1. 2. Learning Objectives. Activate Prior Knowledge. CFU What are we going to do? 12 in 8 cm. diameter. Make Connection
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1 Learning Objectives Name: Thursday, January 3, We will determine 1 the formulas for the circumference and area of a circle.. We will solve problems for the area and circumference of a circle. Activate Prior Knowledge CFU What are we going to do? 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 in 8 cm diameter r = d = r = d = Make Connection 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. Vocabulary 1 figure out
2 Concept Development 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 (π) is the constant ratio of the circumference to the diameter of a circle. Using the diameter (d) C= π d A tire has a diameter of 0 inches. C= π d C = π 15 C = = in. Using the radius (r) C= π r The same tire has a radius of 10 inches. C= π r C= π 3 C = = 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. CFU The distance around the tire is inches. How is radius related to diameter? What formula is used to find circumference using the radius of a circle? 10 inches Vocabulary a number that does not change
3 Concept Development The area of a circle is the amount of space inside the circle. is always written as units squared (in², cm²). A formula is an equation that declares the relationship between two or more quantities. Pi (π) also used in the formula to find the area of a circle. Using the radius (r) area Formula: A= π r A round carpet disc has a radius of 3 ft. A= π r A= π 3 A = = 8.6 The rug takes up 8.6 ft² of space. 3 ft CFU 1 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. CFU How is radius related to diameter? In your own words, the radius is exactly of the diameter. diameter CFU 3 What can you do if you only know the diameter of the circle, but you want to find the area of the circle? Vocabulary a number that does not change
4 Concept Development 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 (π) is the constant 3 ratio of the circumference to the diameter of a circle. A rug has a radius of 4 feet. C = r π A = π r 4 feet 4 feet Animated CFU 1 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. CFU 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. Vocabulary 3 a number that does not change
5 Skill Development/Guided Practice 1 The area of a circle is the space inside the circle. Determine the formulas for the circumference and area of a circle. a Identify 4 the given measurement. (underline) b Identify the measurement that needs to be found. (circle) Determine 5 the correct formula to find the measurement. (write on line) 3 Substitute the given value into the formula. C = r π A = π r Vocabulary 4 find (synonym) 5 figure out 6 replace (synonym) 1. A cookie has a diameter of 8 centimeters. Write the equation that could be used to find the circumference of the cookie. 8 cm. A basketball hoop has a diameter of 9 inches. Write the equation that could be used to find the circumference of the basketball hoop. 9 in. formula: equation: 3. A barrel has a diameter of 4 feet. Which equation could be used to find the circumference of the barrel? formula: A C = π B C = π 4 C C = π D C = π 8 5. A wheel has a radius of 8 inches. Which equation could be used to find the circumference of the wheel? formula: A C = π 8 B C = π 8 C C = π 8 D C = π 4 formula: equation: 4. A tablecloth has a diameter of 6 yards. Which equation could be used to find the circumference of the tablecloth? formula: A C = π 1 B C = π 3 C C = π 3 D C = π 6 6. A pizza has a radius of 6 inches. Which equation could be used to find the circumference of the pizza? formula: A C = π 6 B C = π 6 C C = π 6 D C = π 3
6 Skill Development/Guided Practice (Continued) The area of a circle is the space inside the circle. Determine the formulas for the circumference and area of a circle. a Identify 4 the given measurement. (underline) b Identify the measurement that needs to be found. (circle) Determine 5 the correct formula to find the measurement. (write on line) 3 Substitute the given value into the formula. C = r π A = π r Vocabulary 4 find (synonym) 5 figure out 6 replace (synonym) 7. A pizza has a radius of 8 inches. Write the equation that could be used to find the area of the pizza. 8 in. 8. A pie has a radius of 4 inches. Write the equation that could be used to find the area of the pie. 4 in. formula: equation: 9. A circular stage has a radius of 9 feet. Which equation could be used to find the area of the stage? formula: A A = π 9 B A = π 9 C A = π 9 D A = π A table has a diameter of 6 feet. Which equation could be used to find the area of the table? formula: A A = π 6 B A = π 3 C A = π 6 D A = π 6 formula: equation: 10. A circular rug has a radius of 5 feet. Which equation could be used to find the area of the rug? formula: A A = π 10 B A = π 5 C A = π 5 D A = π 5 1. A mirror has a diameter of 1 centimeters. Which equation could be used to find the area of the mirror? formula: A B A = π 1 A = π 1 C A = π 6 D A = π 1
7 Skill Development/Guided Practice a Identify 7 the given information. (underline) b Determine 8 which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) 1. A cookie has a diameter of 8 centimeters. What is the circumference of the cookie? CFU 1a How did I/you identify the given information? 1b How did I/you determine which formula to use? 3 How did I/you interpret the answer? C = r π A = π r The circumference of the cookie is centimeters. Vocabulary 7 find (synonym) 8 figure out
8 Skill Development/Guided Practice (Continued) a Identify 7 the given information. (underline) b Determine 8 which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) CFU 1a How did I/you identify the given information? 1b How did I/you determine which formula to use? 3 How did I/you interpret the answer? C = r π A = π r. A junior (kid s) basketball hoop has a diameter of 10 inches. What is the circumference of the basketball hoop? Vocabulary The circumference of the hoop is inches. 7 find (synonym) 8 figure out
9 Skill Development/Guided Practice (continued) a Identify the given information. (underline) b Determine which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) CFU 1a 1b 3 How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? 3. A BMX bicycle wheel has a radius of 10 inches. How far will the wheel travel each time it turns? C = r π A = π r The wheel will travel inches each time it turns a full turn (360 o ) around.
