Lesson 11-Identifying and applying the relationship among the parts of theCircle.pptx

This will help much in the study if the students to learn more in mathematics

1. LESSON 11: Identifying and Applying Relationships among the Parts of a Circle

2. Short Review Directions: In answering the questions the learners will shout the phrase “ Pak ganern , Alam ko yan !”. On the graph at the right side identifying the following terms based on the definition given below. Time: 7 minutes

3. Question 1: 1. Each of the circle parts 𝐴C, 𝐵C, 𝐵D and 𝐴D that make up the circumference of the circle is called an/a _________ AC BC BD AD A. Arc B. Radius C. Chord D. Diameter AC BC BD AD AC BC BD AD

4. Question 1: AC BC BD AD Answer: A. ARC Each of the circle parts 𝐴C, 𝐵C, 𝐵D and 𝐴D that make up the circumference of the circle is called an ARC . The measure of an Arc is the measure of its central angle. AC BC BD AD AC BC BD AD AC BC BD AD

5. Question 2: 2. A/an _________ of a circle is a straight line that joins the center of the circle to a point on the circumference. A. Arc B. Radius C. Chord D. Diameter

6. Question 2: A RADIUS of a circle is a straight line that joins the center of the circle to a point on the circumference. It is half its size from the diameter. Answer: B. RADIUS

7. Question 3: 3. A straight line joining any two points on the circumference of a circle is called a ___________ A. Arc B. Radius C. Chord D. Diameter

8. Question 3: A straight line joining any two points on the circumference of a circle is called a CHORD. Answer: C. CHORD

9. Question 4: 4. A straight line joining any two points on the circumference of a circle and passing through the center of the circle is called a _________ A. Arc B. Radius C. Chord D. Diameter

10. Question 4: A straight line joining any two points on the circumference of a circle and passing through the center of the circle is called a DIAMETER . It is Twice its size from the Radius. Answer: D. Diameter

11. Question 5: 5. A/An ______ angle is an angle whose vertex lies on the circumference of a circle and whose arms are two chords of the circle. A. Central Angle B. Inscribe Angle C. Chord D. Diameter

12. Question 5: An Inscribe Angle angle is an angle whose vertex lies on the circumference of a circle and whose arms are two chords of the circle. It is half its measure from the central angle that encloses the same arc. Answer: B. Inscribe Angle

13. Lesson Purpose and Intention

14. Lesson Purpose and Intention Time: 3 minutes Teacher states: Have you ever seen pulling a cart, or riding a bus with wheels that aren’t round? Do you think you can easily move heavy items from one location to another, or fly far away as quickly as you can? Without circles, what challenge do you think you will experience?

15. Lesson Purpose and Intention Time: 3 minutes Teacher states: “ relationships among the parts of a circle in finding the solutions to such problems. ”

16. Lesson Language Practice Instruction: Group activity, the class will be divided into 4 groups. each group will be given a manila paper with the illustration of the crossword. Within 5 minutes each group will complete the crossword puzzle and paste it on the board. Time: 5 minutes

17. Lesson Activity

18. LET’S CHECK! CRITERIA BEGINNER (1) ACCEPTABLE (2) PROFICIENT (3) PROCESS SKILLS The group got at least 2 correct answers. The group got at least 4 correct answers. The group got at least 6 correct answers. TIME MANAGEMENT Beyond 10 The group didn’t finish the activity on the allotted time (exact 10mins) The group finish the activity on the allotted time (less than 10mins) COOPERATION AND TEAMWORK 3 of the members are not working 2 of the members are not working 1 of the members are not working NEATNESS At least 3 erasures At least 2 erasures No erasures

19. FOCUS GROUP DISCUSSION : (10 mins) In Design 1 part (a), Carl has divided a circle into three parts. 𝑂 is the center of the circle. 𝐴, 𝐵, 𝐶, and 𝐷 are points on the circumference of the circle. 𝐴B and 𝑂C are straight lines. In Design 1 part (c), Carl has added chords AD and 𝐵D. He measures the inscribed angle, ∠ADB, and notes that it measures 90°. He also observes that this is the case regardless of where he places 𝐷 on the arc ADB. In Design 1 part (b), Carl has drawn straight lines from B to C and from A to C, to form the triangles BOC and AOC. He knows that OC is 25 cm long and he measures the line AC to be 43.3 cm long.

20. Processing Questions: (10 mins) Reporting Follow-up Questions Item 1 Questions How many times longer than OC is AB ? What terms should Carl use to describe the parts of the circle AB and OC? 3. What shape is formed by arc ADB and line AB? 4. What fraction of the area of this shape is the shaded area OBC? 5. If using string to form the two smaller triangles in Design 1 part (b) (without forming OC twice), how much string will Carl need?

