# To Accumulate a Rate — Integrate!

Teaching High School Mathematics

# Position, Velocity, and Acceleration Graph Puzzles

I just really like puzzles… Whenever I get a problem I don’t know how to solve, I think of it as a puzzle. I feel like when most students get a problem they don’t know how to do, they think of it as impossible(for them). “You didn’t teach us how to do that!” Have you ever heard that from a student? Do I even have to ask? Wait… This is another blog post…

Here is my desmos activity:
https://teacher.desmos.com/activitybuilder/custom/5812b6a26889940d0f5d88e1

Before I used activity builder, this activity was a worksheet. I believe that Desmos with activity builder improves this lesson. I can easily see on my computer or iPad while walking around who is getting the problems correct or incorrect. All students can share their ideas online and I can share any of them with the class.

Here is the situation:

1. Students have learned how to sketch the graph of a derivative.
2. Students have learned that velocity and acceleration are the 1st and 2nd derivatives of position and have done problems on this.
3. Student know the shortcuts for derivatives using the power rule.
4. Students are given a graph with position, velocity, and acceleration all graphed on the same graph with no indication as to which is which. The goal is for them to sort out which graph is the position, the velocity and the acceleration.
5. Many students really struggle with this when given this type of problem in the middle of a homework assignment.
6. I like these problems because of how much they feel like a puzzle or a challenge. I created an activity on Activity Builder in Desmos where they can spend some more focused time on this type of problem.
7. I’ve adjusted this activity from last year to include 2 problems at the beginning with only position and velocity to ease some students into these problems.
8. Last year I just shared a desmos document with the graphs in folders and they had to click around. This year I added the graphs I created to Activity Builder.
9. After this adjustment I added 3 new problems at the beginning and used the new multiple choice feature. Previously I had students fill out their answers on a worksheet. Now they can select their answer out of the six possibilities and write their reasoning right on desmos. Yeah!
10. At the end of the activity students are invited to create their own puzzle which can then be shared with the class for more practice at a later time.