2023.DLL.Pre-Calculus.11.prelims.W.1.docx

2023.DLL.Pre-Calculus.11.prelims.W.1.docx

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  school year 2023- 2024 Saint Catherine’s School PRE – SCHOOL, ELEMENTARY, JUNIOR AND SENIOR HIGH SCHOOL PAASCU ACCREDITED Real St., Buag, Bambang, Nueva Vizcaya DAILY LESSON LOG Department Mathematics Department Grade Level Grade 11 Teacher Jolita I. Lisbog Learning Area Pre-Calculus 11 Teaching Dates and Time September 4 – September 8, 2023 Quarter Prelims SESSION #1 SESSION #2 SESSION #3 SESSION #4 I. STANDARDS, MELC/s, & OBJECTIVE/S A. Content Standards The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations. B. Performance Standards The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations. C. Learning Competencies/ Objectives: At the end of the lesson, the learners are expected to: 1. Illustrates the types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases. STEM_PC11AG-Ia-1 a. Define conic sections, b. Illustrate the types of conic sections, and c. Appreciate the concept about conic sections. At the end of the lesson, the learners are expected to: 1. Define a circle. STEM_PC11AG-Ia-2 a. Define circle and b. Appreciate the concept about circles. At the end of the lesson, the learners are expected to: 1. Determine the standard form of equation of a circle. STEM_PC11AGIa-3 a. Illustrate the standard form of equation of a circle. b. Solve an equation applying the standard form of equation of a circle. c. Appreciate the concept about standard form At the end of the lesson, the learners are expected to: 1. Define conic sections, 2. Define circle, 3. Illustrate the types of conic sections, 4. Illustrate the standard form of equation of a circle and; 5. Solve an equation applying the standard form of equation of a circle. fides luceat! 1
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  school year 2023- 2024 of equation of a circle. II. CONTENT A. Lesson/Topic An Overview of Conic Sections Circles Standard Form of Equation of a Circle Long Quiz III. LEARNING RESOURCES A. References Text book: Albay, Eduard M. (2016). Precalculus. Makati City, Philippines. Diwa Learning Text book: Albay, Eduard M. (2016). Precalculus. Makati City, Philippines. Diwa Learning Text book: Albay, Eduard M. (2016). Precalculus. Makati City, Philippines. Diwa Learning 1. Teacher’s Guide pages 2. Learner’s Material pages 3. Textbook/Module pages Chua D.T., S. L., et.al. (2018). B. Other Learning Resources Laptop, PowerPoint, TV, Blackboard, Chalk Laptop, PowerPoint, TV, Blackboard, Chalk Laptop, PowerPoint, TV, Blackboard, Chalk Laptop, PowerPoint, TV, Blackboard, Chalk IV. PROCEDURES A. Reviewing previous lesson or presenting the new lesson The teacher will let the students guess the parts of the cone by giving them a short activity. The teacher will let the students guess the types of conic sections illustrated by the given pictures. The teacher will let the students recall the circles. Guide questions:  How can we define circle? Review the 4 types of conic sections, circles and the standard form of equation of a circle. Conic Section Four Types Of Conic Sections fides luceat! 2
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  school year 2023- 2024 B. Establishing a purpose for the lesson The teacher will let the students realize that recognizing the parts of a cone is needed to understand the concept of the conic sections. The teacher will let the students realize that recognizing the types of conic sections is needed to understand the concept of the circles. The teacher will let the students realize that recognizing the types of conic sections is needed to understand the concept of the standard form of equation of a circle. Circle A circle is a conic section that is formed by intersecting a cone with a plane that is perpendicular to the axis of the cone. A circle is the set of all points in a plane that are equidistant from affixed point called the center. The distance from the center to any point on the circle is called the radius of the circle center, denoted by r, where r ¿ 0. Standard Form of Equation of a Circle C. Presenting examples/instances of the new lesson The teacher will present a picture and the students will guess if what types of conic sections it is. The teacher will present a picture and the students will analyze it. The teacher will define with the students about the circles. A circle is a conic section that is formed by intersecting a cone The teacher will present the standard form of equation of a circle. Let the center C of a circle be located at point (h,k) and the radius be equal to r also, let the point P(x,y) be any point on fides luceat! 3
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  school year 2023- 2024 with a plane that is perpendicular to the axis of the cone. the circle. Then the distance C to P is r, that is, √(x−h) 2 +( y−k) 2 =r Squaring both sides of the equation leads to (x−h)2 +( y−k)2 =r2 fides luceat! 4 A circle is formed when a cone is cut by a plane that is parallel to the base.
