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What are we going to do?

Learning Objectives. 1. We will determine 1 the formulas for the area and circumference of a circle . 2. We will solve problems for the area and circumference of a circle. What are we going to do?. CFU. Activate Prior Knowledge.

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What are we going to do?

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  1. Learning Objectives 1. We will determine1 the formulas for the area and circumference of a circle. 2. We will solve problems for the area and circumference of a circle. What are we going to do? CFU Activate Prior Knowledge • The diameter(d) of a circle is the distance across the center of the circle. • The radius (r) of a circle is the distance from the center to any point on the circle. • The radius is half the length of the diameter. 1. 2. Students, you already know how to find the diameter and radius of a circle. Now, we will use the diameter and the radius of a circle to solve problems for the area and circumference of a circle. Make Connection radius 12 in 8 cm diameter 6 in. 12 in. 8 cm 16 cm r = ______ d = ______ r = ______ d = ______ 1 figure out Vocabulary

  2. (Pair-Share) What do you think the difference is between the CIRCUMFERENCE of a circle and the AREA of a circle? CFU c i r c u m f e r e n c e Area

  3. Concept Development 20 in.   3.14 The circumferenceof a circle is the distance around the circle. Circumference is like the perimeter, but is only used with circles. A formula is an equation that declares the relationship between two or more quantities. Pi () is the constant2ratio of the circumference to the diameter of a circle. CFU 2 CFU 1 What is the formula for using diameter to find the circumference of a circle? In your own words, what is the circumference of a circle? “The circumference of a circle is _____________.” How is radius related to diameter? What formula is used to find circumference using the radius of a circle? Using the diameter (d) Using the radius (r) The same tire has a radius of 10 inches. A tire has a diameter of 20 inches. 20 in. 10 in. 20 in. 20 in. 62.80 Circumference The distance around the tire is _____ inches. 2a number that does not change Vocabulary 10 inches

  4. Concept Development area radius diameter 3 ft   3.14 The areaof a circle is the amount of space insidethe circle. Area is always written as units squared (in², cm²). A formula is an equation that declares the relationship between two or more quantities. Pi () also used in the formula to find the area of a circle. CFU 3 CFU 1 CFU 2 What is the formula for using radius to find the area of a circle? In your own words, what is the area of a circle? “The area of a circle is _____________.” What can you do if you only know the diameter of the circle, but you want to find the area of the circle? How is radius related to diameter? In your own words, the radius is exactly ________ of the diameter. Using the radius (r) Area Formula: A round carpet disc has a radius of 3 ft. The rug takes up 28.26 ft² of space. 2a number that does not change Vocabulary

  5. Concept Development (Continued)   3.14 The circumferenceof a circle is the distance around the circle. The area of a circle is the space inside the circle. A formula is an equation that declares the relationship between two or more quantities. Pi () is the constant1 ratio of the circumference to the diameter of a circle. CFU 1 CFU 2 Chan is creating a circular garden. For which will he need to find the circumference? How do you know? A Chan wants to build a fence around the garden. B Chan wants to add soil to cover the garden. In your own words, what is the circumference of a circle? “The circumference of a circle is _____.” Chan is creating a circular garden. For which situation will he need to find the area? How do you know? A Chan wants to build a fence around the garden. B Chan wants to add soil to cover the garden. In your own words, what is the area of a circle? “The area of a circle is _____.” A rug has a radius of 4 feet. Circumference Area C = 2  r  A =   r2 Animated 4 feet 4 feet 1 a number that does not change Vocabulary

  6. Skill Development/Guided Practice 1 8 cm 9 in. The circumference of a circle is the distance around the circle. The area of a circle is the space inside the circle. C = 2  r  OR C = d  Determine the formulas for the circumference and area of a circle. Solve problems for the area and circumference of a circle. Read the problem carefully. Identify4the given measurement. (underline) Identify the measurement that needs to be found. (circle) Determine5 the correct formula to find the measurement. (write on line) Substitute the given value into the formula. 1 a b 2 Circumference 3 Area A =   r2 4 find (synonym) 5figure out 6replace (synonym) Vocabulary

  7. Skill Development/Guided Practice (Continued) 4 in. The circumference of a circle is the distance around the circle. The area of a circle is the space inside the circle. 8 in. C = 2  r  OR C = d  Determine the formulas for the circumference and area of a circle. Solve problems for the area and circumference of a circle. Read the problem carefully. Identify4the given measurement. (underline) Identify the measurement that needs to be found. (circle) Determine5 the correct formula to find the measurement. (write on line) Substitute the given value into the formula. 1 a b 2 Circumference 3 Area A =   r2 4 find (synonym) 5figure out 6replace (synonym) Vocabulary

  8. Skill Development/Guided Practice 2   3.14 The circumferenceof a circle is the distance around the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. CFU How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? Solve problems for the area and circumference of a circle. 1a Read the problem carefully. Identify2 the given information. (underline) Determine3 which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 1b a 3 b 2 3 Area Circumference C = 2  r  A =   r2 C = 2  r  C = 2  4  “The circumference of the cookie is 25.12 centimeters.” C = 8 3.14 C = 25.12 2 find (synonym) 3 figure out Vocabulary

  9. Skill Development/Guided Practice 2 (continued)   3.14 The circumferenceof a circle is the distance around the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. CFU How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? Solve problems for the area and circumference of a circle. 1a Read the problem carefully. Identify2 the given information. (underline) Determine3 which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 1b a 3 b 2 3 Area Circumference C = 2  r  A =   r2 2 find (synonym) 3 figure out Vocabulary C = 2  r  C = 2  5  “The circumference of the hoop is 31.4 inches.” C = 10 3.14 C = 31.4

  10. Skill Development/Guided Practice 2 (continued)   3.14 The circumferenceof a circle is the distance around the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. CFU How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? Solve problems for the area and circumference of a circle. 1a Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 1b a 3 b 2 3 Area Circumference C = 2  r  A =   r2 C = 2  r  C = 2  10 C = 20 3.14 C = 62.80 “The wheel will travel 62.80 inches each time it turns one full turn around.”

