Pre-Calculus: Daily Lesson Log

DAILY LESSON LOG PRE-CALCULUS Republic of the Philippines

Department of Education Region XI Division of Davao City Davao Doctors College Inc. General Malvar St., Davao City

JUNE 2018-0CTOBER 2018

WEEK 1 – 7: 7: ANALYTIC GEOMETRY

Week 1 Grade 11 DAILY LOG

LESSON

School

Davao Doctors College Inc

Grade Level

11

Teacher

Ms. Khatrine Ann T. Arabilla

Learning Area

Specialized Subject

Teaching Dates and Time

Week 1 Sessions 1-2

Quarter

1ST

Session 1

Session 2

I. OBJE OBJE CTIVES

3 hours and 30 minutes

1 hour

A. Content Standard

The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations. The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations The learners... The learners… 1. illustrate the different types of conic sections: parabola, 1. define a parabola ellipse, circle, hyperbola, and degenerate cases STEM_PC11AG-Ia-5

B. Performance Standards C. Learning Competencies/ Objectives

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2. define a circle. 3. determine the standard form of equation of a circle 4. graph a circle in a rectangular coordinate system STEM_PC11AG-Ia-1 STEM_PC11AG-Ia-2 STEM_PC11AGIa-3 STEM_PC11AG-Ia-4 Analytic Geometry: A. The Circle, B. The Parabola, C. The Ellipse, D. The Hyperbola, E. General Second-degree Equation and F. System of Nonlinear Equations

II . CONTENT CONTENT III.

LEARNING

RESOURCES

A. References

B. Other Learning Resources

Pre-Calculus for Senior High School


White board and white board marker Graphing Paper Graphing Tools Projector

White board and white board marker Graphing Paper Graphing Tools Projector

I V. PROCEDURES PROCEDURES

PLOTTING POINTS – FULL FULL BODY STYLE. Transform the whole classroom into a Cartesian Plane. Elaborating the x and y axis. The students must be able to identify their coordinates according to their location inside the classroom. The students are presented with this problem. Every year, the Philippines gets hit by approximately 20 typhoons. Suppose typhoon X is in the country and is predicted B. Establishing a purpose for a to have 350-km radius. Further, it was reported that town A lesson located 260 km south and 225 km west from its eye is at the periphery of the typhoon. The townsfolks want to verify this news. The facilitator asks questions about the given problem being C. Presenting the Lesson presented and give the students students the topic for the session. session.

A. Reviewing previous lesson or presenting the new topic

2

The class will be asked questions about the lessons tackled last meeting through the index cards.

The teacher will present a scenario about a parabola revolving about its axis, the result is what we called a paraboloid.

The teacher now presents the lesson in which the learners can identify the properties of the parabola and also its definition.

D. Discussing the concepts

E. Developing Mastery

F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions H. Evaluating Learning I. Additional activities for application or remediation

Using the projected image, the teacher will discuss the terms The teacher provides illustrations about the parts of right circular principal axis, vertex. Latus Rectum, focus focus and directrix. Every cone, the conic sections formed by cutting the cone through a now and then, the teacher must review their idea about the plane. Also, discusses discusses the properties of circle through graphing. graphing. properties of the parabola. SIMON SAYS “PARABOLA” The students will illustrate the following parabolic properties The learners are given 5 problems to solve for a given time. using only their arms: principal axis, vertex. Latus Rectum, Then, after that they have to share it within the class. focus and directrix. The teacher will increase the pace of the commands and see if the students can keep going. The students are now tasked to apply their output first from the Using a worded problem, the students are t asked to identify the worded problems involving real life applications and also in different properties of the parabola. their daily experiences as students. The instructor summarizes everything that have been discussed The instructor summarizes everything that have been discussed. by every group. The students are given illustrations and they must identify the The students are given 20-item quiz. parts of the parabola. The students are tasked to answer their Problem Sets about The students are tasked to answer their Problem Sets about circle. properties of parabola.

V. REMARKS VI. RE FLECTION

3

WEEK 2 Grade 11 DAILY LOG

LESSON

School

Davao Doctors College, Inc.

Grade Level

11

Teacher


Learning Area

Specialized Subject


Week 2 Sessions 1-2

Quarter

1st

Session 1

Session 2

I. OBJE OBJE CTIVES

2 hours

2 hours

A. Content Standard

The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations

B. Performance Standards C. Learning Competencies/ Objectives

Analytic Geometry: A. The Circle, B. The Parabola, C. The Ellipse, D. The Hyperbola, E. General Second-degree Equation and F. System of Nonlinear Equations

II . CONTENT CONTENT III. RESOURCES

The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations At the end of the two-hour session, the learners are expected to At the end of the two-hour session, the learners are expected to determine the standard form of equation of a parabola. graph a parabola in a r ectangular coordinate system

LEARNING

A. References


Pre-Calculus for Senior High School White board and white board marker Graphing Paper Graphing Tools Projector Illustration Board Chalk


I V. PROCEDURES PROCEDURES

4


B. Establishing a purpose for a lesson

C. Presenting the Lesson



The students will be asked through a board work to il lustrate or solve the following: • Degenerate form as intersections of a plane and a twonapped cone- Circle • Distance Formula • Midpoint Formula The students are asked to name a thing that is parabolic in shape or name any place in which we can see a parabola.