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  school year 2023- 2024 D. Discussing new concepts and practicing new skills #1 The teacher will define with the students about the conic sections. A circle is the set of all points in a plane that are equidistant from affixed point called the center. The distance from the center to any point on the circle is called the radius of the circle center, denoted by r, where r ¿ 0. Therefore, the standard form of the equation of a circle whose center is at (h,k) and whose radius is r is given by (x−h)2 +( y−k)2 =r2 , where r ¿ 0. If the center of the circle is at the origin, that is h=0 and k=0, and the radius is r, then the equation of the circle is given by x 2 +y 2 =r 2 , where r ¿ 0. The teacher will let the students answer the given activities. E. Discussing new concepts and practicing new skills #2 The teacher will illustrate with the students about the types of conic sections. Given the center and radius, it would be easy to determine the equation of the circle. Example 1: Determine the standard equation of the circle given the coordinates of its fides luceat! 5
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  school year 2023- 2024 center and the length of its radius. a. center at (2,-3) and r=3 b. center(0,0) and r=5 Example 2: Given the standard form of the equations. Find the coordinates of the center and the radius of each of the following circles. a. x 2 +y 2 =64 b. (x+9) 2 +( y−1) 2 =25 F. Developing mastery (Leads to Formative Assessment) The teacher will let the students recite orally. Guide Questions:  What are the four types of conic sections that we have discussed? The teacher will let the students recite orally. Guide Questions:  How can we define circle in your own understanding? The teacher will let the students solve in the blackboard. 1. center(2,-5) and r=10 2. x 2 +( y−2)2 =49 G. Valuing Finding practical applications of concepts/skills in daily The teacher will let the students give a real life situation about the conic sections. Circles represent completeness encompasses all space and time. The circle symbolizes unity, stability, rationality. It is also the symbol of infinity, without . fides luceat! 6
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  school year 2023- 2024  Water from a fountain takes a path of parabola to fall on the earth.  Electrons on the atom move around the nucleus in an elliptical path of orbit.  A guitar is an example of hyperbola as its side’s hyperbola. beginning or end, perfection, the ultimate geometric symbol. Core Values Integration Excellence  Critical Thinking Excellence  Critical Thinking Excellence  Critical Thinking Excellence  Critical Thinking H. Making generalizations and abstractions about the lesson The teacher summarizes the lesson by asking volunteer students to answer the following: 1. What is conic section? 2. What are the four types of conic sections? The teacher summarizes the lesson by asking volunteer students to answer the following: 1. How does the conic sections, circle is being form? The teacher summarizes the lesson by the students to state the formula of a circle at (h,k) and circle with center at the center. I. Evaluating learning The teacher will let the students The teacher will let the students The teacher will let the fides luceat! 7
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  school year 2023- 2024 identify the type of conic sections illustrated by the given pictures. to complete the definition of circle by filling the blanks. A ______ is the set of all points in a plane that are ________from affixed point called the ______. The distance from the center to any point on the circle is called the ______ of the circle center, denoted by r, __________. students answer the given activities. J. Assignment Additional activities for application or remediation Guide Question: What is a circle? Guide Question: What is the standard form of the equation circle? Let the students review their lessons for the long quiz. V. REMARKS Students’ Mastery Level  Beginning  Developing  Approaching Proficiency  Proficient  Advanced  Beginning  Developing  Approaching Proficiency  Proficient  Advanced  Beginning  Developing  Approaching Proficiency  Proficient  Advanced  Beginning  Developing  Approaching Proficiency  Proficient  Advanced Intervention/s Made Prepared by: Checked: JOLITA INWAY LISBOG OLIVER V. RAZA Subject Teacher Department Chair Noted: CLARISSA S. SILVA, MED – SL School Principal fides luceat! 8