An AP Statistics FRQ for "Moneyball"

Since I had a few weeks of school after the AP Stats exam, we spent two and a half classes watching the movie Moneyball. I wanted watching the movie to be a low key activity, but also wanted to have some academic value attached besides just answering a set of questions about the movie itself. I asked Gemini to make an FRQ similar to AP Statistics FRQs with topics within the CED and also within the context of Moneyball. Here's the Moneyball FRQ. I did format it a little differently and fixed up the computer output, but didn't change any of the numbers. The rubric is right after the question. 

Of course after I asked Gemini to make the FRQ, I finally had time to look at and work on the released FRQs from the 2026 exam. I think FRQ 6 is a perfect Moneyball question! Maybe I'll use that one next year when we are watching the movie in class.

An AP Environmental Science FRQ for "The Martian"

Since I teach in New York, even though we're a private school, we have about three or four weeks of classes after the AP exam. We work on eco-columns during this time, but I don't need all of the class periods to work on this. We spend about half of the class time taking measurements from the eco-columns and then we've been watching The Martian during the second half of class. In the end, I think we'll take 4 days to finish the movie. I want this time in class to be low key, but not so low key that students completely check out. Instead of a long sheet of questions to fill out as students watch the movie, I decided to ask Gemini to make an FRQ using task verbs and topics from AP Environmental Science that corresponds to the Martian. This allows students more practice for FRQs since they still have a final exam to take for me, but is still not a huge assignment. 

I was happy with what Gemini gave me and appreciated the rubric that goes along with it. 

Here's a link to the Martian FRQ. The rubric comes right after the FRQ itself. 

Right Triangle Scavenger Hunt for Geometry

 

I use Math Medic for all of the math classes I teach and they made a scavenger hunt for AP Precalculus that I love. This year, I've returned to teaching Geometry and at least in the beginning unit, the Math Medic Geometry units didn't include review activities. I decided to try my hand at making scavenger hunts to review some of the Geometry units. The first two that I made, I used questions from Math Medics assessment platform, so I'm not free to share those resources. When the class got to right triangle trigonometry, I made another scavenger hunt, but this time used questions from past Geometry Regents exams. This hunt I can share, since past exam questions are publicly available. 

The premise of a scavenger hunt: Start at any lettered question that's taped around the classroom and write the letter down on paper or a whiteboard. Solve the question and the correct answer choice will lead you to the next question to find. Continue until you've answered all questions. If done correctly, the last question's answer will bring you back to the letter you began with. Most students won't begin with the first letter, but can figure out the secret word that the letters spell by the end. The word also makes it easy for me to check their answers no matter what letters they've been to because I know what order the letters should be in. 

Here's my Geometry Right Triangle Trig Scavenger Hunt.

AP Environmental Science LOs and EKs for all Units

 

So, I finally finished polishing up the documents for the last three units of AP Environmental Science. If you need any other information about what these include or what I use them for, you could check out this post. Here are the links for each unit:

Unit 1 "I can" statements

Unit 2 "I can" statements

Unit 3 "I can" statements

Unit 4 "I can" statements

Unit 5 "I can" statements

Unit 6 "I can" statements

Unit 7 "I can" statements

Unit 8 "I can" statements

Unit 9 "I can" statements

My AP Statistics Plans for Notes and Homework

 I'm teaching AP Statistics for the first time this year. I'm using Math Medic for class activities and notes. Math Medic is my go-to for all of my math classes. I don't have Math Medic's assessment platform for AP Stats, but I felt I needed more practice for students than just the check your understanding questions. We do have a textbook, but it isn't easily organized by topic, so I wanted another source for practice questions.  

I had heard Skew the Script referenced regularly in the AP Stats communities that I'm a part of, so decided that I would use their practice sets. Over the summer, I planned out every day of the year to make sure we would get through all of the content before the AP exam. 

Both Math Medic and Skew the Script provide answer keys to each of their lessons, which is helpful to me as a first year Stats teacher.

In my year-long plans, I include the name and number of the Math Medic lesson and the lesson number of the Skew the Script lesson as well as the topic numbers from the AP Statistics CED. 

