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 6 (I NEED TO TEACH)

There’s so much that I want to say, but I’m not sure how much of it I should say on a public forum. I didn’t have any lessons to teach today. It was another day of answering questions and giving input for those who wanted it. Some brief notes from the day:

1) I NEED TO TEACH. Sitting and watching someone else teach in a way that is the antithesis of everything you believe about teaching and learning is frustrating. Really really frustrating.

2) I did manage to pick up an activity to teach tomorrow on probability and its meaning. It’s not a favorite activity of mine, but it’ll give me a chance to grow.

3) I’m really proud of the group of teaching I’ve been working with. They’re building lessons about statistics and they’re asking great questions. These 25 teachers really want to grow as professionals and it makes me proud to be a teacher.

4) It still amazes me how unprepared a lot (the term “a lot” may be hyperbole but I’m sensing a lot of discomfort) of our teachers are to teach statistics the right way. I feel like we’re trying to fill a needed ocean of statistical knowledge with a leaky bucket.

Probability starts tomorrow…be prepared!

Two Area Problems

Geometric solids week is coming! Prior to starting a unit on surface area and volume, I wanted to spend a couple days working on their concept of area. I pillaged a couple of text books for some ideas.

Problem One:
Introduction to Area Meaning Field Dimensions Lesson_1

We ended up having a great conversation about the best way to answer the question. They immediately wanted to tell me what they knew. I showed them the results from the poll here on my blog (thanks to all of you who voted), and asked them to vote themselves:

Introduction to Area Meaning Field Dimensions Lesson_2

Then I asked them to justify their votes. Some students started to go into defining what larger meant (a really important idea). They wanted to give me that they “knew” that the soccer field is larger, but did not have a mathematical justification. Finally they asked for some measurements:

Introduction to Area Meaning Field Dimensions Lesson_3

Some calculations ensued:

Introduction to Area Meaning Field Dimensions Lesson_4

They eventually decided the area of the soccer field was larger. A student made a great point that the football field is longer and that we had to make sure we were clear about how we defined “larger.”

Problem Two:
Which Pizza Deal is Better_1

These deals were taken straight from Papa John’s website. They immediately wanted measurements.

Which Pizza Deal is Better_2

Which Pizza Deal is Better_4

I wanted my students to explore which deal was better, and sent this problem home with them to work on. The work you see on the slide did not come easily. They came back with thoughts that I wasn’t expecting. I felt like this question was tailor made for area, yet a few of my students didn’t go there at all. They wanted to make the argument that they get “more inches of pizza” with the larger pizza deal, so it was worth it. We took some time to explore if an extra inch of pizza is the same whether you start with a one inch pizza or a fifty inch pizza:

Which Pizza Deal is Better_6

They decided that that an extra inch isn’t always the same in a circle. Eventually, with more probing than I expected, we got to the idea of a unit rate. I know they’ve seen unit rates and they’ve seen area, but I don’t know that they’d seen them together before. To everyone’s surprise (including mine) the unit rates for both deals works out to cost about $0.06 per square inch of pizza. Therefore, there isn’t a better deal…only how much pizza you actually want!