1.
1
Warm Up
OBJECTIVE: Students will be able to describe the shortcut to calculate the
area of any circle in the world.
Find the area of each shaded region:
#1 #2
Explain how you found your answer to problem 1.#3

2.
2
A = 36 square units
Describe how
you found the
area of this
shape.
WHY?
Warm Up Review
1
Agenda

3.
3
Warm Up Review
A = 9 square units
Describe how
you found the
area of this
shape.
WHY?
The shaded part
is called a “radius
square”.
Why do you think
it is called this?
1
Agenda

4.
4
Launch – Finding the Area of a Circle
Think-Pair-Share
1) How would you find
the area of this circle?
2) Why is it hard to find
the area of a circle?
Agenda
wait..

5.
5
• 1) Not all of the
squares are
completely in the
circle.Hey, is this
a square?
What about
this?
1 2
3 4 5 6 7 8
??? ?
• 2) There are just
TOO many to count!
Nice Job!
I found the same two problems.
• PROBLEM 1
With these 2 problems, do you think there is a way to
find the area of a circle more quickly ?
• PROBLEM 2
Agenda
1wait..
Launch

6.
6
People have always run into these problems, when
finding the area of a circle years ago, the Babylonian
mathematicians discovered that the radius square was
the key to quickly finding the area of a circle.
Radius Square = r2
A certain number of radius squares fits inside
of every circle.
Agenda
Launch

7.
7
Explore: Getting Ready
How many radius squares fit
inside one circle?
This is a radius.
This is a
radius
square.
• To find out the shortcut for the
area of a circle you will first
answer this question.
What is your prediction?
1
Agenda
wait..

8.
Explore:
The Question…
How many radius squares fit
inside a circle?
More than 1 square?
More than 2 squares?
How many radius squares do YOU think
fit inside one circle?
1wait..
8

9.
9
Explore: The Activity
• You will get a paper circle and 4
radius squares.
• You need to find out the answer
to this question:
How many radius squares fit
inside a circle?
by cutting and gluing the radius
squares into the circle.
Agenda
wait..

10.
10
Explore: How to do the activity
• To count a radius square all
parts of it must be inside the
lines of the circle.
How many radius squares fit inside one circle?
This circle does not have one
whole radius square covering
its surface.
Agenda
wait..

11.
11
How many radius squares fit inside one circle?
You may cut the squares to make
them fit inside the circle.
1
Agenda
Explore: How to do the activity

12.
12
How many radius squares fit inside one circle?
• But all parts of the radius square
must be inside the circle to
count.
This circle does have one
whole radius square covering
its surface.
# of RADIUS
SQUARES
THAT FIT INSIDE
1
wait..
Explore: How to do the activity

13.
13
Explore: Area of a Circle Challenge
How many radius squares fit inside one circle?
r
r
r
You will have 10 minutes to try
this activity.
Agenda
wait..

14.
14
Explore: Clean Up
Even though you may not have finished
the activity, it is time to clean up.
Agenda

15.
15
Think-Pair
• Now that you have tried the activity do you know…
• Take one minute to think about the answer to this
question.
• Next, talk to your partner. Take turns sharing the
answer to this question.
How many radius squares fit inside a circle?
Agenda

16.
Debrief
How many radius squares fit inside one circle?
• What is a number that you recently learned that is more than 3?
It’s π
• Is that true for every circle no matter its size?
YES!
1wait..
Agenda17

17.
18
Debrief: Is There a Shortcut?
• We know that EXACTLY π (3.1415…) radius squares fit inside a circle.
• Can we write a rule that will work for any circle?
The area of a circle is a little bit more than 3 times the radius square.
A shortcut
makes you
faster!
Looking at
the Rule
Agenda
wait..

18.
Exit Ticket
• What is the best estimate for the area of this circle?
When I say so “go” make the gesture next to the answer you think is correct..
A) 5 square units
B) 15 square units
C) 25 square units
D) 75 square units
Agenda
20