This is an accessible investigation which guides pupils to arriving at Pick's Theorem which states for a polygon drawn on a lattice grid with vertices on grid points:

$A = I + \frac{B}{2} - 1$

$, A =$ area

$, , I =$ interior points

$B =$ boundary points

It does not require pupils to solve simultaneous equations. Instead pupils tabulate results and arrive at the formula through guided questions.

• Forming equations including fractions

• Knowledge of areas of shapes up to and inlcuding trapezia.

Check the attached teacher sheet to see if the investigation is appropriate for your class.

It is suggested that you clarify the definition of edges and vertices before beginning the investigation, and be sure to distinguish boundary points from vertices.

You may want to check pupils answers on the first side of the sheet before they move onto the second side.