Here are my AP Statistics Unit Plans. 

A New Way to Do Test Corrections for AP Environmental Science

Curves on Unit tests in AP classes is always a hot topic in the AP Facebook groups...at least the ones that I'm a part of. For the AP Unit tests that I give, I give the square root curve. Yes, I know it's a big curve, but I am determined to keep these AP classes accessible to any student who would like to take them, and this curve is part of what helps make that happen. The curve doesn't come for free though. Students must complete test corrections to "earn" the curve. I want to do whatever I can to help them actually learn this material. 

I used to have students explain why the right answer was the right answer for the multiple choice questions, but many students struggled with it and tended to just restate the question and answer or would write an incorrect explanation, which isn't helpful.  So now, for each question they get wrong, they write the essential knowledge statement that they feel goes with the question. (And this adds another use to the document I give them with all the LOs and EKs for the unit.) I have decided to expand that to them also using statements from their video notes and review book, so they don't write the same EK more than once. 

To help students narrow down which EK to use, I download the assessment that I've made on AP Classroom and then use adobe acrobat to add which topic each question is from. Students take the MCQ portion of their unit tests in the lockdown browser of AP Classroom, but when they do corrections (in my classroom), I give them the printed copy of MCQs to work with. 

Even though they take their test through AP Classroom, I have them also bubble their answers into a Zipgrade form. After the test, I print out their results from Zipgrade which includes their answers and what the correct answers are. This way, they know exactly which questions they need to do corrections on. They need this since I only allow access to their scores on AP Classroom, no question information. I print a few sets of MCQs, since only a few students come in to do corrections at a time, so there are typically enough copies to share. 

I have been liking this new way of doing test corrections far more than the old way, and at least students are writing true statements on their corrections!

AP Environmental Science LOs and EKs by Unit

In past years I had been using another AP Environmental teacher's documents that outlined the learning objectives and essential knowledge statements for each unit. I had some students who appreciated seeing the list of key concepts that they needed to know for the units as they prepared for tests. When I tried to use the first unit document at the end of the summer, I realized that the link was no longer active. I searched through the AP Environmental teachers Facebook group and found a spreadsheet with all of the information for every unit. I thought I might try to use ChatGPT to help me remake the documents by unit. This turned out to be a bigger challenge than I anticipated. By the beginning of the school year, I had rough drafts of each of the documents, but so far, only the first 6 units are finished as final documents. 

In these documents, the learning objectives have been converted into "I can" statements, organized by topics with essential knowledge statements below. At the end of the document there are tables that include the key enduring understandings and science practices for that unit. 

I've turned out to use the documents far more than I thought I would for this year's class. These documents are the first pages in the packet I hand out to students at the beginning of the unit. As we are reviewing for the unit test, I make note of some of the key essential knowledge statements based on the questions that will be on the test. Students highlight and make notes as well on their copies. I also started using the document for test corrections. This needs a blog post of its own though. 

One other note. I teach at a Christian school and last year, my scores for Biblical integration were not stellar. I was surprised, since for me I think of AP Environmental Science as a way to learn how God expects us to take care of the earth. To me, it's all Biblical. Part of my change to be more explicit this year, was to add a verse to these documents that I felt fit well with the topics of the units. Obviously, this will not work for all classes, but if you want to use these documents, feel free to edit after you make your copy of the document. 

Here are links to the documents that are final draft.

Unit 1 "I can" statements

Unit 2 "I can" statements

Unit 3 "I can" statements

Unit 4 "I can" statements

Unit 5 "I can" statements

Unit 6 "I can" statements

APES Sustainability Lab

Right after Thanksgiving Break, we're doing the Sustainability AP Lab AKA Tragedy of the Commons. 

Last year, we used Kristi Schertz's Happy Fishing Lab that you can find here. The only modification that I made was that our fishing poles were straws with paper clips to catch Fruit Loops instead of mini marshmallows. Well, that and we used way too many fish. I'll be using AP's suggested number of fish this time!

