Super Six 2.0

After reading the FRQ’s from 2023, I saw an opportunity to write a new version of the Super Six review questions. If you are not familiar with this resource, the idea is simple, but I think effective. I carefully select six FRQ’s, in this case from 2023 and 2022 exams. For each problem I retain the original question and then add more (and more, and more!) parts until all the first semester topics have been covered.

For this new version, I read through the CED as I wrote. Thus I hope that my coverage of the topics in Units 1-4 is very thorough. I am also pleased to use an Investigative Task for one question. It is an accessible IT and a solid question for students to work on their careful communication.

As a number of people expressed an interest in using these questions for a first semester review on units 1-4, I left out unit 5, sampling distributions. However, it was simple to create an addendum with a few extra questions for unit 5. See below.

As of the time of this post, no one has edited my work. Thus I am confident that typos will be found. I’ll gather input for about a week and then post version 2.1.

I hope you find this resource helpful. If you appreciate the way I approach AP Stats, you or your students can always pick up a copy of 5 Steps that DeAnna and I work on year after year (and that Corey also added so much great material too).

But most of all, I trust this resource will be useful to a lot of people. I had a great time creating it. Enjoy!

Edit: My friend Jeff found a couple of typos. Now updated to version 2.1

Edit 2.2: minor edits

• Super Six 2.2 (Word)

• Super Six Key 2.2 (Word)

• Super Six 2.2 (PDF)

• Super Six Key 2.2 (PDF)

• Super Six Unit 5 Addendum

AP Test Prep

I have assembled three different tools that are pretty useful for cumulative review.

• The Nifty Nine: 9 quizzes in AP Classroom, with one multiple choice question per section. This forms a reasonable coverage of much of the AP stats curriculum. A good start before students take a full practice exam.

• The Super Six: 6 old FRQ’s with extra parts added. These 6 questions provide a very thorough coverage of topics prior to inference.

• Name that Test: Old FRQ’s arranged in sets of 12. Students start by naming/identifying the correct inference procedure for each problem.

Funko Pop and the CLT

I have been a fan of using real datasets to teach sampling distributions for quite some time. Several of my friends have helped me along the way, especially my buddy Jeff E.

This google doc will launch my current draft of the new lesson. Question #7 is especially rough at the moment. Note that you will need to create a google form for students to send their statistics to you. If you know how use response validation, use it make sure students give you only numbers.

I used the eBay seller research tool to grab data on 2500 Funko Pop sales. The query resulted in 2.7 million items sold for an average of $33.71. However, I did not have the coding skills necessary to dump all 2.7 million data points into a spreadsheet. I grabbed 2500 using a Chrome extension scraping tool and you can see the parameters of my “population” as you work through the activity.

Need lessons?

Here is one way to teach AP Stats.

Summer 2021

If you're looking for an AP Summer Institute, I would be pleased to meet you! Here are my three institutes for this summer.

Boise, Idaho

In person!! June 22-June 25

AP for All--Colorado Education Initiative

July 13-16--virtual delivery

AP in the OC

July 26-30--virtual delivery

My summer Institutes will offer:

• Thorough coverage of the CED

• Activities, both in-class and virtual, to increase student understanding and engagement

• A host of resources to improve your lessons

• Ideas for improving access and equity

• Insights into AP scoring guidelines and improving student performance on the exam

Regression Project

Here is my regression project for distance learning. Word. PDF.

Enjoy!

Projects

I’ve been using projects instead of tests as my primary assessment tool.

Here’s the first project (will open as a new google doc in your drive). This project is examining two categorical variables, finding marginal and conditional percents, and looking at independence.

Here’s one version of the quantitative project. Nothing new here! Just making parallel boxplots and comparing them, etc…

I use StatCrunch. And Canvas. These projects could instead be directed to free tools like StatKey and Stapplet pasted into a Google Doc.

APSI-summer 2020

I will be presenting at five summer workshops. As this is the summer of distance learning, you can sign up for any APSI that interests you! It definitely won’t be the same as being together in the same room, but I am going to work hard to transition my materials to a combination of synchronous and asynchronous learning.

