The Magic Ruler investigation first introduces students to a ruler that can measure perimeter and area of a square just by measuring the side-length. This allows students to find the relationship between SL, P and A. Then, students will apply their findings to circles. From measuring the circumference of a circle, students will create a ruler that will automatically give them the diameter. Ultimately, I used these rulers to get out into the woods and measure trees. For most trees, age is easily determined by diameter if you have the correct growth-rate. See Tree Investigation if you're interested in continuing this direction.