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Investigate the fundamental properties of circles including diameter, radius, and circumference using hands-on activities. Learn about the concept of pi and its role in circle calculations.
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radius diameter Circle A closed curved with all points the same distance from center • origin area circumference
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
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 islower case d. diameter
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.
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.
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
Making Connections • An odometer is an instrument used to measure the distance a vehicle travels by counting the number of wheel revolutions.
Properties of a Circle – Internet Activity SITE: www.harcourtschool.comSELECT: Math / Grade 7 / Glossary Words to Define circle, circumference, diameter, radius • 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 1stGeometry Version of Non-Java Games. Tools Required pencil, eraser, ruler, red pen, disc, looseleaf
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 exactlyin half and crease along the fold line. • Measure the diameter of each circle. • Record results in the chart provided. Check with me.
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.
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.
Group # Object # Circumfer-ence (C) Diameter (d) C/d
Circle Properties • closed curved • all points same distance from centre (origin) • radius • diameter • circumference • area • pi
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 Concepts you Should Now Know
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)
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)
How Helps 2cm • 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 ____
Circumference of a Circle • C = x d • C = 3.14 x 3 • C = 9.42cm If the diameter is 3cm
Circumference of a Circle Estimate Is . . . • C = x d • C = 3.14 x 1.5 • C = 4.71cm If the diameter is 1.5cm
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
Circumference of a Circle • C = x d • C = 3.14 x 5 • C = 15.7 Estimate is . . If the diameter is 5
Diameter of a Circle What formula could I use? What is the diameter of a circle if the circumference is 18.8?
Diameter of a Circle What is the diameter of a circle if the circumference is 13.2?
Diameter of a Circle What is the diameter of a circle if the circumference is 33.9?
Area of a Circle Estimate the area of this circle.
Area of a Circle Seeing the square units can help. Remember each block is one square unit Estimate is
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
Area of a Circle Estimated area is Remember A = x r x r or r2 Actual area is
Area of a Circle Estimated area is Actual area is
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?
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
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
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.
