## Learning Math: Measurement

# Circles and Pi (π)

## Investigate the circumference and area of a circle. Examine what underlies the formulas for these measures, and learn how the features of the irrational number pi (π) affect both of these measures.

### In This Session

**Part A:** Circles and Circumference

**Part B:** Area of a Circle

**Homework**

In this session, we will explore the common measures that involve circles — circumference and area — and work on activities that help us understand the formulas for these measures. We will also revisit accuracy, precision, and scale in relation to circles. Finally, we will explore how properties of the irrational number pi (π) affect calculations of circumference and area.

For information on required and/or optional materials for this session, see **Note 1**.

### Learning Objectives

In this session, you will do the following:

- Investigate circumference and area of a circle
- Understand the formulas for these measures
- Learn how features of the irrational number affect both circumference and area

### Key Terms

**Previously Introduced:**

**Accuracy: **The accuracy of a measure (an approximate number) refers to the ratio of the size of the maximum possible error to the size of the number. This ratio is called the relative error. We express the accuracy as a percent, by converting the relative error to a decimal and subtracting it from 1 (and writing the resulting decimal as a percent). The smaller the relative error, the more accurate the measure.

**Area: **Area is a measure of how much surface is covered by a figure.

**Precision: **The precision of a measuring device tells us how finely a particular measurement was made.

**Scale Factor: **A scale factor is a constant used to enlarge or reduce a figure. For example, if the sides of a triangle are enlarged to twice the length of the original triangle, we say the scale factor is 2.

**Similar Figures: **Similar figures are figures that have the same shape but may be of different sizes. In similar figures, corresponding angles are congruent and corresponding segments are in proportion.

**New in This Session:**

**Circumference: **Circumference is a term used to indicate a circle’s perimeter.

**Diameter: **Diameter is the distance between two points on a circle, measured through the center.

**Irrational Number: **An irrational number is a number that cannot be written in the form a/b where both a and b are integers and b is not equal to 0. Informally, we often state that an irrational number has decimal places that continue infinitely without repeating.

**Perimeter: **Perimeter is the length or distance around a closed curve or a shape.

**Pi (π): **Pi () is the ratio between the circumference and diameter of a circle. Pi is a constant number, approximately 3.14159, and is irrational. The numbers 22/7 and 3.14 are frequently used as approximations to .

### Notes

**Note 1**

**Materials Needed:**

- Variety of circular objects such as lids, CDs, buttons, Frisbees, bottles, and cans
- Bicycle wheel (If you do not have a bicycle wheel, use another circular object such as a large bowl or can.)
- Measuring tape
- Compass (optional)
- String
- Scissors (optional)
- Graphing calculator (To use a free graphing calculator online, go to http://www.coolmath.com/graphit/index.html.)