statistics Institute Day 7 (Back in the Saddle Again)

I’m back to teaching again!!…and I’m sure my participants are oh so excited.

Our new unit is about understanding probability. I want my students, my teachers and their students to understand probability as so much more than the probability of a red marble coming out of a bag. I want them to understand probability as a way to make predictions and drive decisions. So we started here:

brain

The focus of the discussion was on the idea of randomness and what should have happened. I kept emphasizing that their students will need to tackle the idea that what does happen and what should happen may not be the same thing. There’s a drastic difference the in the questions.

We started discussing numerical probability with this video:

We had a quick discussion about the “probability number line” and what different values meant.

Most of the lesson revolved around the following situation:

You and your partner have a bet. You are going to play a dice game and the winner receives $100,000,000. Each of you will roll one die. Next you will sum the two dice. If the sum is 2, 3, 4, 5, or 6, player 1 wins. If the sum is 7, 8, 9, 10, or 11, player two wins. If 12 is rolled, then the round is a tie and will be rerolled.

I asked the question of whether the game is fair. We simulated the game and calculated the theoretical probabilities. There was a lot of interesting discussion. We have a foundation laid for dealing with experimental and theoretical probabilities. We’ll see how they take the lesson in the morning!

Mr. Cloud’s Foul Shots

We are getting dangerously close to dealing with inference in statistics. We have been working for a while on sampling distributions for means and proportions and calculating probabilities for them. I wanted to give my students an opportunity to apply their probability calculations for a purpose other than answering a question on a handout, so I gave them this:

Mr. Cloud's Free Throws Lesson_1

Any athlete in the class immediately said “no way.” I asked them to defend their argument and someone asked me to prove it. We talked and they got to the conclusion that I couldn’t prove it, but they could disprove my claim. They wanted to see me shoot some foul shots:

This confounded them a bit. I only made 45% of my free throws. They couldn’t tell whether that was different enough from 50% to say my claim was wrong. Someone finally asked for a probability to quantify their feelings:

Mr. Cloud's Free Throws Lesson_2

There’s a 32% chance that I could be a 50% free throw shooter and make 9 or less out of 20. They concluded that probablity was too high and they couldn’t disprove my claim.

Hopefully this groundwork will pay off when we officially start inference on friday.