10 Skill Development/Guided Practice (continued) a Identify the given information. (underline) b Determine which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) 4. A personal sized pizza has a radius of 6 inches. How long is the crust around the pizza? CFU 1a How did I/you identify the given information? 1b How did I/you determine which formula to use? 3 How did I/you interpret the answer? C = r π A = π r The crust is inches long.
11 Skill Development/Guided Practice The area of a circle is the space inside the circle. a Identify the given information. (underline) b Determine which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) CFU 1a How did I/you identify the given information? 1b How did I/you determine which formula to use? 3 How did I/you interpret the answer? 5. A barrel has a radius of 1 inches. What is the area of the top of the barrel? C = r π 6. A pie has a radius of 7 centimeters. What is the area of the top of the pie? The area of the top of the barrel is square inches. A = π r The area of the top of the pie is square centimeters.
12 Skill Development/Guided Practice (continued) The area of a circle is the space inside the circle. a Identify the given information. (underline) b Determine which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) 7. An X-Large Lucia s pizza has a diameter of 18 inches. How much space will be on top for toppings? 8. A round dining table has a diameter of 6 feet. How much cloth is needed to make a tablecloth? The top of the pizza has square inches for toppings. CFU 1a 1b 3 How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? C = r π A = π r square feet of cloth is needed to make a tablecloth.
13 Skill Development/Guided Practice (continued) CFU 9. Ephraim wants to make a round garden 6 feet across. How much fencing will he need to go around the outside? How much ground will he need to cover in fertilizer? C = r π 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? Ephraim will need feet of fencing. He will have to cover square feet with fertilizer. 10. Mr. Garcia is building a circular stage that has a radius of 9 feet. How much planking will it take to cover the stage? The cast would like to cover the edge of the stage with garland. How long will it have to be to go all the way around? A = π r C = r π Mr. Garcia will need square feet of planking to cover the stage. The cast will need feet of garland to go around the stage.
14 Relevance The area of a circle is the space inside the circle. Solving problems for the area and circumference of a circle will help you when building things in real life. 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 C= π d to solve for circumference. C = r π A = π r 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?
15 The area of a circle is the space inside the circle. Skill Closure a Identify the given information. (underline) b Determine which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) 1. A mirror has a radius of 5 centimeters. How long will the frame have to be to go around the mirror? C = r π A = π r. What is the area of the mirror? 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. Word Bank circumference area circle pi (π) radius diameter
16 Independent Practice The area of a circle is the space inside the circle. a Identify the given information. (underline) b Determine which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) 1. A platter has a diameter of 14 inches. What is the circumference of the platter? C = r π A = π r. A round pool has a radius of 14 feet. How long is the edge around the pool?
17 Independent Practice (continued) The area of a circle is the space inside the circle. a Identify the given information. (underline) b Determine which formula to use. Substitute the given information into the formula and solve. 3 Interpret the answer. (sketch and explain) 3. A tree stump has a radius of 4 inches. How much area is on top of the stump? C = r π A = π r 4. James is replacing a stool top that has a radius of 13 centimeters. How much wood is needed to make a new top?
18 Independent Practice (continued) C = r π 5. A round patch of grass is 48 feet across. How much area does the patch cover? How long would a fence around the grass be? A = π r 6. An oil pipeline has a radius of 1 inches. How long must each bracket be to go around the pipe and hold it up? How large is the cap on the end of the pipe?
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