The teacher now presents the lesson in which the learners can able to write the standard equation of the parabola. The instructor provides input about the 8 cases of parabola namely: 1. Center at the origin, opens upward 2. Center at the origin, opens downward 3. Center at the origin, opens to the right 4. Center at the origin, opens to the left 5. Center at (h, k), opens upward 6. Center at (h, k), opens downward 7. Center at (h, k), opens to the right 8. Center at (h, k), opens to the left BEST THREE: The class will be divided into 18 groups with 3 members per group. They will be given problems about parabola by projecting the questions using the projector. They will be using illustration board and chalk to show their answers. The first group who can raise their illustration board with the correct answer will be given the corresponding points for each question. The group who has the highest accumulated points will be the winner

5

The teacher will give a review about the properties and standard equations of the parabola using flash cards. Every student is given a chance to answer one problem in a minute. The students are asked with these questions: 1.Can we graph a parabola using its pr operties? 2. How can we use the standard equations of the parabola to illustrate its graph? 3. Is it possible to determine the standard equation of the circle given its graph? The teacher now presents the lesson in which the learners can be able to graph the parabola.

Using the knowledge about the properties and standard equations of the parabola, the teacher will discuss the aids in graphing the parabola. Step by step process in which students can easily follow.

The class is divided into 10 groups with 5 members per group. Each group is given a problem about graphing the parabola. Then, the students will present their outcome.

F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions H. Evaluating Learning I. Additional activities for application or remediation

Each group presents and discusses their output in the class. Each group should present some techniques on how to graph the parabola. The instructor summarizes everything that have been discussed The instructor summarizes everything that have been discussed in the class by every group. The class is given a 10-item quiz The class is given a 10-item quiz . The students are tasked to answer their Problem Sets about the The students need to research about definition which will be standard equations of the parabola. discussed by next meeting.

The students must be able to analyze the different cases of the parabola and the process in identifying those cases.


6


LESSON

School

Davao Doctors College Inc.

Grade Level

11

Teacher


Learning Area

Specialized Subject


Week 3 Sessions 1-2

Quarter

1st

I. OBJE CTIVES

A. Content Standard B. Performance Standards C. Learning Competencies/ Objectives

II . CONTENT

Session 1

Session 2

2 hours

2 hours

The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations. The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations. At the end of the two-hour session, the learners are expected to At the end of the two-hour session, the learners define an ellipse, graph an ellipse in a rectangular coordinate system determine the standard form of equation of an ellipse STEM_PC11AG-Ic-3 STEM_PC11AG-Ic-1 STEM_PC11AG-Ic-2 Analytic Geometry: A. The Circle, B. The Parabola, C. The Ellipse, D. The Hyperbola, E. General Second-degree Equation and F. System of Nonlinear Equations

III.LEARNING RESOURCES

A. References




White board and white board marker Graphing Paper Graphing Tools Projector Illustration Board Chalk

White board and white board marker Graphing Paper Graphing Tools Projector Illustration Board Chalk

I V. PROCEDURES

7


The class will be asked questions about the lessons tackled last week.

The class will be asked questions about the lessons tackled last meeting through oral participation (randomly choosing index card with names of students).

The students are asked a problem about a whispering gallery, an enclosure wherein whispers emanating from one location may be heard clearly in another location. With the given information, The students are asked with these questions: B. Establishing a purpose for a two friends want to validate if indeed the room is a whispering 1.can we graph the given ellipse given the standard equation? lesson gallery, how far should they stay away from the center of the 2. How can we graph an ellipse given its properties. room and how far should they be from each other. The teacher now presents the lesson in which the learners can be able to define ellipse and determine the standard equations. The instructor discusses the definition and properties of an ellipse. Using the projected image, the following are being illustrated as properties: foci, center, vertices, co-vertices, principal axis, major axis and minor axis. Also, the 4 cases of D. Discussing the concepts the standard equations are given as follows: Case 1: Center at the origin: major axis along x axis Case 2: Center at the origin: major axis along y axis Case 3: Center at (h, k): major axis parallel to x-axis Case 4: Center at (h, k): major axis is parallel to y-axis THINK-GROUP-SHARE EXERCISE The students must think individually about determining the standard equations given the properties of the ellipse. Next, E. Developing Mastery group students into 5 to discuss their results and findings. Finally, have each group to share their ideas with the rest of the class, and open the floor for further discussion. F. Finding Practical Each group presents and discusses their output in the class. Each Applications of concepts and group should present their techniques in arriving the standard skills in daily living equations of the ellipse. G. Making Generalizations The instructor summarizes everything that have been discussed and Abstractions by every group. H. Evaluating Learning The students will answer 10-item quiz C. Presenting the Lesson

8

The teacher now presents the lesson in which the learners can be able to graph the said conic section.

Using the graphing tools, the teacher will discuss the step by step process in graphing the ellipse.

The class is divided into 10 groups. Each group is given a problem and must arrive with a graph

Each group presents and discusses their output in the class. Each group should present their answer in the class The instructor summarizes everything that have been discussed by every group. The students will answer 10-item quiz

I. Additional activities for application or remediation

The students are tasked to answer their Problem Sets about the standard equations of the ellipse.


9

The students are tasked to answer their Problem Sets about graphing an ellipse.


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject


Week 4 Sessions 1-2

Quarter

1st

I. OBJE CTIVES


Session 2

2 hours

2 hours

The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations. The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations. At the end of the session, the learners can be able to: At the end of the session, the learners can be able to: define a hyperbola, graph a hyperbola in a rectangular coordinate system determine the standard form of equation of a hyperbola STEM_PC11AG-Id-3 STEM_PC11AG-Id-1 STEM_PC11AG-Id-2 

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II . CONTENT III.

