We have calculus for you this week! And aviation vocabulary! And movable points! Come join us in our weekly celebration of online lesson goodness. It’s time for your Friday Five. Up first, a pair of calculus activities.

## Average Value of a Function

This one is straight out of Chapter 7 of Stuffy McProf’s Major Publisher College Calculus textbook. You know, the one about Applications of Integration?

But with a Desmos twist—it was authored right here at Desmos HQ. That means you can drop it right in to whatever else you’re doing in that chapter and your students will cheer with delight! (claim not guaranteed)

## Functions Defined by Integrals

Actually, it turns out the Desmos Teaching Faculty have been busy little calculus beavers. The Fundamental Theorem of Calculus is one of the most beautiful, elegant parts of the sequence, but it is also tremendously challenging for students to wrap their minds around it. This activity does not replace any of your efforts to help students do that, but it should provide a helpful supplement. Go check it out, try it out, and report back, won’t you?

## Hit the Runway

Danny Whitaker puts a creative twist on the patented Desmos “Match My Function” genre with this activity that asks students to take on the role of piloting an airplane that has neither roll nor yaw (which is to say it always flies in a straight line). Their job is to land that plane and not let it run off the runway.

## Creating Functions

Activities 4 and 5 this week make a two-fer. From the incomparable and beagle-rich Megan Schmidt, check out Creating Functions, Part 1 and Creating Functions, Part 2. Ms. Schmidt asks students to build functions under constraints: increasing on a given interval on one screen, symmetrical about the y-axis on another. Together with some Desmos expertise, she has students move from structured explorations with movable points to more open and challenging tasks that have a world of possible solutions. If your algebra students have some basic polynomial work in their backgrounds, they’re read for Creating Functions.