Here is the information.

LAUSD teachers only, June 16-18. (not an official APSI)

Florida, June 29-July 3

Fairfax, Virginia, July 6-July 10

Sacramento, July 13-July 16

Orange County, July 20-July 24

Course Description

This AP Statistics Institute will prepare new teachers to launch their course with a strong foundation and will also supply experienced teachers with fresh ideas to take their course to the next level. Over the 30 hours of a/synchronous instruction, participants and the instructor will work together towards the following goals.

• Complete coverage of the statistical content in the CollegeBoard course description

• High quality classroom activities that reinforce student learning

• A thorough examination of AP scoring guidelines and extensive tips for maximizing

  students’ scores

• An introduction to AP Classroom and other CollegeBoard resources

• A robust discussion of methods for improving access and equity

  And new, for 2020!

• A thorough overview of distance teaching websites and tools

Mock Some More

Alright. One last time. I wrote another exam this weekend. I like the Poke Bowl problem a lot. The other problem is OK. I made this one REALLY long. And then right after I finished it, a sample problem came out from CollegeBoard that is not so long. But I still want my students practicing writing until they run out of time. Your mileage may vary. Here’s the PDF, the Word, and the Pages versions. I start in Pages (because I have not spoiled my new MacBook with MS Office…. yet…) so if the Word version is wonky, I apologize.

I have called these exams B and C because I made Mock A by combining Josh’s Encouragement problem with 2014B #2.

Finally, my good friend Jeff Eicher has also been busy making Mock materials of all sorts. He is graciously letting me share them with you all. They are in this cloud drive. Help yourself.

Good luck to everyone!

Mock Exam

I made a mock exam to match 2020. Use as you’d like. There are solutions and a few teacher notes. Enjoy.

Thanks to my friend Jeff for editing help!

Edit: The answer to #2e is incorrect. It should be (56/75)^4. Sorry about that!

Edit 2: NOPE! #2e is 1 - (19/75)^4 = 99.6%. Thanks Steve! So sorry everyone!

Mock Exam (Pages)

Mock Exam (PDF)

Mock Exam (Word)

Even more super?

I added extensions to a few more problems. I added extra questions to 2005B #3 and #4. And I also wrote some instructions and extras for Name That Test, set A. I am assigning set A on Thursday. Students will name the 8 problems for this year’s test (skipping 3 and 9) and then do what is on the PDF below. I am trying to help them focus on inference problems that are not heavy on calculator use. The work will be due the next Tuesday.

Enjoy!

Edit: A small typo in #3 (less, not greater, in part f, has been fixed).

2005B #3 Super Edition

2005B #4 Super Edition

Instructions for Name that Test Set A

More Super?

Someone noted that that Super 6 are similar to this year’s AP exam. Each question takes one context and asks students to use various parts of the curriculum and apply them. This is not unheard of on the AP test. But this year we know that both of the questions will draw from at least two portions of our course.

With that in mind, I have decided to make more super problems for my students.

Here’s the first one. There is a key. I do not plan on writing rubrics for the extra parts I create. I hope you find it helpful.

And thanks to my friend Jeff E for inspiring me to work on this!

Super 6

A few years back I wondered if I could review the entire AP Stats course with only a few problems. So I took six old FRQ’s and I kept adding parts until I covered the entire course, up to inference.

Given that the 2020 AP test will have FRQ’s that will be longer than normal and will pull from various pieces of the course, all using the same context, it seems these problems are especially useful right now.

Super 6

Super 6 Key

Name that test

When surveyed, AP Statistics teachers state that picking the right inference procedure is the second toughest task they face (probability is the toughest!). To that end, I have developed these documents, which I affectionately call “Name that Test”. It is fun to use a little Herb Albert and the Tijuana Brass and introduce a naming activity as if you’re a game show announcer. YMMV. Enjoy! I’ve found these documents to be very helpful.

