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Concavity Posters

Help your students remember the difference between concave up and concave down with these free printable concavity posters. They would be the perfect addition to your precalculus or calculus classroom!

Bulletin Board Mock-Up with Text "Free Printable Concavity Posters" Two Posters with Text "Concave Up Like a Cup" and "Concave Down Like a Frown"

Why I Created These Posters

It’s almost August here in Oklahoma, and that means one thing: back to school is right around the corner! I really don’t know where this summer went. It seems like almost everything I put on my summer to do list is still there.

One thing that I did mark off my list was attending an APSI (Advanced Placement Summer Institute) for the new AP Precalculus course that is being offered this coming school year.

I’m excited for the new AP Precalculus course, but it is definitely going to stretch me this year as a teacher.

I am used to introducing my calculus students to the concept of concavity and determining where a graph is concave up or concave down. This is now an AP Precalculus standard.

Since I expect my AP Precalc students might struggle a bit with this concept, I decided to create a set of concavity posters that could be used in an AP Precalculus classroom or any calculus classroom for that matter.

After all, I never turn down the opportunity to create some new math posters to decorate my classroom.

Memory Tool for Concave Up vs Concave Down

I can’t tell you exactly where I first heard the phrase “Concave up like a cup. Concave down like a frown.” But it has stuck with me for many years.

Maybe it was my calculus teacher in high school? Maybe I heard it at some point in college?

I did a quick google search which brought up a 2013 blog post from Ben Orlin on how to remember concavity with the same memory tool for remembering concave up vs concave down. So I think it’s a pretty common phrase for math teachers.

Concave Up Like a Cup Poster

Concave Up Like a Cup Poster for Remembering Concavity

Concave Down Like a Frown Poster

Concave Down Like a Frown Poster for Remembering Concavity

Printing and Prepping the Posters for the Math Classroom

I created two different sizes of these concavity posters, and I’m not quite sure which one I am going to use myself just quite yet. They are available to download in 8.5 x 11 (letter sized) and 11 x 17 (tabloid sized – very similar to A3) formats.

I won’t really do much decorating of my classroom until the 7th or so of August, so I’ve got some time to think about it.

I guess I’m trying to decide if I want to splurge on a package of 11 x 17 colored cardstock for making new posters this summer. Or should I print them on my usual 11 x 17 cardstock that is just a boring white color? Or should I print them on bright Astrobrights letter-sized paper?

Decisions, decisions, decisions…

Don’t worry. Once I have these printed and up in my classroom, I will update this post with a photo of the posters in my classroom.

Free Download of Concavity Posters

These posters are available to download as PDF files and editable Microsoft Publisher files.


Concavity Posters – 8.5 x 11 (PDF) (665 downloads )


Concavity Posters – 11 x 17 (PDF) (490 downloads )


Concavity Posters (Editable Publisher Files ZIP) (561 downloads )