1. 12-5 6 th grade math Circumference

2. Objective To find circumference of circles Why? To know how to use formulas and evaluate variable expressions using the order of operations. To further your knowledge of geometry and measurement.

3. California State Standards MG 1.1 : Understand the concept of a constant, such as Π ( pi); know the formulas for the circumference … of a circle. MG 1.2: know common estimates of Π ( pi) (3.14, 22/7) and use these values to estimate and calculated the circumference … of circles; compare with actual measurements AF 3.1: Use variables in expressions describing geometric quantities … (e.g., C = Π x d or C = Π x ½ r: the formula(s) for … the area of a circle …) AF 3.2: Express in symbolic form simple relationships arising from geometry. MR 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, … and observing patterns.

4. Vocabulary Circumference – The distance around a circle (similar to the perimeter of a polygon). The distance around a circle is a little more than 3 times the length of the diameter. The ratio of the circumference to the diameter C d is always the same. The ratio is called pi Π. Its value is ≈ 3.14 or 22. 7 Read the story: Sir Cumference. Circum= Greek for around. C = Π x d C = Π x 2r Pi = 3.14 or 22/7. Use the decimal or fraction value of pi that best accommodates the computation of the problem.

5. Vocabulary Diameter – A line segment that passes through the center of a circle and has both endpoints on the circle. Radius – A line segment with one endpoint on the circle and the other endpoint in the center. The radius is ½ the diameter.

6. The Relationship of Circumference. ObjectCircumferenceDiameter C d Pan lid71.4 cm22.7 cm 71.4 ÷ 22.7 ≈ 3.145 Glass11 in3.5 in 11 ÷ 3.5 ≈ 3.143 Pool47 ft15 ft 47 ÷ 15 ≈ 3.133

7. How to Remember the Formula: Circumference 1) A circle is round (duh). So remember a circle uses pi (pie), 3.14 or 22/7 2) Look at the word: ‘circumference’ – The word circumference begins with c and d, for diameter, is next to it – The word circumference is a long word to stand for the long line of diameter. Remember the story Sir Cumference? Lady Di was tall and had a long reach? – Circumference has 4 syllables and Diameter has 4 also – Area has 3 syllables and Radius has 3 also. 3) Therefore the formula = C = 3.14 x d ( 3.14 x 2r)

8. How to Find the Circumference of Circles 1)Observe the circle figure. Be sure the radius or diameter is labeled. 2)Write out the formula: 3.14 x d or 3.14 x 2r 3) Be sure to use the diameter or twice the radius. 4) Check work and add label to answer. Hoop: diameter = 28 in. C = 3.14 x 28 C = 87.92 in C ≈ 88 in or C = 22 x 28 7 1 C = 22 x 4 C ≈ 88 in Tire: radius = 8m C = 3.14 x (8 x 2) = 3.14 x 16 ≈ 50.24

9. Try It! Find circumference of circles. Round to the nearest whole number. 1)D = 5m 2)D = 3 in 3)D = 3.5 4)D = 7 ft 5)R = 11 in 1)D = 5m = 3.14 x 5 = 15.7 ≈ 16 m 2) D = 3 in 3.14 x 3 = 9.42 ≈ 9 in 3) D = 4.5 3.14 x 4.5 = ≈ 14 cm 4) D = 7 ft 3.14 x 7 = 21.98 ≈ 22 ft 5) R = 11 in 3.14 x (11 x 2) = 69.08 ≈ 69 in

10. Objective Review To find circumference of circles Why? You now know how to use formulas and evaluate variable expressions using the order of operations. You have furthered your knowledge of geometry and measurement. To find the circumference of a circle, multiply pi times the diameter or pi times twice the radius.

11. Independent Practice Complete problems 6- 13 Copy original problem first. Show all work! If time, complete Mixed Review: 14-20 If still more time, work on Accelerated Math.