This year, we'll still start with the data tables from the Happy Fishing Lab, but it will be Part 1 of the AP Sustainability Lab. Then we'll move onto the actual AP lab for Part 2. I put together this Google Sheet to help students keep track of their data for part 2. I like to keep all of the class data together so students can see what other groups are doing. I also just add another tab each year by making a copy of the master tab. I have some Sheets from labs in AP Bio that have nearly 10 years of data!

The sheet is set up for four groups of four, but the groupings could always be copied and pasted for more groups, or even multiple tabs made. 

AP Environmental Science Cemetery Demographics

There is a wonderful, large, old cemetery less than a five minute drive from my school. This year I decided that we'd take a trip to the Albany Rural Cemetery to gather data for APES Lab #5. Because the cemetery is so close, I think we can gather lots of data during one of our 80 minute classes.

I want students to be able to focus on the graphs made and what they mean in terms of demographic transition and mortality rates. I started with Kristi Schertz's spreadsheet, and then converted it to work with College Board's math to go with the Cemetery Lab. This way, students just need to enter their raw data and the sheet will do the calculations for them. Then they can focus on what all of the numbers mean, and I don't need to give quite as much class time to calculations since we're taking an entire block class to collect the data.

We haven't used the sheet yet, so there may need to be some corrections made to formulas, but I wanted to share what I have just in case it would be helpful to another class that's about to do this lab. If you are wondering, the initials in cells B1 to L1 are my students' initials so they each know where to enter their data. If you'd like, you could add rows for each of your students, or assign lab groups to each column instead.

Here's the spreadsheet.

I also made a data collection sheet for students to bring to the cemetery. My thought was that each student would collect 25 dates from pre-1900 and 25 from post-1900, which gives us a total of 550 pieces of data. I made a dashed line in the middle-ish of the paper so they could aim to get about half female and half male data as well. 

Year Long Revised Plans for Pre-AP Algebra 2 and My Rational

Last year, I agreed to teach Pre-AP Algebra 2 as an overload about two weeks before the school year began. Although I had taught Algebra 2 before, it had been over 20 years ago. I definitely felt like a first year teacher as I was teaching AP Environmental Science for the first time and was switching from the Precalculus curriculum that I had been teaching to the AP Precalculus course. The order and focus of AP Precalculus was different enough from my class before, that I pretty much needed to scrap my old curriculum and start over...fortunately Math Medic had put a a whole set of lessons together. All of this to say, I was strapped for planning time. As a result, I followed the Pre-AP Algebra 2 lessons as presented by College Board, and just found or created lessons only for the topics that the curriculum said were not addressed.

Here were some of my frustrations: 

1. Although the lessons were described in detail in the teacher materials, not all of the materials needed were compiled for the student facing documents, specifically, the formative assessments. And not all of the parts of the lessons were in a presentation. Some of the questions could be presented verbally, but for many of the lessons, I needed to put together a Google Slides presentation. This was different from Pre-AP Biology, where all parts of the student lessons were provided as well as Google Slides presentations for lessons as needed.

2. The lessons were great at getting the students thinking, but I felt like they were missing consolidation. Students could work through the lesson, but in the end didn't know/realize what they were doing. The Pre-AP units will tell you what percent of the topics are covered and I'd be surprised that the course map would say 40% of instructional time was covered by model lessons in Unit 1 when in the unit outline, there was only one learning objective out of 9 that was not addressed by the model lessons. Maybe the percentage was lower because the lessons were missing consolidation or maybe because students needed more time to practice? I think this is the case, but I'm not sure of what College Board's reason was for the difference in % vs. learning objectives covered.

3. Besides needing consolidation, there was an assumption that students remembered everything they learned in Algebra 1, like completing the square and different forms for the equation of a parabola. My students definitely needed a refresher. I learned this as we went through the year. I needed to remind myself that this was not a complete curriculum, and by unit 3, I was adding lots of refreshers, lessons and practice. 