Session 1

LEARNING

RESOURCES

A. References



White board and white board marker Graphing Paper Graphing Tools Projector Illustration Board

Pre-Calculus for Senior High School White board and white board marker Graphing Paper Graphing Tools Projector Illustration Board

I V. PROCEDURES


Using index cards, the teacher will randomly pick students that will answer questions about the previous lessons about the three 10

CABBAGE PASS : Have the students sit in their place. Give them the cabbage and let them pass it right next to them. When

conic sections. If a student can answer the question, she/he will be given the chance to choose the next student to be asked. The teacher presents a problem about the panoramic B. Establishing a purpose for a photography, a technique that captures a broad view into a lesson photo. C. Presenting the Lesson


The teacher will present the lesson through the projected images about the hyperbola. The instructor discusses the definition of the hyperbola. Individually explains the different properties of hyperbola namely: center, vertices, co- vertices, conjugate axis, transverse axis, Latus Rectum, and equations of the asymptotes. With the knowledge about the properties, the teacher will further discuss the standard equations of the hyperbola namely: 1. Center at the origin; tr ansverse axis along x-axis 2. Center at the origin; tr ansverse axis along y-axis 3. Center at (h, k); tr ansverse axis parallel to x-axis 4. Center at (h, k); tr ansverse axis parallel to y-axis

the music stops, the one holding the cabbage will peel it, read the problem indicated and answer it. If the student can’t answer, he/she can ask for a friend or another classmate to answer. The students are asked with these questions: 1.Can we graph the hyperbola using its properties? 2. How can we graph a hyperbola given only its standard equations. The teacher will present the lesson using the graphing tools.

The teacher will discuss the step b y step process in graphing the hyperbola.

1 vs. 55. All the students must secure an illustration board and E. Developing Mastery F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions H. Evaluating Learning I. Additional activities for application or remediation

chalk. The teacher will give problems about hyperbola. Each question corresponds to a specific time and points. The student who will garner the highest point will be the winner. The teacher will group the students into 4. Each group will try to solve the problem given on the first part of this session about the panoramic photography. The instructor summarizes everything that have been discussed by every group. The students will answer 10-item quiz The students are tasked to answer their Problem Sets about the standard equations of the hyperbola

V. REMARKS

11

Individually, the students will graph the hyperbola given the standard equations and properties for 5 minutes per problem. The teacher will try to congest all the ideas about conic sections to deliberately understand their application. The instructor summarizes everything that have been discussed inside the class. The students will answer 10-item quiz The students are tasked to answer their Problem Sets about graphing hyperbola

VI. RE FLECTION


LESSON

School


Grade Level

11

Teacher


Learning Area

Core Track


Week 5 Sessions 1-2

Quarter

Ist

I. OBJE CTIVES


Session 2

2 hours

2 hours

The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations. The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations. The leaners can be able to: The leaners can be able to: recognize the equation and important characteristics of solves situational problems involving conic sections the different types of conic sections STEM_PC11AG-Ie-2 STEM_PC11AG-Ie-1 

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II . CONTENT III.

Session 1

LEARNING

RESOURCES

A. References




I V. PROCEDURES

12


B. Establishing a purpose for a lesson C. Presenting the Lesson



The students will be asked through practice exercises about the following: • Completing a square Using flash cards, the teacher will try to show equations and the • Equation of a line students must recognize the conic sections. • An empty set represented by an equation • Solution of a literal equation Understanding that not all equations of the conic sections are The teacher will show different pictures of a conic sections then written in standard form. There is also what we called the the student will identify the standard equations and their General Second-Degree Equations. Through this, student can be properties. able to understand the characteristics of each conic sections. The teacher now presents the lesson in which the learners can The teacher now presents the lesson in which the learners can be able to write a text in cause and effect. able to comprehend and analyze the given in every problem. The teacher will present the general guidelines on how to solve any worded problem such as: a. Determine what is being asked b. Identify the given The instructor provides input on how to rewrite the standard c. Show illustration and representation form of the equation of the conic sections to general equation by c. Analyze what formula or equation to be used understanding the characteristics. d. Solution e. Answer Given worded problems about conic sections, the teacher will use the guidelines to solve the problem. ROUND ROBIN BENEFIT. The teacher will put students in group of four. Assign each student a color pencil and have them record his/her name so you can see who is responsible for STUDENTS IN ACTION . In group of four, the students will specific steps in the activity. Each group will have one problem collaborate to complete engineering and architectural challenges to solve about the conic sections. Each teammate will complete about the four conic sections. They must able to arrive in one operation or problem, and then pass on the worksheet to the illustration and design, calculations and techniques. next teammate. If students feel though someone on the item has made a mistake, they may politely ask their teammates to reconsider

13

F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions

Each group presents and discusses their output in the class. Each The students will act as engineers and architects while group should present the techniques on how they arrive and presenting their outcome. recognize the conic section given only the equation. The instructor summarizes everything that have been discussed The instructor summarizes everything that have been discussed by every group. by every group. Each group generates two questions for every other group which H. Evaluating Learning The students will answer 10-item quiz must be answered in a piece of paper. The students are tasked to answer their Problem Sets about I. Additional activities for The students are tasked to answer their Problem Sets about the recognizing conic sections given the general second-degree application or remediation worded problems involving the 4 Conic Sections. equations. V. REMARKS VI. RE FLECTION

14


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject


Week 6 Sessions 1-2

Quarter

1st

I. OBJE CTIVES

A. Content Standard B. Performance Standards

C. Learning Competencies/ Objectives

Session 2

2 hours

2 hours

The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations. The learners can be able to: The learners can be able to: determine the solutions of systems of nonlinear illustrate systems of nonlinear equations equations using techniques such as substitution, STEM_PC11AG-If-1 elimination, and graphing*** STEM_PC11AG-If-g-1 

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II . CONTENT III.

