First Homework Assignment

Alright.  We’re back online.  I know it’s been a while.

This year, it’s time to really revamp Algebra II.  I have to do a better job of advocating for thinking mathematically and persevering through problems.  So we’re going to start day one.

Here’s their homework assignment:

Mr. Cloud tries to be a healthy person and takes multi-vitamins daily.  He absolutely LOVES the gummy ones!

Here they are:


As he was finishing this bottle, Mr. Cloud thinks he was ripped off (he didn’t get what he paid for).  Here’s what he saw:


Circle One:

Did Mr. Cloud get ripped off?     YES         NO         Can’t Tell

Provide a well written justification for your answer:



So that’s it.  That’s the whole assignment.  And I’m going to leave this right here.  Feel free to comment and argue your point!



AP Statistics: How Many Penguins?

A little while ago, we began a unit on sampling and experimental design.  In the recent past, I have not done the shift from descriptive to inferential statistics any sort of justice.  Before exploring any sort of formal sampling methods, I wanted to have my students experience the idea of using a set of data to estimate a parameter.

I started the lesson with an example of this process that they’re familiar with:

5.1 Samples and Populations_1

My students were given a screenshot of this ESPN poll and I asked them to tell me anything they could about it (as well as ask any questions they wanted).  With a bit of probing, my students were able to map out the process/purpose of this poll:  ESPN wants to take a small group of fans’ opinion on who will win the NFC East and use that to generalize to the population (of which we never came to a consensus about).

Next, I wanted to put them in a situation where the process they described could be used.  I remembered that I had seen an interesting question while working with FCR-STEM facilitating a summer statistics workshop:

5.1 Samples and Populations_5

The premise is that this is an overhead shot of a section of Antarctica and each dot represents a penguin.  My students’ goal was to estimate the number of penguins.  First, I did a cheap method of getting some engagement…I had them guess how many penguins there are:

5.1 Samples and Populations_6

Then began the process of how to use the information we had quickly and efficiently. We discussed that, while it is possible to count every penguin, it was inefficient and really darn annoying to do so.  We devised a plan (or at least the class did): everybody chooses a square on the grid, we average those number of penguins and then multiply by 100.  Personally, I thought it was a good plan.

This is where the new material began for this unit.  We needed to discuss how each person would select their square.  A discussion of randomness and sampling ensued.  We decided that the calculator could be used for random digit generation and we could select rows and columns randomly:

5.1 Samples and Populations_7

Then, each student selected their square and converted that to a number of penguins:

5.1 Samples and Populations_8

We came up with a class estimate of 500 penguins.  As it turns out, that was a pretty good estimate:

5.1 Samples and Populations_9

The next few lessons are about designing proper samples of all types, and what makes a bad sample bad.  Overall, I believe my students have a direction for the next few months thanks to this lesson.  The only change I will make in the future would be to take away the grid from the first picture I should them about the penguins.  I feel like I led them too much.  I want them to come up with that idea themselves.

Summer Lesson Building (AP Statistics Defining Variables)

With EOC scores out and AP scores about to go live, it’s time to start building next year’s curriculum. I am moving forward on the assumption that I’ll be teaching the same preps next year (as dangerous as that may be). I’m posting these lesson plan ideas with the hope to open conversation and develop better lessons. Feel free to post any thoughts you may have:

The first day of school in AP Statistics will begin with this warm-up:
Chapter 1 Introduction_1

I’ve worked with this set-up before with a group of teachers at the Summer Statistics Institute. This question really led to some good conversation:

Chapter 1 Introduction_2

My hope is that the group can come to a definition of what a statistical question is compared to a mathematical question. Somewhere in that conversation, we’ll define what a variable is and the types of variables (categorical vs. quantitative).

Chapter 1 Introduction_3

Chapter 1 Introduction_4

This lesson is built around a MAFS 6th grade standard. I don’t know that my students have ever had a conversation like this one. I’m going to try to do a better job this year of not assuming that my students really understand the difference between mathematics and statistics, and what better way than begin day 1 with that conversation. There will be some practice:

Chapter 1 Introduction_5

Chapter 1 Introduction_6

Then, the rest of the period will be about routines and expectations for the school year.

Any thoughts?

Who is at Fault for This Car Accident?

**Disclaimer** Some of the images in this lesson are not of my own creation. I have borrowed them from Dan Meyer’s blog…although I am repurposing them.

The lesson began with this slide:

5.3 Intro to Radical Graphs Car Accident Problem_1 - Copy

We had a conversation about what we see. My students had to decide what’s important about the car accident and what’s not important about the car accident. Ultimately, the students boiled the question down to whether the van pulled out in front of the car and whether the car was going too fast to stop (just look at those skid marks!).

I asked my students how fast they think the car was going, and they give their guesses. To give my students some extra information, I give my students the following slide:

5.3 Intro to Radical Graphs Car Accident Problem_2 - Copy

My students decided some numbers would be nice:

5.3 Intro to Radical Graphs Car Accident Problem_3 - Copy

Then they wanted this information:

5.3 Intro to Radical Graphs Car Accident Problem_5 - Copy

A very insightful student asked a great question at this point: “Can we just use a proportion to figure out how fast the car was going?”

Another insightful student commented “We can do that if the relationship is linear.”

Needless to say, I was really excited about where the conversation was going.

I asked how could we tell if the relationship is linear. Crickets. I showed them the data again. Someone finally mentioned a graph (imagine…a place where a graph would be useful), so geogebra created us a scatterplot.

skid mark scatterplot

Someone yelled “that’s not linear!” I emphasized their point:

skid mark scatterplot linear

My students noticed that there were a lot of options in the dropdown menu for types of relationships and, after a few clicks, they settled on this graph:

skid mark scatterplot square root

As it turned out, the relationship was radical. My students used the equation to estimate a speed in the neighborhood of 70mph and decided that the car was going too fast.

Note: I guess I should note that the goal of this lesson was to graph square root and cube root functions. In all, this opener took about 15 minutes of class time. I feel they were 15 minutes well spent. Now there’s a context to when these graphs may be useful.

Note: I had to set the data up and ask the question that forced the input of the function to the be the length of the skid mark and the output to be the speed…otherwise, this doesn’t work.