Inference Organizer

Inference Organizer Key

Name that Test

Name that Test FRQ’s

Power Dominos

These dominos were created using ideas of Dave Bock. DeAnna MacDonald and I then worked together to make those statements into a series of dominos that students have to assemble in order.

I find it helpful to have students write a pair of hypotheses to accompany this setting (e.g, Ho: p = 60% pain relief from a drug treatment) and then to discuss what a Type I & II error, and power would be in this context. This context matches the instruction sheet that is part of this document.

These statements are challenging for students. In fact, I think this activity is one of the most challenging I give my students all year!

A three page PDF of this activity is attached here.

As always, I place this activity at mrmathman.com/stuff (see the folder 06b_Inference Concepts). There is a PowerPoint document there that can be used to introduce this activity.

You will notice that there are numbers on each of the dominos. This enables the teacher to quickly check student answers. The digits “spell” the famous phone number from the song “Jenny” by Tommy Tutone. If you enjoy music in your classroom like I do, you can start the activity/day with “I’ve got the power” and then transition to “Jenny” during the activity.

A Crash Course in Curves

From 2012 to 2018, CollegeBoard released seven consecutive AP Statistics exams. On those exams, there was not one question about non-linear data. Thus it is with good reason that most of us have relegated this topic to the bottom of our priority list. But with the advent of all the new resources at AP Classroom, I wanted to teach this topic, very briefly, when I taught regression. Thus I developed the attached lesson. Its goal is simple: introduce this topic with enough depth so that students can answer AP questions about this topic.

Enjoy! As always, I welcome your feedback.

Non-Linear Regression Crash Course

The AP Test 18

I told my students that I would write a blog post about the AP exam. We didn't have any school days together after the exam. So here goes. This blog post is written both to them and to any teacher that might read this, so it's a bit of mess. But you'll figure it out.

Overall I thought the 2018 AP stats exam a bit heavy on probability and mathematics this year, and a little too light on the topics that students really learn in an intro stats course.

Problem one (regression), number four (2-mean t-test), and number five (more below) were the type of questions that I think students who really work hard in AP Stats course should know how to do well. I especially liked number five, which I graded for four days. 

Number five had three parts. The first asked students take two medians and decide which of them belonged to two different histograms. I was really impressed with the different explanations that students used. Some counted into the median. Some made a really nice argument that compared the skewness, the means, and the medians. That was impressive. Part two asked students to calculate a weighted mean. That's an important idea. Finally part three asked students to use the histogram to find a probability. Unfortunately, many students used normality instead. In fact, most students did this (there's a teaching point here, probably worth a separate post). I'm really curious to see how my students answered this question.

Numbers 2 & 3 were a combination of probability, bias, and math/algebra. If you are strong at math, you probably figured out a lot of these problems. If not, they were tougher. We did not spend a lot of time on tree diagrams this year (that's probably worthy of another post), which was the best strategy for number 3. Hopefully that didn't put too big of a dent in my scores this year.

Number 6 ended up being too difficult for most students. The mean score was about 0.33 (out of 4). Thus if you did well on this question, it will definitely help your score. But if you didn't (I'd estimate that at least 75% of students scored zero) then it won't hurt your score.

Overall, this was not my favorite exam. However, I do think my students still scored well. Many of the items on the test we covered in class very thoroughly. And I'm also betting that many of students figured out more of the challenges than they suspected. We'll see on July 5!

Test prep

I am going to post a daily blog for my students as we prep for the AP Exam. I thought some of you might be interested in following. It will be very specific to my classroom and the materials that I have. But if you're new to the course it might give you a window into one teacher's test-prep ebb and flow.

I'm a little hesitant to share this, because this blog will continue some of my most honest test tips to my students. I've already had to admit once that I was lazy and taught them to say something that might end up costing them rubric points. But recently my friend John Stevens  (@Jstevens009) reminded me that all teachers feel like they're still figuring things out. So I suppose that admitting my failings is a fine thing to make public.

