Lesson Plan

# Circles and Pi

Explore the relationship between circles and pi.
Callean H.
Classroom teacher
I.S. 93 Ridgewood
Ridgewood, United States
My Subjects Math
Objectives

Students will be able to develop and explain the relationship between the irrational number, pi, and the circumference and diameter of a circle.

This activity will take 75-90 minute period to complete.

Subjects
Math

#### 1 Hook - I See Math Everywhere

Free, Paid

10 minutes

Ask students to think about the veryday places and situations where they see math.

Examples
- I get change when I buy an item at the grocery store.  Subtraction

- I grew 4 inches over the summer.  Measurement

Direct them to the padlet link.  They should complete the sentence "I see math..." by double clicking on the page.  They should try to identify the "math."

Remind them to include their name and class at the end of their entry.

Student Instructions

I see math....

Go to the above link complete the sentence by naming at least 1 place/situation where you see math.  Try and identify the specific "math" you see.  Include your name and class.

For example: I see math when I help my mom bake a cake.  We use a recipe and measureing cups that have fractions.

#### 2 Mini Lesson (Part 1) - Parts of A Circle

5 minutes

Instruct students to draw a circle and label the parts.

Call students up to label a pre drawn circle with the names.

Watch the khanacademy video on parts of a circle.

Students should correct their original drawing with the correct labels and diagrams.

Student Instructions

Draw a circle and label the parts: center, radius, diameter and circumference.

After watching the video, correct your diagram.

#### 3 Mini Lesson (Part 2) - Vocabulary

Activity: Creating

10 minutes

Direct students to take out their Unit 1 Vocabulary and to complete the necessary words.

Students can use a paper copy. or they can use Google Drive to store an electronic version of the vocabulary.

Students can work independently or collaboratively in pairs or groups to complete the worksheet.

Circle - a set of points that are the same distance from the center.

Radius - a straight line from the center of the circle to a point on the circle.

Diameter - a straight line that goes through the center of the circle

Circumference - the distance around (perimeter) of a circle.

Student Instructions

Take out your Unit 1 Vocabulary worksheet.

Complete the definitions for Circle, Radius, Diameter and Circumference.

#### 4 Guided Instruction

5  minutes

Read pages 1- 13 of "Sir Cumference and the Dragon of Pi" by Cindy Neuschwander.

Student Instructions

Listen as I read alound the story "Sir Cumference and the Dragon of Pi" by Cindy Neuschwander.

Answer the following questions as you listen to the story.

What is the name of the main character?____________
What is the name of the the mother?______________
What is the name of the father?_____________

#### 5 Group Work - The Circle's Measure

Activity: Exploring

25-30 minutes

Provide students with 3 different sized circles, a piece of string, a calculator and a ruler.

Student Instructions

The Circles Measure
Measure the midle and cirlce around. Divide so a number can be found.  Every circle, great and small, the number is the same for all.  It's also the dose, so be clever, or a dragon he will stay...FOREVER."

Help Radius solve the riddle and determine the dose necessary to save his father?

You will work in pairs, you will use a piece of string, a ruler and a calculator to measure the circle.

Circle A/B/C
1. Put one end of your string on the outside edge of the circle. Carefully place the string all the way around
the circle. Pinch the part of the string the meets up with the other end of the string you first placed on the
circle. _______________ inches/centimeters
2. Using the centimeter side of your ruler, measure the part of the string that went around the outside of the
3. Measure the distance across the circle making sure to go through the center. _______________ inches/centimeters
4. Divide the answer you got on #2 by the answer you got on #3.__________
5. Now see how many times that part of the string will go from one edge of the circle to the other, making sure to go through the center of the circle. How many times did it go across?__________________

#### 6 Closing

Activity: Conversing

15 minutes

With your partner, use the results from the activity to answer the closing questions.

Student Instructions

1. What do you notice about all of the answers on #4 for each of your circles?_________________
2. Are your answers similar to the number of times your string would go across the circle going through
the center?______________________
3. What statement could you make about the relationship between the distance around the outside of the circle and the distance across the circle going through the middle?_____________________
4. What term do we use to represent the oustide edge around a circle?______________________
5. What term do we use to represent the distance from one edge of a circle to the other edge of a circle
that goes through the center?______________________
6. What term do we use to represent that relationship between the dsitance around the outside edge of
the circle and the distance across the center of the circle?________________
7. Can you give a formula that would calculate this measurement?___________________