Session 1

LEARNING

RESOURCES

A. References




Solving linear and quadratic equations Sketching the graph of linear and quadratic equations

The teacher will ask questions about the last topic by randomly picking students’ name from the index card.

I V. PROCEDURES


15

Sketching the graph of conic sections. The teacher will present worded problem in which modelling it through system of linear equations is not possible and sufficient. Problem: B. Establishing a purpose for a Majo has a rectangular flower garden whose perimeter is 18m lesson and area is 14 meetr squared. She was told by her frien Anthony that this information is enough to determine the dimensions of her garden. Is Anthony’s claim true? The teacher presents the topic through giving the equations or C. Presenting the Lesson modelling the problem through the equations. The teacher defines the following terms: Nonlinear equation system of nonlinear equations Solution D. Discussing the concepts Solution Set Then, the teacher will illustrate the systems of nonlinear equations by modeling different worded problems. Dependent System Inconsistent System


F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions H. Evaluating Learning

The teacher will show some flashcard of liner equation with one variable. Then, the students will be determining the solution or the value of the variable.

The teacher will give again the problems being presented last meeting and they have to solve for the values of the unknown. The teacher will present the 3 ways on how to solve for the systems of nonlinear equations such as: 1. Elimination 2. Substitution 3. Graphing The teacher will also discuss the four steps in substitution and elimination.

TRY THEM ALL . The class will be divided into three groups. However, these three groups are given one and same problem The students are given the chance to choose their own pair but they have to solve it in different method. whom they can share their ideas and comfortable to work with. Group 1- Elimination Method Each pair, are given the 5 worded problems and they have to Group 2- Substitution Method make equations out of those given problems. Group 3- Graphical Method

The given worded problems depict the real-life applications of system of nonlinear equations in which student can fully grasp and appreciate the topic. The teacher will summarize the both the process and outcomes being presented by the students. The teacher will give 10-item quiz. 16

After they discussed on their group, each group m ust assign two students to share their answers and solution on the other groups. The teacher will summarize the presentation of the three groups The teacher will give 10-item quiz.


The students are tasked to answer their Problem Sets about illustrating systems of nonlinear equations.


17

The students are tasked to answer their Problem Sets about solving systems of nonlinear equations.


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject


Week 7 Sessions 1-2

Quarter

1st

I. OBJE CTIVES


Session 2

2 hours

2 hours

The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of nonlinear equations The learners can be able to: solve situational problems involving systems of nonlinear equations STEM_PC11AG-Ig-2 


II . CONTENT III.

Session 1

LEARNING

RESOURCES

A. References



I V. PROCEDURES


The teacher will ask questions about the previous lessons being tackled thr ough random picking of index card. 18

B. Establishing a purpose for a The teacher will give worded problems and students will try to analyze how to solve the given problem. lesson C. Presenting the Lesson The teacher presents the lesson about the worded problems involving the systems of nonlinear equations. Using the 3 ways on how to solve for the systems of nonlinear equations such as: elimination, substitution, and graphing, the teacher will present five examples of worded problems. The teacher will show how to solve them applying the general guidelines D. Discussing the concepts on how to solve worded problems.


MATH FACTS RACE . Divide the class into 10 groups with 5 students per team at the back of the class, posting a sheet 5 meters away from them. One student from each team will run to the sheet, gets the question and goes back to the team to answer the given question. Once they have the answered, the team raises green flaglet to indicate that they are done. The teacher will check the answer. Next student will get the question and do the same. The team who accumulate the highest points will be the winner

F. Finding Practical Applications of concepts and The students are able to solve worded problem with real life application. skills in daily living G. Making Generalizations The teacher summarizes all the lesson for the day. and Abstractions H. Evaluating Learning The teacher will give 10-item quiz. I. Additional activities for The students are tasked to answer their Problem Sets about worded problems involving systems of nonlinear equations. application or remediation V. REMARKS VI. RE FLECTION

19

WEEK 8-10 Series and Mathematical Induction WEEK 8 Grade 11 DAILY LOG

LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject


Week 8 Sessions 1-2

Quarter

1st

I. OBJE CTIVES

Session 1

Session 2

2 hours

2 hours

A. Content Standard

The learners shall be able to determine key concepts of series and mathematical induction and the Binomial Theorem.

B. Performance Standards

The learners shall be able to keenly observe and investigate patterns, and formulate appropriate mathematical statements and prove them using mathematical induction and/or Binomial Theorem


The learners can be able to: illustrate a series STEM_PC11SMI-Ih-1 differentiate a series from a sequence STEM_PC11SMI-Ih-2 use the sigma notation to represent a series STEM_PC11SMI-Ih-3 





A. References



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Series and Mathematical Induction: A. S equences, Series, and the Sigma Notation, B. The Principle of Mathematical Induction, C. Arithmetic Sequence and Series, D. Geometric Sequence and Series and E. The Bi nomial Theorem

II . CONTENT III. RESOURCES

The learners shall be able to: illustrate the Principle of Mathematical Induction STEM_PC11SMI-Ih-4 apply mathematical induction in proving identities

LEARNING

Pre- Calculus for Senior High School Students

Pre- Calculus for Senior High School Students 20


White board and white board marker Projector Illustration Board Chalk

White board and white board marker Projector Illustration Board Chalk

I V. PROCEDURES


The teacher presents a problem about a man named Alex who wants to train for a full marathon. He started training for a 21km run a month prior to a marathon. Given the information, t he students will try to find out the distance he covers for the next two remaining days.

