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Math+Lesson+-+Nov.+2

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					Materials:

Student work books are in the red bin at the back of the room

String, meter sticks/rulers are on top of the bin

Worksheets



L.O. – To be able to calculate the area of a circle.

Begin first class with a review of circumference – the students had some difficulty with this earlier.

Have students (individuals or in pairs at your discretion) use meter sticks/rulers to measure the diameter
and radius of circular objects found in the classroom. They can then use the string to measure the
circumference as well by laying the string flat and straight on a ruler/meter stick. Have them write
down their findings in a chart. Ask them to leave one column blank for now. They will later use the last
column (circumference divided by diameter) for some analysis.

Encourage students to be as accurate and precise as they can be.

Object                Radius                           Diameter     Circumference           Circumference
                                                                                            divided by
                                                                                            diameter
Bin                   15 cm                 30 cm                   92                      3.06


Upon completion, have the students fill out the last column. Have a classroom discussion regarding how
the students should be finding that the circumference is equal to just over 3 times the length of the
diameter.

Ask students who got the closest to pi – 3.1415

Have a discussion on what pi actually is – it is a ratio between the diameter (and therefore radius) and
circumference of a circle.

         -pi is an irrational number – it’s decimals will never repeat in any fashion. Show students pi to
the first 1000 numbers http://www.angio.net/pi/digits/1000.txt

A discussion of how it was found will also beneficial for the students. Visit the following website, where
it discusses how Archimedes attempted to find pi.

http://betterexplained.com/articles/prehistoric-calculus-discovering-pi/

-Begin at the second section – “Finding Pi” – This explains how Archimedes attempted to calculate pi be
using ratios. They do not have to understand the math – simply that by putting a square around the
outside of any circle, and a square on the inside of the same circle can give us an approximation of the
circumference of a circle. Explain that he realized by using shapes with more size (hexagons, 32-gons,
etc) that the shape became closer and closer to a circle.



Area of a circle

-explain that the area of a circle is the number of squares that can fit inside a circle. Whenever we are
finding area, therefore, we put the number of units “squared”.

Write down the formula for area of a circle:

             - reiterate to students that squared simply means the number times itself.

It can also be expressed as

It is important to reiterate that the diameter of a circle Is equal to 2 x radius

        -if a question is given with the diameter, students must halve their diameters in order to calculate
the radius.

Write and draw an example on the board:

         A circle has a radius of 4 cm. What is the area of the circle?

        An artist is drawing a circular painting with a diameter of 150 cm. How many square centimetres is
the canvas she is drawing on?

Students can complete a worksheet on circles. Copies will be on bin.



http://www.homeschoolmath.net/worksheets/table-
circle.php?col=2&row=3&space=2&metric=1&customary=1&pi=3.14&round=2&image=1&c1=1&c2=1&
a1=1&a2=1&font=Default&FontSize=11pt&pad=5&ptitle=&Submit=Submit

http://www.homeschoolmath.net/worksheets/table-
circle.php?col=1&row=3&space=2&metric=1&pi=3.14&round=2&image=1&d1=1&r1=1&c1=1&c2=1&a1
=1&a2=1&font=Default&FontSize=11pt&pad=10&ptitle=&Submit=Submit
                                                                      Name____________________

                    Area, Circumference, Radius & Diameter of a Circle
1.      A dinner plate has a radius of 6 centimeters. What is the area?




2.      The distance around the wheel of a truck is 9.42 feet. What is the diameter of the wheel?




3.      A lawn sprinkler sprays water 5 feet in every direction as it rotates. What is the area of the sprinkled
lawn?




4.      What is the circumference of a 12-inch pizza?




5.       A dog is tied to a wooden stake in a backyard. His leash is 3 meters long and he runs around in circles
pulling the leash as far as it can go. How much area does the dog have to run around in?




6.      The distance around a carousel is 21.98 yards. What is the radius?
7.     A storm is expected to hit 7 miles in every direction from a small town. What is the area that the
storm will affect?




8.       An asteroid hit the earth and created a huge round crater. Scientists measured the distance around
the crater as 78.5 miles. What is the diameter of the crater?




9.      A semi-circle shaped rug has a diameter of 2 feet. What is the area of the rug?




10.      A spinner has 6 sectors, half of which are red and half of which are black. If the radius of the spinner
is 3 inches, what is the area of the red sectors?




11. The circular opening of a fan is 1 meter in diameter. There are three fan blades that each take up one twelfth
of the fan opening's area. How much of the area of the opening is not covered by the fan's blades?

				
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