By Unit 4 (Trigonometry) I decided to take an entirely different approach. I went to Math Medic for most of the lessons. I also figured this would be a good experience for my students as they would be in my AP Precalculus class the next year, where the class is primarily taught through Math Medic lessons. I then tucked the Pre-AP model lessons where I thought they worked best in the progression. Occasionally, the Pre-AP lessons would be used as an introduction, sometimes as additional practice. I was much more purposeful about consolidation. 

This summer, I decided to give Pre-AP Algebra 2 a complete makeover, including refresher lessons, for topics that students needed to recall, just in time for the lesson that would take that topic deeper. I added in Math Medic lessons for each of the learning objectives, and where I decided that using just a Pre-AP model lesson was sufficient, I added in consolidation. My consolidation included a page with a box for quick notes, Math Medic style. Usually, I would have boxes for quick notes for two lessons on a page so as to not waste paper. I kept all of the topics in each of their set Pre-AP units, and mainly in order, since I do love Pre-AP's assessments and wanted to be able to use all of them. These made-over plans also include homework for extra practice. Sometimes I just used the formative assessments from Pre-AP for homework practice, and sometimes from our textbook, which is Big Ideas Algebra 2 by Larson and Boswell. 

Besides Pre-AP's learning checkpoints and performance tasks, I also give my own quizzes and tests. Problem-attic.com is my go to test-building site. Besides using Algebra 2 Regents questions from the site to build assessments (I am in New York), I would often go to Illustrative Math questions. Those questions are great thinking questions and often matched well with the thinking that the Pre-AP Algebra 2 lessons were geared toward. 

Here's my Algebra 2 Plans for the year. I did remove the time for each lesson column from the Pre-AP template. Each of the Tuesday/Thursday classes are 80 minutes and every other Friday when we meet is 60 minutes.

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Reflections on the EFFL Workshop by Math Medic

I've just completed 106 hours of professional development this summer and decided that if I'm truly going to apply what I've learned, I need to reflect on the takeaways before I forget them. The summer began with the AP Biology Read in Kansas City, MO which accounted for 70 hours. Last week, I participated in an online APSI for AP Environmental Science for another 30 hours. Today was the last day of a 6 hour, online workshop by Math Medic on EFFL (Experience First, Formalize Later). Since this workshop is the freshest in my mind, I'll start with this one. 

I love Math Medic. First of all, they write a whole set of lessons that correlate to the AP Precalculus course. And secondly, they teach math the way I have always wanted to teach math...students learn by doing some activity that they can relate to (Experience First), but points them to the main ideas of the lesson. Anyway, by the end of the year last year I was also using Math Medic lessons for Pre-AP Algebra 2, especially for the way they consolidated the lessons (Formalize Later).

So, here are my takeaways: 

1. Project a blank "Experience" page that I direct students to write in certain work that their group has done. Last year, I just left them blank as I gave margin notes and pointed to student work up on the boards (my classes use whiteboards or windows to write their group work), but the work was hard to see.

2. Have students write the margin notes as I do, and they should write those notes in a different colored writing utensil just like I do, to help the notes stand out. 

3. Only focus on the challenging questions from the Experience page and chose different students to explain their thinking before connecting their explanation to the margin notes that are pointing to the main idea.

4. Know the main ideas before the lesson, so that I can better ask focusing questions that point students to the main idea versus just pointing then to how to get the right answer. Connect their thinking to the main idea(s).  Here's a Math Medic blog post about focusing versus funneling questions.

5. Taking this workshop also gave me the idea to share the essential knowledge statement(s) that go with the lesson and work with the students to determine what would be the most helpful information to write in the quick notes section. There are essential knowledge statements for me to use for both AP Precalculus and for Pre-AP Algebra 2.

I'm excited to see how my math classes will go in the coming school year while using these practices. 

Completing the Square with Blocks

Several years ago, when my Precalculus class made it to our Conic Sections unit, I realized that most of my students did not remember how to complete the square from when they learned it in Algebra 1 (and maybe 2). I was reading through the 5 (Math) Practices in Practice and Building Thinking Classrooms at the time and developed this activity to help walk students through developing their understanding of completing the square.

