CirclesM5G2: Students will understand the relationship of the circumference of a circle to its diameter is pi (π ≈ 3.14)M5M2: Students will extend their understanding of perimeter to include circumference.a) Derive the formula for the circumference of a circle.b)Find the circumference of a circle using the formula for pi ≈ 3.14.

Online Videos

• Circumference and Diameter of Circles (2:12)• Defining Circumference, Radius, Diameter

(4:19)• Perimeter, Circumference, and Area (2:12)• Solving Problems with Circles (6:13)• Song (parts of a circle, formulas) (1:33)

Word DefinitionCircumference Distance AROUND a circle C = πd

or C=2πrDiameter Line from one edge to another

THROUGH the center (2 times r)Radius Line from one edge to the

CENTER (1/2 of d)Pi Relationship between

circumference and diameter. Approximately 3.14.

Center Middle of the Circle

Parts of a Circle

What is given?

What is the diameter?

What is the radius?

Derive Pi (π)Step 1: Measure the diameter of each circular

item.Step 2: Measure the Circumference of each

circular item.Step 3: Divide the Circumference by the

DiameterStep 4: Average the findings for pi. (Add the

final column and divide by how many circles you measured)

Item Circumference Diameter C/d = pi (π)

1

Investigation to Derive π

• Circles and Cylinders (30:00)

Conclusions

Pi is the ratio of the circumference of a circle to its diameter, a commonly used approximate for Pi is 3.14.

How close is your average to Pi?

Find the difference between your average and Pi.

• By definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it.

• Circumference ÷ Diameter = Pi• C ÷ D = π• Or

• Pi x Diameter = Circumference

Formulas

• π = C ÷ d (ORIGINAL FORMULA)

• C = πd (USE WHEN YOU KNOW DIAMETER AND NEED CIRCUMFERENCE)

• d = C ÷ π (USE WHEN YOU KNOW CIRCUMFERENCE AND NEED DIAMETER)

Online Explorations

• Parts of a Circle• Radius, Diameter, Circumference, and Area• Diameter = 2 times radius game• Explore relationship of radius to circumferenc

e *Change investigation parameters to C / d, don’t do problems…requires area

Practice Problems

• Find the Circumference of the following circles.C = πd

1)Diameter = 10 in 6) Diameter = 12 cm2)Diameter = 15 in 7) Diameter = 37 in3)Diameter = 3 m 8) Diameter = 0.75 m4)Diameter = 9 m 9) Diameter = 1 yd5)Diameter = 92 cm 10) Diameter = 4.2 m

Practice Problems

• Find the diameter of the following circles.d = C ÷ π

1)C = 15.7 in 6) C = 78.5 cm2)C = 59.66 in 7) C = 119.32 yd3)C = 31.4 m 8) C = 314 mm4)C = 260.62 m 9) C = 1.57 km5)C = 97.34 yd 10) C = 188.4 cm

Worksheets

• Naming circles, diameter, and radii• Calculate radius and diameter of a circle• Radius and Diameter of a circle• Radius, Diameter, and Circumference• Diameters and Radius