Parametrize This!

Parametrize This! is a collection of GIFs for teachers and students, which can be used for topics ranging from pre-algebra to calculus (and beyond). The intention of each GIF is to offer a non-verbal prompt that warmly invites students into actively engaging with mathematics, regardless of their prior knowledge.

Each GIF invites a variety of mathematical modeling problems. They can be approached concretely by plotting the observable data, and they extend naturally to prediction questions (where would point A be at t=10?) and algebraic modeling (write the coordinates of point A in terms of t). In other words, each GIF offers a low floor and a high ceiling and the difficulty level of the activity can be tuned by finding problems that are appropriately challenging.

There are a million ways you might use these GIFs, but I'll suggest one sequence of prompts that you might like to try, whether you are using these GIFs as a teacher or as a student. In my experience, this series of questions is effective for getting students to self-assess and self-direct in a way that I can observe & steer as needed.

• What math problems does this GIF inspire? Write down at least 5, and be creative! Include at least one easy problem, one medium problem, and one hard problem.
• Of the math problems you just wrote down, which ones can you solve? For each one, prove it by solving the problem yourself, and comparing your answer to a peer who solved it independently.
• Of the ones you haven't solved yet, which one do you want to focus on next?
• How do you want to go about solving that problem? (Independently? With a peer? On a whiteboard? On paper?)

Inspired by Without Words, Visual Patterns, and Collingwood's Precalculus. The chapters are roughly organized by difficulty, but each GIF stands on its own and may be used independently.

We'd love your feedback about how we can make these activities more useful in your practice! If you have any comments or suggestions, please write us at curriculum@thenumbergarden.com .