I divided the activity into four sections. The first samples start with just an expression with "x^2" and an even numbers of "x"s (b). They are asked to build a square, and are allowed to fill in any missing parts with single unit blocks (c). Eventually, we move into an odd number of "x"s, and then expressions with single units as well. 

By the fourth section of exercises, they are thinking through negative b values and the whole quadratic equation to complete the square for. For many students, being able to see the squares being built helps them to remember what to do when they see questions on tests that require completing the square to solve. 

Although I've traditionally done this activity in Precalculus at the start of conic sections, I'm going to add it to my Algebra 2 class next year as well when we are looking at quadratics. 

For this activity, I use some Algebra blocks I have as well as Cuisenaire rods paired with "x^2"s that I made out of card stock. I still didn't have quite enough, so I also cut some sets out of scrapbook paper I had on hand. I actually like the paper sets best when we need to only use half an "x" piece when b is odd. Then we can just tuck half of the rod under the square. 

Here are the documents that I made to go with this activity. This document includes the directions for each section. This document has each of the expressions or equations to work with in each section.  The examples are formatted so that either each group of students can have a quarter sheet of the examples for each section or a large sheet that I post somewhere in the classroom for them to refer to.

Two Labs to Introduce Rational Functions in Algebra 2

 

All the possible sizes for a "Cube-ie"

As our class was working through the Unit 3 topics for Pre-AP Algebra 2, we arrived at rational functions. Rational functions in the Pre-AP curriculum have two key learning objectives with several corresponding Essential Knowledge statements. Rational functions are one of the topics that need to be teacher developed. As I was thinking through LO 3.2.5 Construct a representation of a rational function, I decided that I wanted my students to discover rational functions in a hands-on way. I put together two lab exercises for students to do.

The first exploration involved measuring the length of time it takes a "cubie" to somersault 50 cm along a meter stick. A "cubie" is a segmented worm with anywhere from 1 cube body segment to 10 cube body segments (domain restriction). All we needed were a meter stick, several linking cubes, and a timer. 

One of the group's "cubie" somersaulting its way to 50 cm.

I borrowed the second exploration from an AP Environmental Lab on solar insolation. Students held a flash light above graph paper at different angles, counted how many squares were illuminated, and then divided the pre-measured brightness of the flashlight by the number of squares illuminated. This gave a measure of brightness per square.  We determined the brightness of the flashlight using the free Arduino SJ app on my school iPad. Phones should be able to do this too.

One thing I will do differently next year is to use actual graph paper instead of my big cling whiteboard graph paper because the squares were too big to see much of a difference as the angle of the flashlight changed. I had hoped that using the bigger squares wouldn't leave them counting tons of squares, but it turns out that regular graph paper does work better for this. 

Here's the lab I gave to students.

A Regression Lab for AP Precalculus

Starburst Grab

 I'm teaching AP Precalculus this year. Although I am loving the course developed by the College Board and the thinking it is requiring of my students, I'm a little overwhelmed with all of the prep. It doesn't help that I am also teaching AP Environmental Science for the first time. 

Speedy Squares

Anyway, I spend plenty of time looking through posts from the AP Precalculus teachers Facebook group. One of the posts talked about regression labs that a teacher was doing when they got to topic 2.6. None of these regression labs are my creations, but I put them all together into a form that I could use with my students that guided their thinking, hopefully into deeper understanding. The original activities can be found on Math Equals Love and Stats Medic.

Measured Race Station

I modified Starburst grab so that it would be a cubic regression, although it wasn't a fabulous fit. Then we had two linear and one quadratic regression. 

The labs were a big hit with students. One change I'm planning for next year is to have students answer the questions about each station at the same time that they are making their graph and finding the regression equation and residuals. 

Here's the document that I put together that includes both the handouts that I gave to each student as well as the directions that I placed at each station.

Filling in Unit 2 Lessons for Pre-AP Algebra 2

We've just started Unit 2 in Pre-AP Algebra 2. We've completed the lessons on the composition of functions and have moved onto looking at transformations as composition of functions. There weren't lessons for Concept 2.2 on Transforming Functions. 

