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. In this task students will think about this in two-dimensions by using geoboards and considering the number of pegs inside the shapes.
The lesson plan and materials are provided in Google Slides— click below to view the slides or make your own copy of them. Slides labeled with a “T” in the upper right corner are included for teacher information about the lesson. Slides labeled with an “S” in the upper right corner are for students. If handouts are needed there are links to them in the teacher slides. All slides can be adapted.