__Caching Games__

## Main Concepts

Calculus, AP Calculus AB review

Limits, Derivatives, Integrals

(See Summary for more details of each game)

## Duration

80 minutes in or out of class

## Summary of Activity

A caching game is one where the player starts at a certain url, finds an exercise and by solving it gets the key to the next url, where the process starts again.

For example, at https://robert-nicoud.ch/vivian/ap-calculus-ab/caching-games/caching-example/ , you can find the question: “what is 1+2+3+4+5?”. By substituting the answer you will be lead to a new web page and so on.

The content of “Caching Game 1” includes FRQ-style questions regarding areas, volumes of revolution, tables of values, rates, Riemann sums, average of a function, etc.

The material addressed in “Caching Game 2” includes FRQ-style questions regarding Particle motion, Implicit differentiation, and Piecewise functions.

## Notes and Insights

A valuable improvement we can make to this activity as we observe students finding their way through the problems is to take note of the wrong url’s they reach. By asking them for their thought process, we identify their mistakes, and we can start creating these web pages with immediate feedback comments explaining to students who get there why the solution is wrong (and add hints to the right method).

Another idea is to add scaffolding url’s that students have the option to go to if needed. In a given question, we can suggest a link to see some helping information.

At the conclusion of the last problem, the teacher can give the location of a secret physical cache somewhere around the school that students can go to to find a small prize after completing the game.

Even though I haven’t done it, I have seen caching games where a given web address has multiple math questions, and then it is a combination of the answers that leads to the next (for example: add all answers).

**Note** Solutions, examples and editible documents (Mac) for the projects and activities are available to other teachers. Please email me from a school email address (go to Contact).