The first two learning objectives focus on how different compositions of functions cause different transformations. I decided to make a Desmos activity that would address those LOs. Here's the link for Transformations as Composition of Functions. 

Then we moved our focus to representing a sequence of transformations graphically and paying attention to the order that these transformations needed to be done. We did this with another Desmos activity that I edited from someone else. This activity was Transforming Functions-Shifting and Reflecting. We mainly did this together since there were a lot of questions and students were still building their understanding. Next year, I plan to do Transforming Functions first, and then will move onto the Shifting and Reflecting activity.

After doing the above Desmos activities, I assigned "Talking Transformations and a New Origin" by Julie Reulbach. The worksheet can be found on her i speak math blog here. I also sent them home with notes on the order that transformations need to be performed from MathBitsNotebook Algebra 2.

In our next class I'll challenge students with the Transformations Word Search by Sarah Carter that you can find on her blog Math Equals Love. One word of warning, the pdf file has a transformation of -4f(x), that doesn't actually spell a word with the 4 letters. All of the rest of the transformations do spell common words.

If we have time, I'll also have students work on a matching activity that asks them to match a graph with a function and a list of transformations. The document with the card matching game can be found on this blog post: Partially Derivative.

At the end of Unit 2, the LO for 2.3.3 about restricting a domain of a function so that it is invertible. I found a Khan Academy lesson that covers this, so I plan to use that lesson with my students. It's from the Precalculus curriculum and is titled: Restricting Domains of Functions to Make them Invertible.

Update: I made a set of notes for students to practice restricting domains of functions to make them invertible. The link to that document is here. Since I included a couple of absolute value graphs, students were reminded of how to convert absolute value functions into a piecewise function to be able to find the inverse function.

Fillable Lab Sheets for AP Environmental Science Labs

Another one of my new classes for this year is AP Environmental Science.  Since we are a one to one device school, my goal is for students to complete as many lab analyses by Google Docs as possible. This saves lots of photocopies. A surprising bonus is that I am finding the labs faster to grade this way. Labs that are turned in through Google Classroom as google docs can be commented on. I can quickly type in a few comments to students' lab and count comments to determine the grade. 

One other I like about making fillable labs in Google docs is using 1-cell tables for the answers. Otherwise I find myself searching for answers that blend in with questions.

The labs themselves with teacher editions and student editions with procedures can be found in AP Classroom for Environmental Science if you are an approved teacher. 

I'll add links to the three labs that I've made fillable answer sheets for. If I could find a fillable lab sheet that someone else had done, I used them and didn't reinvent the wheel.

AP Lab #1: Primary Productivity

AP Lab #2: Species Diversity

AP Lab #7: Physical and Chemical Properties of Soil

Finishing Up Unit 1 of Pre-AP Algebra 2

One afternoon toward the end of summer, I got a phone call while at the orthodontist with my youngest daughter. I was a little surprised to see the call was from the head of the math department at my school.  The call was to ask me if I would consider taking on one of the Pre-AP Algebra 2 classes. I was actually delighted to take on another math class, although it meant an overload in an already busy year for me. My class load already included AP Environmental Science, which is brand new for me, and AP Precalculus which is a brand new curriculum. The only prepped and familiar class for this year is AP Biology. 

One of the benefits of Pre-AP Algebra 2 is that the curriculum is primarily put together, although I'm finding that it still takes some time to prep the lessons. Fortunately, unit 1 had lessons for each of the topics except for the last one. Key concept 1.3: Graphing Absolute Value as Piecewise Defined Functions didn't have a lesson. Before the year started I decided to teach the concept through a Desmos activity. I'm still about a week away from using this lesson, but wanted to share it in case it may be helpful to someone else. Feel free to let me know if you catch any errors. I'll also make adjustments as my students try it and help me find any issues.

Here's the link to Absolute Value as a Piecewise Function.

Hexagonal Thinking in AP Biology

I happened to be scrolling through Facebook a couple of weeks ago and saw a post about reviewing for an AP Biology unit test with hexagonal thinking. I was immediately intrigued. I used to give students some time in class to start working on their progress checks in AP Classroom before the test, but I had several students who were not engaged and others who preferred a quieter environment to complete these questions. Although I love a good Kahoot!, I don't always find them incredibly helpful for reviewing for an AP unit test. 

