Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Math Journal (5 Min) Explanation of Process – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they think the process of finding the solution will be before they have been taught the lesson, and at the end of class, write about what they now know is the process of finding the solution after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that explained the process that pertained to the lesson.
Homework Review (5 Min)
Warm Up Simplify. 1. 82 2. 122 3. 6.22 4. 7.52 64 144 38.44 56.25
Problem of the Day A 16 in. pizza sells for $11.99. A 10 in. pizza sells for $5.99. Which size gives you more pizza per penny? Explain. The larger pizza; you get more than twice as much (64 in2 instead of 25 in2) for about twice the price.
Textbook Examples (I Do) (5 Min)
Learn to find the area of circles.
So the area of the parallelogram can be written as A circle can be cut into equal- sized sectors and arranged to resemble a parallelogram. The height h of the parallelogram is equal to the radius r of the circle, and the base b of the parallelogram is equal to one-half the circumference C of the circle. So the area of the parallelogram can be written as 1 2 A = bh, or A = Cr. 1 2 Since C = 2r, A = (2r)r = r2.
Additional Example 1A: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 7 cm A 3.14 · 72 Substitute 7 for r. A 3.14 · 49 Evaluate the power. A 153.86 Multiply. The area of the circle is about 153.9 cm2. The order of operations calls for evaluating the exponents before multiplying. Remember!
Additional Example 1B: Finding the Area of a Circle Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 18 ft A 3.14 · 92 Substitute 9 for r. A 3.14 · 81 Evaluate the power. A 254.34 Multiply. The area of the circle is about 254.3 ft2.
Find the area of the circle to the nearest tenth. Use 3.14 for . Check It Out: Example 1A Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 10 cm A 3.14 · 102 Substitute 10 for r. A 3.14 · 100 Evaluate the power. A 314 Multiply. The area of the circle is about 314 cm2.
Find the area of the circle to the nearest tenth. Use 3.14 for . Check It Out: Example 1B Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 Use the formula. 12 ft A 3.14 · 62 Substitute 6 for r. A 3.14 · 36 Evaluate the power. A 113.04 Multiply. The area of the circle is about 113.0 ft2.
Additional Example 2: Application Park employees are fitting a top over a circular drain in the park. If the radius of the drain is 14 inches, what is the area of the top that will cover the drain? Use 22 7 for . A = r2 Use the formula for the area of a circle. 22 7 A ·142 Substitute. Use 14 for r. 28 22 7 A · 196 Evaluate the power. 1 A 22 · 28 A 616 Multiply. The area of the top that will cover the drain is about 616 in2.
The area of the top that will cover spa is about 154 ft2. Check It Out: Example 2 Albert was designing a cover for a spa. If the radius of the spa is 7 ft, what is the area of the cover that will be made? Use 22 7 for . A = r2 Use the formula for the area of a circle. 22 7 A ·72 Substitute. Use 7 for r. 7 22 7 A · 49 Evaluate the power. 1 A 22 · 7 A 154 Multiply. The area of the top that will cover spa is about 154 ft2.
Additional Example 3: Application Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. 1.5 cm The measurement of the radius of the circle is 1.5 cm. Now find the area of the entire circle. A = r2 Use the formula for the area of a circle. A = 3.14 · 1.52 Substitute. Use 1.5 for r. A 3.14 · 2.25 Evaluate the power. A 7.07 Multiply.
Additional Example 3 Continued Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Since of the circle is shaded, divide the area of the circle by 2. 7.07 ÷ 2 = 3.535. 1 2 The area of the shaded region of the circle is about 3.5 cm2.
Check It Out: Example 3 Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. 2.4 cm The measurement of the radius of the circle is 2.4 cm. Now find the area of the entire circle. A = r2 Use the formula for the area of a circle. A = 3.14 · 2.42 Substitute. Use 2.4 for r. A 3.14 · 5.76 Evaluate the power. A 18.09 Multiply.
Check It Out: Example 3 Continued Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. Since of the circle is shaded, divide the area of the circle by 4 and subtract the answer from the entire area. 18.0864 ÷ 4 = 4.52. 18.0864 – 4.52 = 13.56. 3 4 The area of the shaded region of the circle is about 13.56 cm2.
Class work Problems (We Do) (10 Min) Pg. 366-367 (1-6)
Small Group CW(Yall Do) (10 Min) Pg. 366-367 (8-28 EOE)
Homework (You Do) (10 Min) Pg. 366-367 (7, 11, 13, 17, 21 odd)
Math Journal (5 Min) Explanation of Process – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they think the process of finding the solution will be before they have been taught the lesson, and at the end of class, write about what they now know is the process of finding the solution after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that explained the process that pertained to the lesson.
Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 32
Find the area of each circle, to the nearest tenth. Use 3.14 for . 1. Lesson Quiz Find the area of each circle, to the nearest tenth. Use 3.14 for . 1. 3. The bull’s-eye on a target has a diameter of 2 in. What is the area of the bull’s-eye to the nearest tenth? Use 3.14 for . 4. A round table cloth has a radius of 36 in. What is the area of the table cloth? Use 3.14 for . Round your answer to the nearest tenth. 8 ft 2. 9 ft • 201.0 ft2 • 63.6 ft2 3.1 in2 4,069.4 in2
Lesson Quiz for Student Response Systems 1. Identify the area of the circle to the nearest tenth. Use 3.14 for . A. 907.5 ft2 B. 289 ft2 C. 226.9 ft2 D. 53.4 ft2 17 ft 34
Lesson Quiz for Student Response Systems 2. Identify the area of the circle to the nearest tenth. Use 3.14 for . A. 72.2 in2 B. 144.4 in2 C. 415.3 in2 D. 1661.1 in2 23 in. 35
Lesson Quiz for Student Response Systems 3. A round table has a diameter of 11 ft. What is the area of the table to the nearest tenth? Use 3.14 for . A. 95 ft2 B. 69.1 ft2 C. 54.2 ft2 D. 34 ft2 36