WKSP
HW
Media
Student
Learning Goal
CC
Lesson
Standard
Pre Requisite
Circle
Know formulas for area & circumference of a circle.
7.G.4 Know the formulas for the area and circumference of a circle and solve
problems; give an informal derivation of the relationship between
circumference and area of a circle.
7.G.5 Solve real-world and mathematical problems involving area, volume and
surface area of two-and three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes and right prisms.
7.3.16: The Most Famous Ratio of All
7.3.17: Area of a Circle
7.3.20: Composite Area Problems

Students know the formula for the circumference and area of a circle and use it
to solve problems.
https://www.youtube.com/watch?v=HwSKkKrUzUk
Circle of Life – The Lion King
http://illuminations.nctm.org/Activity.aspx?id=3547
applet giving the circumference of a circle when changing its radius or diameter.
http://www.math.harvard.edu/~knill/mathmovies/swf/night_at_museum.html
Night at the Museum II – Einstein
http://www.math.harvard.edu/~knill/mathmovies/swf/castaway_rocklecture.html
Castaway – area of a circle
http://www.math.harvard.edu/~knill/mathmovies/swf/mi3.html
Mission Impossible – plan
#41
Spiral Review #10
http://www.learningupgrade.com/mathup/index.htm
formula song
Sir Cumference and the First Round Table
Sir Cumference and the Dragon of Pi: A Math Adventure
http://www.math.harvard.edu/~knill/mathmovies/swf/oxfordmurders.html
Oxford Murders – ‘I believe in 𝜋’
http://www.math.harvard.edu/~knill/mathmovies/swf/realitybites.html
Reality Bites – Astronomy class
Circle
Radius & Diameter
With the ruler part of your slide & measure,
create a segment with a length of 3 cm.
.
The segment you just created is known as a ____________.
Using the compass part of your slide & measure, create a circle with a radius of 3 cm.
The entire distance from one side of a circle, through the center, ending at the other
side of a circle is known as a _______________.
If a circle has a radius of 3 cm, what is its diameter?
Circumference
Circumference:
There is a relationship between the circumference and the diameter of every circle!
Example: Pizza
Yesterday, I ordered an 8 inch pizza pie (that’s the diameter of the pie). I then took a
piece of yarn and measured the around the outside of the crust. The circumference of
the pizza pie measured 25.13 inches. What is the ratio of the pizza’s circumference to
its diameter?
Example: Ring
I wear a size 7 ring which has a diameter of 17.3 mm. The circumference of the ring is
54.322 mm. What is the ratio of the ring’s circumference to its diameter?
𝜋=
Circle
Compare:
𝜋
𝜋
3.14
22
7
The formula for the circumference of any circle is hiding in this ratio!
𝜋=
𝐶
𝑑
Given the circle’s diameter, use C = ________
Given the circle’s radius, use C = _________
Example: Paper Plate
Find the circumference of a paper plate that has a radius of 11.7 cm.
Exact:
Approximate to the nearest hundredth
when 𝜋 ≈ 3.14
Approximate to the nearest hundredth
22
when 𝜋 ≈ 7
Example: Circle in a Square
The figure shows a circle within a square. Find the circumference of the circle.
Circle
Area


C = 2𝜋r
Acircle = _____
Example: Sprinkler
A sprinkler rotates in a circular pattern and sprays water over a distance of 12 feet.
What is the area of the circular region covered by the sprinkler? Express your answer to
the nearest square foot.
Exercise:
1. Find the circumference of a circle that has a diameter of 28 cm.
a. Give an exact answer in terms of 𝜋.
b. Use 𝜋 ≈
22
7
and express your answer as a fraction in lowest terms.
c. Use the 𝜋 button on your calculator and express your answer to the nearest
hundredth.
2. Suzanne is making a circular table out of a square piece of wood. The radius of the
circle that she is cutting is 3 feet. How much waste will she have for this project?
Express your answer to the nearest square foot.
3. The area of a circle is 36𝜋 cm2. Find its circumference.
4. Find the ratio of the area of two circles with radii 3 cm and 4 cm.
Circle
Name: __________________________________
Pre-Algebra
Date: ______
Exit Ticket
A circle has a diameter of 14 cm.
a. Find the exact area of the circular region.
b. Find the approximate area using
22
7
to approximate 𝜋.
c. What is the circumference of the circle? (‘Exact’ is implied)
Name: __________________________________
Pre-Algebra
A circle has a diameter of 14 cm.
a. Find the exact area of the circular region.
b. Find the approximate area using
22
7
to approximate 𝜋.
c. What is the circumference of the circle? (‘Exact’ is implied)
Date: ______
Exit Ticket
Circle
Name: __________________________________
Pre-Algebra
Date: ______
HW #113
Complete the boxes using the given information:
1.
diameter =
9 in
area =
circumference =
2.
radius =
14 in
area =
circumference =
radius =
diameter =
area = 25𝜋 in2
circumference =
radius =
diameter =
(nearest tenth)
area =
circumference = 20 inches
3.
4.
Review
5. What is the largest negative integer?
Circle
Round your answers to the nearest tenth.
radius
Circumference
diameter
Area