First, students will be led to conjecture Pick's theorem.

Pick's Theorem by NRICH

Next, students will be led to prove Pick's theorem.

Proof of Pick's Theorem by NRICH

After that, students will see a visual proof of Pick's theorem.

Pick's theorem: The wrong, amazing proof by spacematt

Here's an interesting problem: Which regular polygons can you draw, such that all vertices are grid points?

Conclude by giving your students these challenges:

- Mirror, Mirror... by NRICH
- How Do You React? by NRICH
- Giant Holly Leaf by NRICH
- Overlapping Squares