B. Establishing a purpose for a The teacher emphasizes the importance of this topic to solve lesson problems such as the first problem given. C. Presenting the Lesson



The teacher will present different string of numbers. The teacher will discuss the following terms: a. Sequence b. Term c. Finite Sequence d. Infinite Sequence e. General Term f. Recursive Formula g. Summation Notation h. Index of the Summation i. Upper Limit and Lower Limit j. Series Give more string of numbers as examples. BINGO CARDS. First, let the students create bingo cards that contain answers to different sequence and series problems. They can arrange the answers in any arrangement they want. Make sure they have a separate sheet for calculations. Finally, instead of calling numbers, state the problem like what is the next term 21

TIC-TAC-TOE- Prepare by dividing a sheet into squares — three vertical by three horizontal. Don’t leave them blank. Instead, fill the boxes with questions that test their skills in operations in polynomials, laws of exponents and sigma notation. The first one to link three Xs or Os — by correctly answering questions — wins. The teacher will give a mathematical statement an and will try to let the students identify if it is true or not. Emphasizing that we cannot assume that all mathematical statements are correct. The teacher will now present the topic which is the principle of mathematical induction

The teacher will discuss the following: a. Definition of PMI b. Steps in Proving Using PMI The teacher will discuss examples with different forms of the equations.

KNOWING THE PROCESS. The teacher will put students in group of four. Assign each student a color pencil and have them record his/her name so you can see who is responsible for specific steps in the activity. In round 1, each group will have one statement to prove. Each teammate will complete one step,

for the sequence 1, 5, 9, 13 … , they can check off the number and then pass on the worksheet to the next teammate. If students 17 if it’s on their cards. If somebody formed already vertical, feel though someone on the item has made a mistake, they may horizontal and slant line, he/she will shout BINGO! politely ask their teammates to reconsider. In round 2 and 3, they will interchange steps to complete. F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions

The students will be given worded problems with real life applications. They will also solve the first given pr oblem.

Each group presents and discusses their output in the class.

The teacher will summarize students’ answers in the worded The instructor summarizes everything that have been discussed problems. by every group.

H. Evaluating Learning The teacher will give 10-item quiz. I. Additional activities for The students are tasked to answer their Problem Sets about application or remediation sequence and series. V. REMARKS VI. RE FLECTION

22

The teacher will give 10-item quiz. The students are tasked to answer their Problem Sets about Principles of Mathematical Induction.


LESSON

School


Grade Level

11

Teacher

Ms. Khatrine Ann T. A rabilla

Learning Area

Specialized Subject


Week 9 Sessions 1-2

Quarter

1st

I. OBJE CTIVES



Session 2

2 hours

2 hours

The learners shall be able to determine the key concepts of series and mathematical induction and the Binomial Theorem. The learners shall be able to keenly observe and investigate patterns, and formulate appropriate mathematical statements and prove them using mathematical induction and/or Binomial Theorem The learners shall be able to: illustrate Pascal’s Triangle in the expansion of for small positive integral values of STEM_PC11SMI-Ii-2 prove the Binomial Theorem STEM_PC11SMI-Ii-3 

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Series and Mathematical Induction: A. Sequences, Series, and the Sigma Notation, B. The Principle of Mathematical Induction, C. Arithmetic Sequence and Series, D. Geometric Sequence and Series and E. The Binomial Theorem

II . CONTENT

III.

Session 1

LEARNING

RESOURCES

A. References B. Other Learning Resources

Pre- Calculus for Senior High School Students White board and white board marker Projector Illustration Board Chalk

I V. PROCEDURES

23


B. Establishing a purpose for a lesson C. Presenting the Lesson



STAND UP, SIT DOWN : The teacher will give a straightforward review about evaluating functions: The teacher will pick a number/expression, and students must stand if the answer to an equation the teacher read aloud matches that number. If it isn’t, they remain seated in a circle. For example, you can tell students to stand if the answer is: Greater than 10 An even number (x+1) The students are asked with the following questions: 1. Have you tried expanding binomials with larger exponent? 2. What are the techniques you used to make it easier?

The teacher presents the lesson about the Pascal’s Triangle and Binomial Theorem. The teacher will discuss the following: a. Definition of Binomial Theorem b. Give the Binomial Expansion c. Proof of Binomial Theorem (by PMI) d. Definition of Pascal’s Triangle. e. Give examples CREATE MNEMONIC DEVICES . The teacher will let the students discover a mnemonics/technique in which they can easily expand binomials in a short span of time.