  11. Skill Development/Guided Practice 2 (continued)   3.14 The circumferenceof a circle is the distance around the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. CFU How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? Solve problems for the area and circumference of a circle. 1a Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 1b a 3 b 2 3 Area Circumference C = 2  r  A =   r2 C = 2  r  C = 2  6  C = 12 3.14 C = 37.68 “The crust is 37.68 inches long.”

  12. Skill Development/Guided Practice 2 Skill Development/Guided Practice 2 (continued)   3.14 The area of a circle is the space inside the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. CFU How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? Solve problems for the area and circumference of a circle. 1a Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 1b a 3 b 2 3 Area Circumference C = 2  r  A =   r2 A =   r2 A =   122 “The area of the top of the barrel is 452.16 square inches.” A = 3.14 144 A = 452.16 A =   r2 A =   72 A = 3.14 49 A = 153.86 “The area of the top of the pie is 153.86 square centimeters.”

  13. Skill Development/Guided Practice 2 (continued)   3.14 The area of a circle is the space inside the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. CFU How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? Solve problems for the area and circumference of a circle. 1a Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 1b a 3 b 2 3 Area Circumference C = 2  r  A =   r2 A =   r2 A =   92 “The top of the pizza has 254.34 square inches for toppings.” A = 3.14 81 A = 254.34 A =   r2 A =   32 A = 3.14 9 A = 28.26 “28.26 square feet of cloth is needed to make a tablecloth.”

  14. Skill Development/Guided Practice 2 (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 4 5 A =   r2 C = 2  r  A =   32 C = 2  3  A = 3.14 9 C = 6  “He will have to cover 28.26 square feet with fertilizer.” “Ephraim will need 18.84 feet of fencing.” A = 28.26 C = 18.84 C = 2  r  A =   r2 C = 2  9  A =   92 C = 18  A = 3.14 81 “The cast will need 56.52 feet of garland to go around the stage.” A = 254.34 C = 56.52 “Mr. Garcia will need 254.34 square feet of planking to cover the stage.”

  15. Relevance Tyrone is buying a new tire for his bike. He needs to measure the circumference of the tire but all he has is a wooden yardstick. How can he find the circumference of the tire? Tyrone could measure the diameter of the tire and use the formula to solve for circumference. The circumferenceof a circle is the distance around the circle. The area of a circle is the space inside the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. Solving problems for the area and circumference of a circle will help you when building things in real life. Circumference Area A =   r2 CFU Does anyone else have another reason why it is relevant to solve problems for the area and circumference of a circle? (Pair-Share) Why is it relevant to solve problems for the area and circumference of a circle? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? C = 2  r  OR C = d 

  16. The circumferenceof a circle is the distance around the circle. The area of a circle is the space inside the circle. Pi () is the constant ratio of the circumference to the diameter of a circle.   3.14 Skill Closure C = 2  r  OR C = d  Solve problems for the area and circumference of a circle. Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 a b 2 Word Bank Circumference 3 Word Bank Area circumference area circle pi () radius diameter A =   r2 C = 2  r  “The frame will have to be 31.4 centimeters long.” C = 2  5  C = 31.4 C = 10  A =   r2 A =   52 “The mirror has an area of 78.5 square centimeters.” A =   25 A = 78.5 Access Common Core Gary is replacing the leather cover on a stool. What measurement could he find so that the new leather cover is the same size as the old one? How do you know? Summary Closure What did you learn today about solving problems for the area and circumference of a circle? (Pair-Share) Use words from the word bank.

  17. Independent Practice   3.14 The circumferenceof a circle is the distance around the circle. The area of a circle is the space inside the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. Solve problems for the area and circumference of a circle. Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 a b 2 3 Area Circumference C = 2  r  A =   r2 C = 2  r  C = 2  7  “The circumference of the platter is 43.96 inches.” C = 14 3.14 C = 43.96 C = 2  r  C = 2  14  “The edge around the pool is 87.92 feet long.” C = 28 3.14 C = 87.92

  18. Independent Practice (continued)   3.14 The circumferenceof a circle is the distance around the circle. The area of a circle is the space inside the circle. Pi () is the constant ratio of the circumference to the diameter of a circle. Solve problems for the area and circumference of a circle. Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) 1 a b 2 3 Area Circumference C = 2  r  A =   r2 A =   r2 A =   242 “The top of the stump measures 1,808.64 square inches.” A = 3.14 576 A = 1,808.64 A =   r2 A =   132 “The top of the stool will need 530.66 square centimeters of wood.” A = 3.14 169 A = 530.66

  19. Independent Practice (continued) C = 2  r  A =   r2 C = 2  24  A =   242 C = 48  A = 3.14 576 “The patch of grass covers 1,808.64 square feet.” “A fence to go around the patch would be 150.72 feet long.” C = 150.72 A = 1,808.64 C = 2  r  A =   r2 A =   122 C = 2  12  A = 3.14 144 C = 24  “The brackets must reach 75.36 inches around the pipeline.” “The end caps are 452.16 square inches.” C = 75.36 A = 452.16

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