# Discovering Pi

This lesson introduces students to Pi through the discovery method of instruction. Students practice simple measuring skills to discover the relationship between the circumference and diameter of circular objects (Pi).They will be able to use this concept to find the circumference of any circle when the diameter is given.

**A lesson plan for grades 6 and 8 Mathematics**

## Learning outcomes

Students will:

- discover the relationship between the circumference and diameter of a circle (Pi).
- use that discovery to determine the circumference of any circle with a given diameter or radius.

## Teacher planning

### Time required for lesson

60 Minutes

### Materials/resources

- Rulers
- String for measuring
- Collection of circular objects of various sizes (such as plastic lids)
- Chart for data collection
- Assessment worksheet
- Calculators

## Pre-activities

- A few days prior to this lesson ask students to help begin a collection of various circular objects. Show a few appropriate examples of the kinds of things needed. Strive for variety of diameters. You will need enough for each group of 3 or 4 students to have a variety with which to work.
- Number each of the circular objects you will be using.
- Review the terms diameter and circumference.

## Activities

- Divide the class into small groups of 3 or 4.
- Give each group a collection of the circular objects collected by the class.
- Each group should also have rulers, string for measuring, and a chart for collecting their data.
- Explain that in this lesson students will be measuring the circumferences and diameters of circles of different sizes and recording those measurements on the chart they have been given.
- Discuss the need for the string each group has been given.
- Students collect and record their data on the chart provided.
- They are to discuss the relationships they observe and answer the questions on the page with the chart.
- Small groups share their findings with the entire class.
- Students will have discovered that the circumference is a little more than 3 times the diameter.
- Introduce the concept of Pi, the symbol, and the number itself.
- Using the Math Explorer calculator Pi key, discuss the decimal and how most often it is rounded off as in 3.14. (This may be a good place for a quick review of rounding decimals.)
- Discuss how they have the necessary information to arrive at the circumference of any circle if the diameter or radius is given.
- Return to small groups, exchange circular objects, and measure diameters.
- Estimate and then calculate circumferences using a calculator or pencil.
- Discuss findings in large group.
- Complete the assessment worksheet.

## Assessment

- Observation of small group activities
- Data Collection Charts
- Large group discussion
- Assessment worksheet

## Supplemental information

### Comments

Students who often have difficulty with math will almost always remember this concept after doing this activity.

- Common Core State Standards
- Mathematics (2010)
#### Grade 6

- The Number System
- 6.NS.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

#### Grade 8

- 8.NS.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually...

- The Number System

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 6

**Goal 1**: Number and Operations - The learner will understand and compute with rational numbers.**Objective 1.03**: Compare and order rational numbers.**Objective 1.04**: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.- Analyze computational strategies.
- Describe the effect of operations on size.
- Estimate the results of computations.
- Judge the reasonableness of solutions.