F. Finding Practical Applications of concepts and The students will present their mnemonics inside the class. skills in daily living G. Making Generalizations The teacher summarizes all the lesson for the day. and Abstractions H. Evaluating Learning The teacher will give 10-item quiz. I. Additional activities for The students are tasked to answer their Pr oblem Sets about Binomial Theorem and Pascal’s Triangle. application or remediation V. REMARKS VI. RE FLECTION

24


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject


Week 10 Sessions 1-2

Quarter

1st

I. OBJE CTIVES



Session 2

2 hours

2 hours

The learners shall be able to determine the key concepts of series and mathematical induction and the Binomial Theorem. The learners shall be able to keenly observe and investigate patterns, and formulate appropriate mathematical statements and pr ove them using mathematical induction and/or Binomial Theorem The learners shall be able to: determine any term of , where is a positive integer, without expanding STEM_PC11SMI-Ij-1 solve problems using mathematical induction and the Binomial Theorem STEM_PC11SMI-Ij-2 



Series and Mathematical Induction: A. Sequences, Series, and the Sigma Notation, B. The Principle of Mathematical Induction, C. Arithmetic Sequence and Series, D. Geometric Sequence and Series and E. The Binomial Theorem

II . CONTENT

III.

Session 1

LEARNING

RESOURCES


Pre- Calculus for Senior High School Students White board and white board marker Projector Illustration Board Chalk

I V. PROCEDURES

25

A. Reviewing previous lesson or presenting the new topic B. Establishing a purpose for a lesson C. Presenting the Lesson


E. Developing Mastery F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions H. Evaluating Learning I. Additional activities for application or remediation

PLEASE DON’T STOP THE MUSIC:

the whole will stand and everybody must dance to the beat of the music. Once the music stops, everybody must also stop. If a student failed to do it or stops lately, he/she will be thrown the question about the previous topic they had (Pascal’s Triangle and Bi nomial Theorem) The teacher will elaborate the importance of the new topic by l etting the students solve a question without using the knowledge of the new lesson. Example is find the 7 th term of the binomial (2 + 6)9 The teacher will present the new topic about rth term of the binomial expansion and solve problems involving mathematical induction. The teacher will discuss the following: 1. Formula for the rth term in the binomial expansion 2. Proving mathematical statements through PMI 3. Solving problems about the binomial expansion using the binomi al theorem SCRAMBLED BACK TO BACK . The teacher pre-group the students according to their ability. It involves 2 sets of 5 pair of classmates standing beside the blackboard with chalk and illustration in hand, facing away from one another. The teacher will use the chant “scramble scramble stops …” requiring each competitor to write their answer about binomial expansion and the nth term of the expansion on the board. Using this information, a competitor wins by raising the correct answer first. The students will be given worded problems with real life applications of PMI and Binomial Theorem. The teacher summarizes all the lesson for the day. The teacher will give 10-item quiz. The students are tasked to answer their Problem Sets about Binomial Theorem and PMI.


26

WEEK 11 - 20: TRIGONOMETRY


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject



Quarter

2nd

Session 1 I. OBJE CTIVES


Session 2

2 hours 2 hours The learners shall be able to determine the key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to formulate and solve accurately situational problems involving circular functions The learners shall be able to: illustrate the unit circle and the relationship between the The learners shall be able to: linear and angular measures of a central angle in a unit illustrate angles in standard position and coterminal circle angles STEM_PC11T-IIa-1 STEM_PC11T-IIa-3 convert degree measure to radian measure and vice versa STEM_PC11T-IIa-2 Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k. The Polar Coordinate System 






II . CONTENT

III.

LEARNING

RESOURCES


Pre- Calculus for Senior High School Students Whiteboard and Marker Manila Papers Pentel pen 27

I V. PROCEDURES

A. Reviewing previous lesson The teacher will present illustrations about the angles then the students will identify what type of angle is it according to or presenting the new topic measurement. The students who can give the correct answers will receive a prize. B. Establishing a purpose for a The teacher will show images of anything that has angle. Then, discuss to the students the importance of knowing the measurement lesson of the angles. C. Presenting the Lesson The teacher will present the lesson about angles, angular measures and conversion of radian to degrees and vice versa. The teacher will discuss the following: 1. Definition of angle 2. Illustration of angle 3. Parts of angle D. Discussing the concepts 4. Radian Measure 5. How to convert radian measure of an angle to its degree measure and vice v ersa 6. Coterminal Angles 7. Standard Position

E. Developing Mastery F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions H. Evaluating Learning I. Additional activities for application or remediation

WHO WANTS TO BE A MILLIONNAIRE? The teacher will divide the whole class into 4 sets. The members of the 4 sets will be competing with each other. The teacher will give questions about the discussed topic then whoever accumulate first a million points will be the winner in their set. The winners in 4 sets will also compete with each other on the final round.

The teacher will discuss the importance of angular measures through the projected images on the first part of the class discussion. The teacher will summarize all the lesson for the whole week The teacher will give a 30-point quiz. The students are tasked to answer their Problem Sets about Angels and Angular Measures and Conversion of Radian to Degrees and Vice Versa.