You can find the blog at: mrmathman.com/testprep

A note about my materials. I give my students a booklet with old AP FRQ's and MC. The FRQ's have the year on the problems, but to make life easier I labeled the problems. 1997 is test A, then test B for 1998 and so on. If you have any questions, feel free to drop me a line: jared@mrmathman.com.

Enjoy! 

Just do it

Yesterday I had a student raise her hand. She asked "Will there be a chance to raise our regression grade?"

If you don't have your grading system broken down by standards or units, you are missing out on this kind of awesome. Let me explain.

Notice what she didn't say. She didn't ask for extra credit. She didn't ask to turn in late work. She didn't ask for free points. She named a topic in the class. She asked me if she could have a chance to show me that she improved her learning on that topic (regression is a topic/unit in my AP Statistics course). How amazing is that? In my previous blog post I explained that I stopped trying to grade by standards and instead focus on units. Most teachers cover about 6 units and 6 big tests per semester. So even if you don't want to stop grading homework or adopt other SBG philosophies, you can still simply transform your classroom. Just change this:

• Homework = 15%
• Tests = 50%
• Quizzes = 15%
• Final = 20%

to this:

• Homework = 15%
• Exploring data = 15%
• Regression = 20%
• Design = 20%
• Probability = 30%

That is, remove your tests/quizzes/final/projects categories and replace them with the names of the units you will teach in a given semester. Yes, there is some messiness here. You might have to enter your final exam in four pieces. And you'll have to consider carefully how many points to makes quizzes vs. tests. And other conundrums. And, of course, this implies that you are going to pay attention to growth over time. And some how dive into your gradebook and give your students a fair grade that shows their growth over time. Not just average every score together no matter what.

But won't that be worth it? Wouldn't you love it if a student was worried about their grade and instead of begging actually asked you how they could learn more about a specific topic? I'd say its more than worth it. 

Standards, er, UNIT based grading

My blog is woefully incomplete. I have posted my journey with Standards Based Grading. My last couple of posts discussed problems. But never any solutions. For what they're worth, here they are.

The short description of how I manage to grade growth over time (which is the ultimate goal of Standards Based Grading) is to grade by Units instead of by Standards. To my friends who can keep track of 20 to 30 standards, more power to you! I can't do it.

But I'm reasonably happy with encouraging students to focus on units where they are strong and where they are weak. For a point of reference, here are some of the units in my AP Stats course:

• Describing and graphing categorical variables 
• Designing surveys and experiments
• Inference for proportions

These are bigger than standards. But they are topics that are grouped in one to three chapters in my text (Stats Modeling the World). And I can mark most of my tests, quizzes, projects, etc... as being in one of these units. Here are some of the ways I have implemented this idea.

• Quiz scores are replaced with test scores.
  • Quizzes are essentially formative in nature. When a student performs poorly on a quiz it is a signal that they need to study more for the upcoming test. If they do so and improve their understanding, then I think it is only fair if their quiz score is increased to match their test score.
• Students take a retest.
  • When a student is dissatisfied with their grade, we discuss which unit they have low scores. When I'm at my most organized, the gradebook is marked with a unit on each assignment so that students can identify this for themselves. Students come after school, do some practice work on this unit, and then (usually on a second day) take a reassessment. I often cap the reassessment at 80% because it was shorter and more focused than the full unit test.
• All students take a cumulative test.
  • Sometimes I give a two day midterm. Other times I specifically tell students which extra unit will be added to the current unit test. And then if students show growth over time, their past scores are bumped up. My buffet test continues to be a favorite tool along these lines.

How does all this happen in the gradebook? Not by any magic tool I've discovered! I make these changes manually. And often based on dialog with students. It's not perfect. But there it is. I think it is fair. And I've yet to find an easier method.

I've also switched to total points, instead of weighted categories. In my school's gradebook, I can use total points, but still give assignments a tag. And students see their percentage for each of the tags. So the tags are my units. And if I have an assignment that is a mix of all sorts of units, I can just tag it as an "assignment" and I don't have to stress about it.

So there it is. I like it. For today. For this year. Probably something different in the future, but right now this works for me.