1. Circumference of a Circle Lesson 10.8

2. Perimeter the perimeter is the distance around a figure

3. Find the perimeter to side ratio 6 units

4. Find the perimeter to side ratio Total Perimeter = 6 x 4 or 24 units. SidePerimeterPerimeter/Side 6 units2424/6= 4 units

5. Find the perimeter to side ratio 11 units SidePerimeterPerimeter/Side 11 units4444/11=4

6. Find the perimeter to side ratio 3 units SidePerimeterPerimeter/Side 3 units1212/3=4

7. Find the perimeter to side ratio Why is the perimeter/side ratio always 4? A square consists of 4 sides of equal length. Therefore, the perimeter of a square is 4 times the length of one of its sides.

8. Open Your Math Journals Complete page 370 with a partner that does not sit at your table. You will need to take you time to understand what the question is asking. Read the question 1 carefully. Study the chart to understand the information it presents. Answer questions 2 & 3

9. Now How About Circles? Today we are going to explore similar ratios for circles. What is the name for the perimeter of a circle? ◦ circumference What is the circumference of the Earth?

10. Circumference Vocabulary Time!!!!! Take out your spiral!

11. How about a tune?

12. Add this diagram to your notes diameter radius c i r c u m f e r e n c e

13. What do you notice? 3 inches 6 inches

14. What do you notice? 12 inches 24 inches

15. What do you notice? 1.5 inches 3 inches

16. What do you notice? 50 inches 100 inches

17. So, what did you notice? The radius is ½ of the diameter. The diameter is twice the radius.

18. Is the circumference longer or shorter than the diameter? 1 foot

19. Is the circumference longer than twice the diameter? 1 foot

20. Which path is longer-around the square or around the circle? 1 foot

21. We can conclude that the circumference is more than 2 diameters, but less than 4 diameters. 1 foot

22. Time to measure! You and a new partner will complete MJ page 371. Choose an object from the back table. (It doesn't have to be your object) Measure the circumference by wrapping the string around the widest part of the circle – make sure the string is straight around the object, not on an angle.

23. Time to measure! Carefully remove the string from the object marking the starting and ending point of the circumference. Measure this length of string in centimeters using your ruler. Convert to millimeters. (÷10) 27 cm = 2.7 mm Record the length in millimeters.

24. To determine diameter of spheres, place your object on the corner of a piece of computer paper. Time to measure!

25. The points where the sides of the angle intersect the circle are the endpoints of the diameter. Time to measure!

26. Math Journal page 371 Complete the table When you record your answers, round to the hundredths place Answer question 5 When you complete question 5, come to the board and input your information on the stem and leaf plot We will be working together to answer question 6

27. Results Remember the perimeter/side ratio for a square? 4 The circumference/diameter ratio also appears to be a constant with a value of between 3.1and 3.2 The exact value of this ratio is an irrational number named for a letter of the Greek alphabet – π (pi)

28. Ratio of a circle circumference = π diameter

29. Mathematical Pi

30. I love pi

31. What is π ? It is impossible to calculate the exact value of π In 1949, it was calculated out to 37,000 decimal places on one of the first computers In 1981 to 2 million digits on a supercomputer In 1999, there were more than 206 billion digits

32. What is π ? Because π goes on forever without a pattern, we use an approximation of its exact value. Because we approximate the value, our calculations of π cannot be exact. We will use the symbol ≈ to mean approximately equal to

33. Let’s Practice Return to the chart on MJ page 371 Using the diameter measurement and the value of π, recalculate the circumference of one or two of your objects Remember your answer will be an estimate and will not be exact.