# Blog Archives

## Day 14: Makin’ It Real

AP Statistics is a great course to use data that matters to my students. I asked one of my football player students to get the stats from the last couple of games. Here is the opener I put together using these stats:

It was a nice way to use z-scores in a meaningful way! How have you used kid-stats to help your curriculum come alive?

## Day 171: Infographics Project Starting

I am soooooo excited. Today my AP Stats students start their end-of-year project. I just love to see how everything comes together for them. Every year I try a new medium in which they complete the project and as I posted earlier, this year students will present their results in an infographic.

I spent some time with a social studies colleague of mine who did infographics with her freshman. She shared some best practices she gained when doing the project with her students. One of the key shares was that she had her students use Piktochart as the free medium for actually creating the infographic.

It is easy to use, entering or importing data is easy, there are pre-made templates and once the infographic is complete, it can be made into a slideshow presentation so my students don’t need to create a powerpoint to present their findings.

As part of the set-up I had two basic guidelines:

Ask and Answer an Intellectually Interesting QuestionFor the first part of your application project, your pair will describe a particular problem that can be addressed through the primary statistical techniques we are studying this year—namely, confidence intervals and hypothesis testing, and linear regression.

- Determine an intellectually Interesting Question and at least 5 supporting questions
- Identify the population of interest, needed sample size, etc.
- Design an unbiased survey/method to collect data that answers your question
- Collect the data (you will hand in the raw data collected)
- Analyze question using statistical inference

And then:

Creating the InfographicYou should use appropriate data visualizations and other visual elements (colors, shapes, lines, typography, whitespace, and so on) in ways that enhance your infographic’s potential for communicating your work on the project. Your infographic can be any size or shape, but it must be of sufficient resolution to display well on the course blog. Your infographic should be designed so as to make sense to a fellow student in an AP Statistics course. Thus, you may assume that your audience is familiar with the material we have covered together as a class this year.

- Keep in mind that the central idea of the study should be prominent feature of the poster.
- Infographic Title should be informative
- Use statistical principles studied in this course: data displays, numerical analysis, inference and decisions (interpret p-value)
- Reveal data at several levels of detail, from a broad overview (at a distance) to the fine structure (closer inspection reveals more intricate information).
- Use supporting questions to guide how to display various aspects of your data to convince audience
- Graphic’s legend should clearly match to the graph
- Results of inference for main question as culminating evidence: connects statistical results to the context of the problem.
- Harmonious and strategic use of color and design elements. No trivial or extraneous information, etc.

I am using to collect information from the students about their partner choices, their main and supporting questions, hypotheses, data collection methods, etc. More to come in the following days!

## Day 166: Real-World Conics

This week-end, after reading through my students’ exit slip answers to this question: What questions do you still have about the three conics we have studied this week, I realized from their comments, that we needed to actually see where conic sections are useful in real life, not just in my “geeky math world.”

So today we did some applications:

It was so satisfying to hear students exclaim, “Is that why satellite dishes have that funny thing sticking out beyond the dish?! and “I see how the ellipses foci actually show up in real life!” The most precious comment was “oh, that makes so much sense now!”

## Day 140: Matrix Applications

How can one use matrices in real life….let me count the ways!! On Tuesday we explored how matrices can be used to change the contrast of photos, determine ranking of candidates in an election and count paths between objects.

Yesterday we delve into counting paths and raising matrices to powers based on a lesson I found at Engage NY: NYS Common Core Mathematics Curriculum.

Today we looked at Markov chains and transition matrices. Lots of oooo’s and ahhhh’s. Love it when the math’s coolness shines through to the kids!

## Day 135: Rock, Paper, Scissors Anyone?

Do you remember playing Rock, Paper, Scissors as a kid? As an adult? Against a computer? I’ve seen various lesson plans around RPS and probability of winning, but none seemed to fit the level and sophistication I was looking to use with my AP Stats class. Well the New York Times science section had a great article Rock Paper Scissors: You vs. the Computer. If you haven’t played the computer, its a kick and I highly recommend it!