21. Processing Questions: (5 mins) Checking Follow-up Questions Item 1 Questions How many times longer than OC is AB ? What terms should Carl use to describe the parts of the circle AB and OC? LET’S CHECK! two times longer AB is a diameter; OC is a radius

22. Processing Questions: Checking Follow-up Questions Item 1 Questions 3. What shape is formed by arc ADB and line AB? 4. What fraction of the area of this shape is the shaded area OBC? LET’S CHECK! semi-circle 1/3

23. Processing Questions: Checking Follow-up Questions Item 1 Questions 5. If using string to form the two smaller triangles in Design 1 part (b) (without forming OC twice), how much string will Carl need? LET’S CHECK! In Design 1 part (b), Carl has drawn straight lines from B to C and from A to C, to form the triangles BOC and AOC. He knows that OC is 25 cm long and he measures the line AC to be 43.3 cm long. 143.3 cm

24. Processing Questions: Checking Follow-up Questions Item 1 Questions How many times longer than OC is AB ? What terms should Carl use to describe the parts of the circle AB and OC? 3. What shape is formed by arc ADB and line AB? 4. What fraction of the area of this shape is the shaded area OBC? 5. If using string to form the two smaller triangles in Design 1 part (b) (without forming OC twice), how much string will Carl need? LET’S CHECK! two times longer AB is a diameter; OC is a radius semi-circle 1/3 143.3 cm

25. FOCUS GROUP DISCUSSION : (10 mins) In Design 1 part (a), Carl has divided a circle into three parts. 𝑂 is the center of the circle. 𝐴, 𝐵, 𝐶, and 𝐷 are points on the circumference of the circle. 𝐴B and 𝑂C are straight lines. In Design 1 part (c), Carl has added chords AD and 𝐵D. He measures the inscribed angle, ∠ADB, and notes that it measures 90°. He also observes that this is the case regardless of where he places 𝐷 on the arc ADB. In Design 1 part (b), Carl has drawn straight lines from B to C and from A to C, to form the triangles BOC and AOC. He knows that OC is 25 cm long and he measures the line AC to be 43.3 cm long.

26. Processing Questions: (10 mins) Reporting Follow-up Questions Item 2 Questions 1. Complete the conclusion that Carl can draw from what he observed in Design 1 part (c): ‘For a semi-circle, the measure of the central angle, ∠ AOB, is …………. the measure of the inscribed angle, ∠ ADB.. 2. Carl has discovered that the three chords, AD, BD and AB form the right triangle ABD. Without measuring any of the three sides, which side of the triangle must be the longest side? Why? 3. Carl needs to find the area of triangle ADB for his design. He measures the height DE of the triangle accurately and finds its length to be 24 cm. Find the area of triangle ADB. HINT: Area of Triangle =  

27. Processing Questions: (5 mins) checking Follow-up Questions Item 2 Questions 1. Complete the conclusion that Carl can draw from what he observed in Design 1 part (c): ‘For a semi-circle, the measure of the central angle, ∠ AOB, is …………. the measure of the inscribed angle, ∠ ADB.. LET’S CHECK! Twice In Design 1 part (c), Carl has added chords AD and 𝐵D. He measures the inscribed angle, ∠ADB, and notes that it measures 90°. He also observes that this is the case regardless of where he places 𝐷 on the arc ADB .

28. Processing Questions: (5 mins) checking Follow-up Questions Item 2 Questions 2. Carl has discovered that the three chords, AD, BD and AB form the right triangle ABD. Without measuring any of the three sides, which side of the triangle must be the longest side? Why? LET’S CHECK! AB, because it is opposite the largest angle (∠ ABD = 90°). In Design 1 part (c), Carl has added chords AD and 𝐵D. He measures the inscribed angle, ∠ADB, and notes that it measures 90°. He also observes that this is the case regardless of where he places 𝐷 on the arc ADB.

29. Processing Questions: (5 mins) checking Follow-up Questions Item 2 Questions 3. Carl needs to find the area of triangle ADB for his design. He measures the height DE of the triangle accurately and finds its length to be 24 cm. Find the area of triangle ADB. LET’S CHECK! In Design 1 part (c), Carl has added chords AD and 𝐵D. He measures the inscribed angle, ∠ADB, and notes that it measures 90°. He also observes that this is the case regardless of where he places 𝐷 on the arc ADB. Area triangle ABD = 600  

30. Processing Questions: (5 mins) checking Follow-up Questions Item 2 Questions 1. Complete the conclusion that Carl can draw from what he observed in Design 1 part (c): ‘For a semi-circle, the measure of the central angle, ∠ AOB, is …………. the measure of the inscribed angle, ∠ ADB.. 2. Carl has discovered that the three chords, AD, BD and AB form the right triangle ABD. Without measuring any of the three sides, which side of the triangle must be the longest side? Why? 3. Carl needs to find the area of triangle ADB for his design. He measures the height DE of the triangle accurately and finds its length to be 24 cm. Find the area of triangle ADB. LET’S CHECK! Twice AB, because it is opposite the largest angle (∠ ABD = 90°). Area triangle ABD = 600  

31. Lesson Conclusion

32. Question 1: What do you think were the key mathematical concepts addressed in this lesson?

33. Question 2: Would you rate your level of understanding of the material covered in this lesson as high, moderate, or low?

34. Question 3: Has the lesson helped you gain further insight into aspects of the material covered that represent strengths or represent weaknesses?

35. Question 4: What would you describe as the main barriers, if any, to your ongoing progress and achievement in relation to the topic area addressed in this lesson?

36. Question 5: What do you think would best assist your ongoing progress and achievement in relation to the topic area?

37. Worksheet: