1. Concept of Circle, Circumference and Area

2. Investigating Circles

3. Properties of Circles

5. • Circle  radius diameter A closed curved with all points the same
distance from
center • 
origin
area
circumference

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

7. 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

8. 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.

9. 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.

10. Diameter, Radius, Circumference of a Circle

11. Diameter, Radius, Circumference of a Circle

12. 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

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

14. Properties of a Circle – Internet Activity SITE: www. harcourtschool
Properties of a Circle – Internet Activity SITE: SELECT: 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
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

15. Concept Development Activity 1 Activity 2
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.

16. Concept Development(con’t)
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.

17. 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.

18. End of Part 1

19. Group #
Object #
Circumfer-ence (C)
Diameter (d)
C/d

20. Circle Properties closed curved
all points same distance from centre (origin)
radius
diameter
circumference
area pi

21. 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 ( )
bigger than the diameter or about 3 times bigger

22. Diameter, Radius, Circumference of a Circle

23. 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)

24. Ratio Of The Circumference Of A Circle To Its Diameter
The value of  is approximately
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)

25. 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

26. Circumference of a Circle
C = x d
C = 3.14 x 3
C = 9.42cm
If the
diameter is 3cm

27. Circumference of a Circle
Estimate
Is . . . 
C = x d
C = 3.14 x 1.5
C = 4.71cm
If the
diameter is 1.5cm

28. Circumference of a Circle
C =  x d
…but we don’t 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

29. Circumference of a Circle
C = x d
C = 3.14 x 5
C = 15.7
Estimate is . .
If the
diameter is 5

30. What formula could I use? What is the diameter of a circle if the
circumference
is 18.8?

31. What is the diameter of a circle if the
circumference
is 13.2?

32. What is the diameter of a circle if the
circumference
is 33.9?

33. Area of a Circle

34. Estimate the area of this circle.
Area of a Circle
Estimate the area of this circle.

35. Area of a Circle Seeing the square units can help.
Remember each block is one square unit
Estimate is

36. 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

37. Pie are square? NO, pie are round!

38. Area of a Circle Estimated area is Remember A =  x r x r or  r2
Actual area is

39. Area of a Circle
Estimated area is
Actual area is

40. 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?

41. Read the site information. Read, review, understand the examples.
Site: Under lessons choose Circumference & Area of a Circle 1st 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

42. Site: www.mathgoodies.com/lessons/vol2/circumference.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

43. You Need: Pencil, paper, calculator.
Site: Choose 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.