28


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject



Quarter

2nd



II . CONTENT

III. RESOURCES

Session 2

2 hours 2 hours The learners shall be able to determine the key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to formulate and solve accurately situational problems involving circular functions The learners shall be able to: illustrate the different circular functions STEM_PC11T-IIb-1 uses reference angles to find exact values of circular functions STEM_PC11T-IIb-2 Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k. The Polar Coordinate System  

LEARNING

A. References


Pre- Calculus for Senior High School Students White board and white board marker Projector Illustration Board Chalk Pentel pen

I V. PROCEDURES


BATO-BATOBATO-BATOTOY: The teacher will lead the group. If the teacher will say BATO, the students will place their hands on their head, BATOBATOstudents will place their hands on their shoulders and BATOTOY- students will place their hands on their knees. Here’s the catch,

29

the teacher will intentionally mismatch her actions to the command emphasizing “follow what I say, but do not follow what I do” and increase the pace of the command. If students got wrong, they will choose a number that corresponds to a question about angle in standard position, terminal, reference and coterminal angles. B. Establishing a purpose for a The teacher will introduce a new set of functions in which resulting values are dependent on the coordinates of points in the circle. lesson C. Presenting the Lesson The teacher will present the lesson about the circular functions. The teacher will discuss the following: 1. Definition of the six Circular Functions a. Sine function b. Cosine function D. Discussing the concepts c. Tangent function d. Cosecant function e. Secant function f. Cotangent function 2. Finding the six circular functions given each angle in radian and degree form MENTAL MATH: The teacher required the students to secure the following materials: Folder, Marker, Compass and any coloring E. Developing Mastery materials. Each student must illustrate the circular functions and must make a mnemonic to help them familiarize the circular functions of special angles. After they familiarize, question and answer follow. F. Finding Practical The teacher will discuss the importance of familiarizing the circular functions of special angles. (The students can be able to Applications of concepts and identify circular functions without calculator skills in daily living G. Making Generalizations The teacher will summarize all the lessons discussed and Abstractions H. Evaluating Learning The teacher will give a 30-point quiz. I. Additional activities for The students are tasked to answer their Problem Sets about the Circular Functions. application or remediation V. REMARKS VI. RE FLECTION

30


LESSON

School

Davao Doctor ’s College, Inc.

Grade Level

11

Teacher


Learning Area

Core Track



Quarter

2nd


A. Content Standard B. Performance Standards C. Learning Competencies/ Objectives II . CONTENT

III.

Session 2

2 hours 2 hours The learners shall be able to determine key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to formulate and solve accurately situational problems involving circular functions The learners shall be able to: determine the domain and range of the different circular functions STEM_PC11T-IIc-1 Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k. The Polar Coordinate System 

LEARNING

RESOURCES

A. References



I V. PROCEDURES

A. Reviewing previous lesson or presenting the new topic B. Establishing a purpose for a lesson

The teacher will give the review about the lesson tackled last meeting through reshuffling index card, randomly picking names of students.

31




The teacher will present the lesson about the domain and range of six circular functions. The teacher will discuss the following: 1. Domains of the Six Circular Functions 2. Signs of the Six Circular Functions 3. Range of Sine and Cosine Functions 4. General Sine and Cosine Functions 5. Range of the General Sine and Cosine Fun ctions 6. Period of the General Sine and Cosine Functions 7. Range of the Tangent, Cotangent, Secant, and Cosecant Functions 8. Domain of the General Tangent, Cotangent, Secant, and Cosecant Functions 9. Range of the General Tangent, Cotangent, Secant, and Cosecant Functions. POWER RANGER : The whole class will be divided into 10 groups with 5 members per group. Each member has a corresponding color like red, yellow, blue, pink and orange. Using fish bowl, the teacher will get the question as well as the color assigned to answer. The group who can give the first correct answer will be given the corresponding points.

F. Finding Practical The teacher will show to the students the importance of knowing the range and domain of the circular functions specially in Applications of concepts and graphing. skills in daily living G. Making Generalizations The teacher will summarize all the lessons discussed and Abstractions H. Evaluating Learning The teacher will give a 30-point quiz. I. Additional activities for The students are tasked to answer their Problem Sets about the Domain and Range of the Circular Functions. application or remediation V. REMARKS VI. RE FLECTION

32


LESSON

School

Davao Doctors’s College, Inc.

Grade Level

11

Teacher


Learning Area

Core Track



Quarter

2nd




2 hours 2 hours The learners shall be able to determine key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to formulate and solve accurately situational problems involving circular functions The learners can be able to: graph the six circular functions (a) amplitude, (b) period, and (c) phase shift STEM_PC11T-IIc-d-1 solve problems involving circular functions STEM_PC11T-IId-2 



Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k. The Polar Coordinate System

II . CONTENT

III. RESOURCES

Session 2

LEARNING

A. References



Pre- Calculus for Senior High School Students

I V. PROCEDURES

33

A. Reviewing previous lesson or presenting the new topic B. Establishing a purpose for a lesson C. Presenting the Lesson



The teacher will discuss the following: 1. Periodic Functions and its Period 2. Period of the General Sine and Cosine Functions 3. Definition of Amplitude 4. Amplitude of Sine and Cosine Functions 5. Phase Shift of a Sine and Cosine functions 6. Period of the General Tangent, Cotangent, Secant and Cosecant Functions 7. Solve problems involving Circular Functions SCAVENGER HUNT: The teacher will prepare ample of questions or items and let the students answer them. Through navigating their phone or laptops, they can easily find the answers or anything that will help them solve the problems. Here’s the catch . They must answer as many problems as they can in just a short period of time.

F. Finding Practical Applications of concepts and The teacher will be calling some students to explain their work. skills in daily living G. Making Generalizations and Abstractions

The teacher will summarize all the lessons discussed

H. Evaluating Learning

The teacher will give a 30-point quiz.


The students are tasked to answer their Problem Sets about Graph of Circular Functions.


34


LESSON

School

Davao Doctor’s College, Inc.

