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Area of circle discovery ppt shortened

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Discovering Area of a Circle lesson from 21st Century Lessons, adapted

Veröffentlicht in: Bildung, Seele & Geist, Technologie
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Area of circle discovery ppt shortened

1. 1. 1 Warm Up OBJECTIVE: Students will be able to describe the shortcut to calculate the area of any circle in the world. Find the area of each shaded region: #1 #2 Explain how you found your answer to problem 1.#3
2. 2. 2 A = 36 square units Describe how you found the area of this shape. WHY? Warm Up Review 1 Agenda
3. 3. 3 Warm Up Review A = 9 square units Describe how you found the area of this shape. WHY? The shaded part is called a “radius square”. Why do you think it is called this? 1 Agenda
4. 4. 4 Launch – Finding the Area of a Circle Think-Pair-Share 1) How would you find the area of this circle? 2) Why is it hard to find the area of a circle? Agenda wait..
5. 5. 5 • 1) Not all of the squares are completely in the circle.Hey, is this a square? What about this? 1 2 3 4 5 6 7 8 ??? ? • 2) There are just TOO many to count! Nice Job! I found the same two problems. • PROBLEM 1 With these 2 problems, do you think there is a way to find the area of a circle more quickly ? • PROBLEM 2 Agenda 1wait.. Launch
6. 6. 6 People have always run into these problems, when finding the area of a circle years ago, the Babylonian mathematicians discovered that the radius square was the key to quickly finding the area of a circle. Radius Square = r2 A certain number of radius squares fits inside of every circle. Agenda Launch
7. 7. 7 Explore: Getting Ready How many radius squares fit inside one circle? This is a radius. This is a radius square. • To find out the shortcut for the area of a circle you will first answer this question. What is your prediction? 1 Agenda wait..
8. 8. Explore: The Question… How many radius squares fit inside a circle? More than 1 square? More than 2 squares? How many radius squares do YOU think fit inside one circle? 1wait.. 8
9. 9. 9 Explore: The Activity • You will get a paper circle and 4 radius squares. • You need to find out the answer to this question: How many radius squares fit inside a circle? by cutting and gluing the radius squares into the circle. Agenda wait..
10. 10. 10 Explore: How to do the activity • To count a radius square all parts of it must be inside the lines of the circle. How many radius squares fit inside one circle? This circle does not have one whole radius square covering its surface. Agenda wait..
11. 11. 11 How many radius squares fit inside one circle? You may cut the squares to make them fit inside the circle. 1 Agenda Explore: How to do the activity
12. 12. 12 How many radius squares fit inside one circle? • But all parts of the radius square must be inside the circle to count. This circle does have one whole radius square covering its surface. # of RADIUS SQUARES THAT FIT INSIDE 1 wait.. Explore: How to do the activity
13. 13. 13 Explore: Area of a Circle Challenge How many radius squares fit inside one circle? r r r You will have 10 minutes to try this activity. Agenda wait..
14. 14. 14 Explore: Clean Up Even though you may not have finished the activity, it is time to clean up. Agenda
15. 15. 15 Think-Pair • Now that you have tried the activity do you know… • Take one minute to think about the answer to this question. • Next, talk to your partner. Take turns sharing the answer to this question. How many radius squares fit inside a circle? Agenda
16. 16. Debrief How many radius squares fit inside one circle? • What is a number that you recently learned that is more than 3? It’s π • Is that true for every circle no matter its size? YES! 1wait.. Agenda17
17. 17. 18 Debrief: Is There a Shortcut? • We know that EXACTLY π (3.1415…) radius squares fit inside a circle. • Can we write a rule that will work for any circle? The area of a circle is a little bit more than 3 times the radius square. A shortcut makes you faster! Looking at the Rule Agenda wait..
18. 18. Exit Ticket • What is the best estimate for the area of this circle? When I say so “go” make the gesture next to the answer you think is correct.. A) 5 square units B) 15 square units C) 25 square units D) 75 square units Agenda 20