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### Pi Filling, Archimedes Style!

9-12

Inscribe and circumscribe regular polygons in and around the
unit circle, which is known to have an area of π.### Making Your First Million

3-5, 6-8

In this activity for grades 4-6, students attempt to identify the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition until a million is reached. Additionally, they use critical thinking to analyze situations and to identify mathematical patterns that will enable them to develop the concept of very large numbers.### A Ratio that Glitters: Exploring the Golden Rectangle

6-8, 9-12

In this lesson, students will develop an understanding of the Fibonacci Sequence (and its connection to Golden Rectangles), Golden Ratio, Golden Rectangle, and the term *ratio*(as it applies to rectangles). Students will use tools and construction techniques to demonstrate geometry prowess and be able to observe the Golden Rectangle in nature and in the classroom.

### Tree Talk

3-5, 6-8

If a tree could talk, we could ask it how old it is. Here is a mathematical way to estimate the age of your schoolyard trees. Students will measure circumference of trees in order to find diameter and calculate age of local trees using a growth rate table.### Improving Archimedes' Method

9-12

Archimedes was the first mathematician to develop a converging series
approximation to π. That highly influential discovery guided the
development of calculus many hundreds of years later. However, his
method only gives lower and upper boundaries that form intervals known
to capture π, not a single numeric estimate of π. In this lesson,
students ask, “Where is π located in those intervals?” They also
discover an improvement to Archimedes' method that generates the
infinite digits of π more efficiently and accurately.### Inscribed and Circumscribed Polygons

9-12

By calculating the areas of regular polygons inscribed and circumscribed about a unit circle, students create an algorithm that generates the never-ending digits of π, a common curiosity among high school students. ### Square Circles

6-8

This lesson allows students to use a variety of units when measuring
the side length and perimeter of squares and the diameter and
circumference of circles. From these measurements, students will
discover the constant ratio of 1:4 for all squares and the ratio of
approximately 1:3.14 for all circles.### Pi Line

9-12

Students measure the diameter and circumference of various circular
objects, plot the measurements on a graph, and relate the slope of the
line to π, the ratio of circumference to diameter.