APES Math Strategy That Really Works

(Updated in July 2019 to reflect the new AP® calculator policy)

The million dollar question in AP® is “How can I help struggling students while not boring or giving busy work to high achieving students?” This is especially true for math concepts in science courses where students are enrolled with differing math skills and strengths. How can teachers help ALL students with APES math?

I’ve been trying different ways to approach APES math for 12 years. Last year, I tried something new–a math diagnostic and then individualized, differentiated math review and practice.  The verdict? According to my instructional planning report from the CB……it worked!

(To learn about the types of math needed in AP Environmental Science click here. )

Math Diagnostic

The first thing I did was develop an APES math diagnostic that students took at the beginning of the year covering the types of math they should have already learned. Most students didn’t remember how to solve some or all of the topics.  You can find the diagnostic I developed here.

Math Review Diagnostic for AP Environmental Science

The diagnostic took 60-90 minutes for students to complete. When finished, they self-graded with the solution key and circled the topics on their answer sheet that they believed they needed to review. This allowed them to take ownership of their learning. I told them that I would look over them and circle any other areas they needed to work on, but for the most part, they were pretty honest. They knew they needed to know how to do the APES math for their own exam grades and wanted the practice.

There are special APES math topics that we learn during the year (population math, energy math and productivity, for example) and these are not part of this diagnostic. I teach those math topics differently–as they come up in certain chapters.

After students have self-corrected and indicated their weaknesses, I entered the topics they needed practice on a spreadsheet and used the spreadsheet to assign review papers to them individually.

Update: in 2019, I used Shelby Childress Riha’s idea of using a Google Form where students where they can click the areas they need to review. This was great. I could print out a spreadsheet to assign review papers more easily.

I also made the process easier by creating a folder for each student that I kept in my classroom. Since I flip, I have time to do math in class. If you don’t flip, you could have students pull a paper out the folder to do for homework. 

Choices for students on how to solve

Students had choices on how to approach each  APES math review paper. (Use your own math review papers or you can purchase mine with keys)

Students could

  1. Attempt to solve and then use a solution key to check their work.
  2. Use videos for help. I made videos of all the review sheets. They could watch me solve one or all of the problems on my Youtube Playlist
  3. A hybrid of the two–solve any they could without video help and then fast-forward the videos to only the problems they struggled with.
APES Math Review papers with keys.

I prepared 9 pages of review topics along with solution keys and videos. You can easily do this with your own math review papers….but a warning…it does take many hours to prep. After students were finished with the specific papers they needed to do (for some students it was all 9 math papers and for others it was only 1-2 papers), they switched to FRQ math practice. 

I rotated around the room making sure students were on task on math days. I estimate that I did about 10-12 math days in class last year (55 minute periods on a traditional schedule).  I flipped (lecture at home) which allowed this amount of time in class.

One of the amazing, awesome things about this method using videos is that I just monitored students. I did not run around to try help individual students in the period and this prevented exhaustion. The kids just opened the video for the review paper they needed and fast-forwarded to the problem they needed help with.

When Students were Finished with Review

After review papers, students practiced APES math with released FRQ #2s from each year on the AP Exam.  I assigned 2017 back through 2009–two at a time and had keys and videos for them.  I used the snipping tool on Microsoft word to cut out the non-math portions of the FRQs. I also did not assign problems previous to 2009 as the math is structured a bit differently in recent years. The math is also easier in recent years so I wanted them to start off with easier problems.

2017 key for students to use after solving APES math problems.

Some students finished all the released FRQs and were then assigned to do peer tutoring with other students who needed help with APES math.


It worked!  I am thankful, because it was HOURS of work to prepare and implement. I compared my students’ (group) mean with the global mean each year. This was the highest difference on FRQ#2 in years. My students average was 1.4 points higher than the global mean which is an increase of 56% over the global mean (Percent change!!)  Last year, I had only a 13% gain over the global mean so I am very pleased with the results.

These are results from the 2018 exam. FRQ #2 was the Wind Energy FRQ. I have marked out all other scores for confidentiality

Implementation was challenging, however. It took a lot of organization to keep track of what each student needed to do and turn in. Next year, I plan to organize better and create folders for each kid with the papers they need for the year and give them 1-2 pages at a time.

Update in 2019: My FRQ #2 results also improved!

Each student gets a folder. My student service place papers in the folder as indicated by the check-off paper.
I keep the folders in my classroom. On math days, students take out one paper from the folder to do that day. They turn in the paper to my basket to be checked off for points.
Checkoff list for items assigned to this student. Even though they’re not checked off, all students will do old FRQs.

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