teaching

This task introduces students to Ehrhart Theory, an area of mathematics that comes up in advanced college courses or beyond, but one that at its core can be explored and understood without the need for any particularly advanced concepts. Ehrhart Theory concerns itself with counting the integer-valued points inside convex shapes. A simple concept, but one with remarkable and fascinating depth.

This task presents variations on a dice game (appropriate to the different grade levels the task is written for), and encourages students to practice their number flexibility and leads them toward working on generalization and proofs.

This task is an open, exploratory activity. We invite students to examine an idea that starts with a fairly natural question: “what if instead of skip counting on a line, we do it on a circle?” And to take it in whatever directions they find interesting. We hope this helps students exercise their agency and creativity as they play with some introductory ideas in the fields of graph theory and group theory.

In this task, students explore “windows” made from dice and ask: How many pips can you see? Students explore patterns through multiple representations, different types of growth, grouping strategies, writing algebraic expressions and develop their algebraic thinking.

I worked on writing grade-appropriate variations of this task for grades 3-12.

This activity invites students to explore a geometric pattern. This task allows students to visualize, identify, and generalize a pattern. As students explore the visual pattern they have opportunities to make decisions about how to represent how the pattern is changing.