1. Circles M5G2: 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.

2. Online Videos Circumference and Diameter of Circles (2:12) Circumference and Diameter of Circles Defining Circumference, Radius, Diameter (4:19) Defining Circumference, Radius, Diameter Perimeter, Circumference, and Area (2:12) Perimeter, Circumference, and Area Solving Problems with Circles (6:13) Solving Problems with Circles Song (parts of a circle, formulas) (1:33) Song (parts of a circle, formulas)

3. WordDefinition Circumference Distance AROUND a circle C = πd or C=2πr Diameter 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. CenterMiddle of the Circle

4. Parts of a Circle

5. What is given?

7. What is the diameter?

8. What is the radius?

9. 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 Diameter Step 4: Average the findings for pi. (Add the final column and divide by how many circles you measured) ItemCircumferenceDiameterC/d = pi (π) 1

10. Investigation to Derive π Circles and Cylinders (30:00) Circles and Cylinders

11. 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.

12. 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

13. 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)

14. Online Explorations Parts of a Circle Radius, Diameter, Circumference, and Area Diameter = 2 times radius game Explore relationship of radius to circumference *Change investigation parameters to C / d, don’t do problems…requires area Explore relationship of radius to circumference

15. Practice Problems Find the Circumference of the following circles. C = πd 1)Diameter = 10 in6) Diameter = 12 cm 2)Diameter = 15 in7) Diameter = 37 in 3)Diameter = 3m8) Diameter = 0.75 m 4)Diameter = 9 m9) Diameter = 1 yd 5)Diameter = 92 cm10) Diameter = 4.2 m

17. Practice Problems Find the diameter of the following circles. d = C ÷ π 1)C = 15.7 in6) C = 78.5 cm 2)C = 59.66 in7) C = 119.32 yd 3)C = 31.4 m8) C = 314 mm 4)C = 260.62 m9) C = 1.57 km 5)C = 97.34 yd 10) C = 188.4 cm

18. 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