Then I remembered reading Bob Lochel’s post Rock-Paper-Scissors and Two-Way Tables. And found his second post, Chi-Square Tests: Rock Paper Scissors. I liked the idea, but the gold came in the response sections of both posts. Doug Page shared a worksheet he has developed for using the Rock, Paper, Scissors applet and also a Google Form for having students submit results. I stole blatantly!

Since my students use the iPad, they can’t access Flash animations, so I had to assign the play as homework. I hate to do this because so many kids just don’t follow-up and complete the assignment – and we don’t get the data we could if we collected in the classroom. And the same happened with this class, but at least we had enough to continue with the introduction to Chi-Square test of Homogeneity. I think next year, they will use their own data rather than the class data…or compare their results to the class results. Will have to think more about this next year.

I required the students to calculate the components by hand – they need to know where the components come from and how they are related to the final χ² statistic. Once we finished this problem, we tackled another problem using the calculator. Because of the hand-calculating of the components earlier, they then understood what the expected values matrix meant and the components matrix.

How do you incorporate electronic experiences to develop engagement?

## Day 133: Is it Fair?

Last week I was perusing Twitter and saw Bob Lochel’s post about “clay dice are drying.” I wanted to know more, so Bob posted a blog entry Statistics Arts and Crafts about his Chi-Square GOF activity. We are starting GOF today in AP Stats, so no time to have my students make their own die this year (sigh, would have loved this experience for them…but there’s always next year).

I loved the idea but how could I simulate the basic idea of a non-regular die being or not being fair?! I racked my brain when suddenly I remembered my recent purchase of these dice. I’m not sure the photo shows how irregular these dice are, but they really are!

Using Bob’s basic plan, I adjusted to fit these cute little puppies. Each group got to choose a differently shaped but irregular die.

Through the activity, kids learned about the parts of a Chi-Square GOF situation, about components and about the shape of a Chi-Square distribution. I think my statisticians were surprised that the oddly shaped die was actually fair. Love this aspect of the activity! What seems to be true isn’t always true…and statistics helps us look at our world through an unbiased lens.

I do plan to get some air drying clay and having my students make their own dies next year. I think if students try to make their die fair and it isn’t (or is) is much more motivating than using pre-made dice.

## Day 104: Thinking About the Future

How do I make Precalculus relevant to my high school students? We study the mathematics of finance! In particular, we use the Present Value and Future Value formulas for situations that are meaningful to teenagers who are looking forward to becoming independent. In comes the Partner Finance Activity.

Students are introduced to the scenario: You have just graduated from college and managed to land a job (hopefully using the degree you just earned.) You are ready to buy your first dream house or condo. I have the students use the randint( function on their Nspires to determine the range of house values they qualify for. Then they define some terms such as FICO score, points, and ARM. Then they use the internet to search for a home that fits their range.

Once they have a house chosen, they determine the type of loan and calculate their monthly payment.

## Day 1: The Road Less Traveled…

I came across the idea of “using images that illustrate statistical ideas” at statpics (via a Pinterest image) and thought I must include experiences like this regularly in my class. As I was on my Saturday morning walk with my pup, I was struck by how one side of the path seemed to be used much more than the other side and the edges and middle almost not at all….and wondered, “why was that?”

So on the first day in my AP Stats class, I showed them this photo and asked, “What can you tell me about this path?” I wanted to get a sense of how they could think about and talk about data in a different way. At first they were dumbstruck…didn’t even see the “data” that had been collected – I suspected this would happen. But very soon, with a little prompting and Think-Pair-Sharing, they were able to tell me lots of things that revolved around the Who-What-Where-When-Why-How idea and some statistical ideas of frequency and comparing two data sets. Interestingly, I was in a social studies class later in the day and found the same 5W and How lesson was going on…it’s so great to see how different curricular areas are still connected with key critical content. What physical situations have you seen that could spark a conversation around the implied mathematical ideas and how would you use them?