The hexagonal thinking exercise engages students and makes them think about the concepts we were studying and how all of these concepts were related. I decided that this is what we needed to strengthen our review sessions. I went to Amazon to start looking for potential hexagons to use. In the end, I settled on these cards because there were a lot of them, they were a comfortable size for writing on and fitting several on a table, and they were fairly inexpensive. Because they are just matte card stock, I laminated them. It was a little time consuming to laminate and cut out, but now I have a set of 120 cards that can be used over and over. 

I listened to this Cult of Pedagogy podcast about hexagonal thinking to get a feel for how it might work in my classroom. The podcast talked about students not just building connections with their hexagons, but also to choose several key connecting points to describe why there was a connection there. There are several digital versions that are free to use to do the hexagonal thinking exercise virtually, but since we're in class, I enjoy my students being able to get their hands on. 

When we were ready to do this in class, I made a list of key words and phrases for the unit as well as sets of 5 connection arrows and a shared document for students to share their connections and a picture of their hexagonal web. 

So far we have made hexagonal webs for our Ecology unit and our Metabolism unit. Here is the copy of the document that I made for unit 8 and also the document students used for unit 3. 

Trig Graph Match-ups

When we were working through our first trigonometry unit in Precalculus, I wanted students to be able to make the connection between the equation of the trig function and the graph. Before I'd ask students to graph the trig equations themselves, I wanted students to practice finding amplitude, frequency, period, midline, and phase shifts and be able to look for those in a graph. I found a card set of trig functions and their matching graphs on TES here...

Trig graph match ups.  https://www.tes.com/teaching-resource/transformations-of-trigonometric-graphs-match-up-6407000

There are three sets of functions and graphs, so I copied each set on a different color of paper. I had teams of students work with one color and when their matches were made correctly, they moved onto another color. 

As I would check student matches, I'd ask questions such as: How did you decide that this graph matched with this equation? What part of the equation gives you a clue to how tall your graph will be? What's the difference between the frequency and period and how can you explain the difference using this graph and equation?

I know these concepts are all learned in Algebra 2, but students sure do need the refresher when they get to Precalculus.

AP Bio Instructional Adjustments after attending the 2022 AP Read

 

The view from Loews Hotel in Kansas City, MO.

This year, I went to the in person Read for the first time.  Readers always say that doing the Read will make you a better AP teacher. I want to make sure to reflect on my learning now while it is fresh in my mind to get the most out of the experience. 

I read last year, but it was virtual. After last year's Read, my big take away was to tell students to write more. Not off topic and don't contradict yourself, but make sure to answer the whole question in detail. So often I'd be reading an FRQ and although the student was going in the right direction, they were missing a little piece of critical information and didn't earn the point. There were other students who wrote an answer, and then added a little more detail in another sentence, and often times, the information required for the point was in that second sentence. 

Being in person left me with so much more to reflect on, or at least being trained on and reading the two FRQs that I did gave me plenty to consider. Here are a few:

1. If the FRQ has a data table that includes SEM, make sure to talk about statistical significance in your answer (and don't leave out the word statistical). It's also fine to talk about overlapping error bars. 

2. Remember, even if the means look different, if error bars overlap, the means are the SAME.

3. Be more specific in your answers. Keeping it general will not earn you any points. And keep track of what the question is actually asking. (I know this is a challenge when students feel time pressured.)

4. If asked to describe how some process will happen, make sure to describe the process from beginning to the very end. Don't stop half way through the process. To me, this is one of the biggest takeaways. 

5. I'm planning to find more data sets that are graphed best with scatter plots. I'll do some scouring of Data Points in HHMI Biointeractive such as Patterns of Predation. In fact, I may encourage students that when in doubt, graph a scatter plot and add a line of best fit if they feel they must.

6. Spend less time on how the processes happen correctly and more time asking students what will happen if something goes wrong along the way.

7. The independent and dependent variables should never be one word answers.