Investigating Circles

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Investigating Circles
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Properties of Circles
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radius
diameter
Circle A closed curved with all points the same
distance from center

?
origin

area
circumference
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Origin

• The origin is the center of the circle.
• All points on a circle are the same distance from
  the origin.
• A circle is named by its center.
• Name Circle A

origin
A
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Diameter

• The diameter is the distance of a line segment
  going across a circle through its center. AB
• It divides the circle exactly in half.
• Is viewed as a line of symmetry.
• Symbol is lower case d.

diameter
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Radius

• Radius is the distance from the center of the
  circle to any point on the circle.
• Radius is one-half the length of the diameter.
• Symbol is lower case r.

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Circumference

• Circumference refers to the total distance around
  the outside of a circle.
• Can also be called the perimeter of a circle.
• Symbol is an upper case C.

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Diameter, Radius, Circumference of a Circle
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Diameter, Radius, Circumference of a Circle
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Making Connections

• You can estimate the age of a tree by measuring
  the circumference of a tree. For many kinds of
  trees, each 2 cm represents one year of growth.

100 cm
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Making Connections

• An odometer is an instrument used to measure the
  distance a vehicle travels by counting the number
  of wheel revolutions.

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Properties of a Circle Internet Activity
SITE www.harcourtschool.comSELECT
Math / Grade 7 / Glossary

• For each word given, write a definition and
  illustrate an example.
• Record work neatly and space between each
  definition.
• title and date your page
• Subtitle Properties of a Circle (underline)
• When you finish, go to site www.aplusmath.com
• Select Games, then the
• 1st Geometry Version
• of Non-Java Games.

Words to Define circle, circumference, diameter,
radius
Tools Required pencil, eraser, ruler, red pen,
disc, looseleaf
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Concept Development

• Activity 1
• With masking tape label the 4 circular shaped
  objects 1,2,3 and 4.
• b) Use the tape measure to find the
  circumference of each object. Measure carefully!
  (Use cm)
• c) Record results in the chart provided as you
  measure each object. Include unit of measure.
• Activity 2
• Trace around each object and then cut your
  tracing out. Trace and cut carefully! Label
  traced copy (object ?) Also, put your names on
  the trace copy.
• Fold each circle exactly in half and crease along
  the fold line.
• Measure the diameter of each circle.
• Record results in the chart provided. Check with
  me.

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Concept Development(cont)

• Activity 3
• Using the calculator provided, divide each
  objects circumference by its diameter.
• Record results to the nearest hundredths in
  column C/d. Check results.
• Look carefully at your results and discuss with
  your partner any similarities you notice. Think,
  and answer the question below chart.
• Check with me.

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Clean UP

• Return circular objects to table
• Calculators, scissors, tape and measuring tapes
  back in envelope, return to front table.
• Staple circles together give to me.
• Turn chart in to me.
• Pick up all small bits of paper and put in trash.
• Large pieces of paper to table.

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End of Part 1
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Circle Properties

• closed curved
• all points same distance from centre (origin)
• radius
• diameter
• circumference
• area
• pi

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Concepts you Should Now Know

• Origin
• Diameter
• Radius
• Circumference
• Ratio of C d

• center of a circle
• distance across center of circle (d)
• half the distance of diameter (r)
• distance around the outside of a circle ( C )
• Circumference is actually 3.14 (? )
• bigger than the diameter or about 3 times
  bigger

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Diameter, Radius, Circumference of a Circle
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Ratio Of The Circumference Of A Circle To Its
Diameter

• If you measure the distance around a circle (C)
  and divide it by the distance across the circle
  through its center (d), you should always come
  close to a particular value
• We use the Greek letter ? to represent this
  value.

? (pi)
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Ratio Of The Circumference Of A Circle To Its
Diameter

• The value of ? is approximately
  3.14159265358979323. . .
• So, C/d always ___
• Using ? is a quicker way to find the
  circumference of a circle.
• Using ? allow us to calculate circumference with
  less measuring,

? (pi)
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How ? Helps

• Knowing the value of ?,allows us to use formulas
  to calculate circumference.
• If the diameter of a circle is 2 cm, how could
  you calculate the circumference?
• C ? x ___
• Estimate the circumference
• The circumference is ____

2cm
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Circumference of a Circle
?

• C x d
• C 3.14 x 3
• C 9.42cm

If the diameter is 3cm
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Circumference of a Circle
Estimate Is . . .
?

• C x d
• C 3.14 x 1.5
• C 4.71cm

If the diameter is 1.5cm
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Circumference of a Circle
C ? x d but we dont know the diameter
?

• C x d
• d 2 x r
• d 2 x 3
• d 6
• C 3.14 x 6
• C 18.84m

If the radius is 3m
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Circumference of a Circle
?

• C x d
• C 3.14 x 5
• C 15.7

Estimate is . .
If the diameter is 5
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Diameter of a Circle
What formula could I use?
What is the diameter of a circle if the
circumference is 18.8?
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Diameter of a Circle
What is the diameter of a circle if the
circumference is 13.2?
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Diameter of a Circle
What is the diameter of a circle if the
circumference is 33.9?
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Area of a Circle
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Area of a Circle
Estimate the area of this circle.
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Area of a Circle
Seeing the square units can help.

Remember each block is one square unit
Estimate is
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Area of a Circle
Counting square units can give you a good
estimate, however, can be time consuming.
Counting will not always give an exact answer.

Actual is
The formula for finding the area of a circle is
A ? x r x r or ? r2
Estimate is
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Pie are square? NO, pie are round!
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Area of a Circle
Estimated area is
Remember A ? x r x r or ? r2
Actual area is
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Area of a Circle
Estimated area is
Actual area is
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Choosing a Formula

• To cut across a circular park has a you would
  travel 0.8 of a kilometer. How far would you
  travel around the park?
• A spoke of a bicycle wheel is 12 cm. What will
  be the distance of one turn of the wheel?

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Site www.mathgoodies.comUnder lessons choose
Circumference Area of a Circle1st Start with
Circumference of a Circle
Symbols are not always is lower case. R and D
instead of r and d

• Read the site information.
• Read, review, understand the examples.
• Read directions for the questions.
• Do the questions until correct.
• Check with me.
• Repeat steps above, using
• - Area of a Circle
• - Challenge

Units of measure are not metric. Miles (mi)
instead of kilometers (km)
You Need Pencil, paper,calculator
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Site www.mathgoodies.com/lessons/vol2/circumferen
ce.html
Symbols are not always is lower case. R and D
instead of r and d

• Read the site information
• Read, review, understand the examples
• Read directions for the questions
• Do the questions until correct.

Units of measure are not metric. Miles (mi)
instead of kilometers (km)
You Need Pencil, paper,calculator
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Site www.mathgoodies.comChoose Challenge
Exercise Read Directions Carefully
FORMULAS C ? x d d r x 2 r d 2 A ? x r
x r

• This activity is to be completed with a partner.
• Read the site directions carefully.
• You DO NOT need to copy questions or show your
  work.
• With your partner you are attempting to answer as
  many of the challenge questions as possible.
  Remember, get a mental picture, decide what is
  being asked, choose a formula or create your own,
  work it out. Scrap paper can be used.
• When you get a correct answer, number and record
  the answer on paper. This paper is to be turned
  in.
• If you are unable to get an answer you are
  allowed to skip a question. each questions, put
  ? if skipped.
• DO NOT share information or communicate with
  other groups. Work using a quiet voice as this is
  a competition.
• Have fun, but remember the guidelines.

You Need Pencil, paper, calculator.