Grade Level

11

Teacher


Learning Area

Specialized Subject



Quarter

2nd



Session 2

2 hours 2 hours The learners shall be able to determine the key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to apply appropriate trigonometric identities in solving situational problems The learners shall be able to: determine whether an equation is an identity or a conditional equation STEM_PC11T-IIe-1 derive the fundamental trigonometric identities STEM_PC11T-IIe-2 derive trigonometric identities involving sum and difference of angles STEM_PC11T-IIe-3 Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k. The Polar Coordinate System 






II . CONTENT

III. RESOURCES

LEARNING

A. References


Pre- Calculus for Senior High School Students White board and white board marker Projector Illustration Board Chalk Manila Papers 35

Pentel pen I V. PROCEDURES

A. Reviewing previous lesson SHOW US WHAT YOU’VE GOT . The teacher will give review in a form of questions about the six circular functions and or presenting the new topic evaluation of circular function values. If the student failed to give the correct answer, he/she must show his/her talent. B. Establishing a purpose for a The teacher will ask the students to bring out their calculators and let them solve the Secant, Cosecant and Cotangent functions if lesson they are available in then calculators. If not, the lesson for this session is widely needed. C. Presenting the Lesson The teacher will present the new lesson for the seek about the identities of trigonometric functions. The teacher will discuss the following: 1. Identity and Conditional Equation 2. The Fundamental Identities a. Reciprocal Identities D. Discussing the concepts b. Quotient Identities c. Pythagorean Identities 3. Tips on Proving Identities Circular Functions 4. Sum and Difference Identities


GIVE ME A NUMBER : The class will be divided into 5 groups with 10 members per group. Each member must have an assigned number card. So, if the teacher will tell give me number 1, all number one’s will stand and represent their group. The group with the highest point will be the winner.

F. Finding Practical Applications of concepts and The teacher will give worded problems involving real life applications of the identities. skills in daily living G. Making Generalizations The teacher will summarize all the lessons discussed and Abstractions H. Evaluating Learning The teacher will give a 30-point quiz. I. Additional activities for application or remediation

The students are tasked to answer their Problem Sets about Graph of Circular Functions.


36


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject



Quarter

2nd



Session 2

2 hours 2 hours The learners shall be able to determine the key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to apply appropriate trigonometric identities in solving situational problems The learners can be able to: derive the double and half-angle formulas STEM_PC11T-IIf-1 simplify trigonometric expressions STEM_PC11T-IIf-2 prove other trigonometric identities STEM_PC11T-IIf-g-1 Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k. The Polar Coordinate System   

II . CONTENT

III.

LEARNING

RESOURCES

A. References



I V. PROCEDURES

37

A. Reviewing previous lesson or presenting the new topic B. Establishing a purpose for a lesson

The teacher will give a review about the evaluation of circular functions values, fundamental identities and sum and difference identities.


The teacher will discuss the lesson about double-angle identities, trigonometric expressions and identities. The teacher will discuss the following: 1. Double-angle Identities 2. Half- angle Identities 3. Simplifying Trigonometric Functions 4. Proving Trigonometric Identities AROUND THE WORLD : The teacher presents flashcards with series of questions. Let all the students stand up, the first student stands next to the student behind them. The teacher will show a flashcard and whoever is the fastest to say the correct answer between the two moves on. Here’s the catch, the idea is to be the best in the whole class.


The teacher will let the students discover that some identities discussed already are equal with double- identities

E. Developing Mastery For a bonus, if a student makes it all the way around the room then they get to go against the teacher. Surely, they will LOVE this. Since the teacher made the questions and knew the answers faster, the teacher will give them 3 tries to beat her/him. If they beat the teacher, the student will receive bonus points and a special prize F. Finding Practical Applications of concepts and skills in daily living G. Making Generalizations and Abstractions H. Evaluating Learning I. Additional activities for application or remediation

The teacher will ask the students to give and share their techniques and strategies on how to familiarize the tr igonometric identities. The teacher will summarize the lesson for the week. The teacher will give a 30-point quiz. The students are tasked to answer their Problem Sets about Double and Half-angle identities and tri gonometric expressions


38


LESSON

School


Grade Level

11

Teacher


Learning Area

Specialized Subject



Quarter

2nd


A. Content Standard B. Performance Standards C. Learning Competencies/ Objectives II . CONTENT

III.

Session 2

2 hours 2 hours The learners shall be able to determine the key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to apply appropriate trigonometric identities in solving situational problems The learners shall be able to: solve situational problems involving trigonometric identities STEM_PC11T-IIg-2 Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k . The Polar Coordinate System 

LEARNING

RESOURCES

A. References



I V. PROCEDURES


GET OUT OF HERE: The teacher divides the class into 10 groups. All groups must go outside thei r classrooms and if possible outside the campus. T hey have to list all the tall things that they can see minimum of 10 things or buildings, infrastructure.

39

B. Establishing a purpose for a The teacher will emphasize the importance of knowing the tri gonometric identities to determine the height of the buildings or any lesson high infrastructures C. Presenting the Lesson The teacher presents the steps on how to solve worded problems involving trigonometric functions. The teacher will present the general guidelines on how to solve any worded problem such as: a. Determine what is being asked b. Identify the given c. Show illustration and representation D. Discussing the concepts c. Analyze what formula or equation to be used d. Solution e. Answer Given worded problems about trigonometric, the teacher will use the guidelines to solve the problem Session 1 Same groupings a while ago, each group constructs a clinometer, uses it to measure angles, and prepares for a practical application of trigonometry to be undertaken in Session 2. Issue each group with a clear plastic ruler, a clear plastic protractor, clear tape, cotton and a small weight. Before the session it is suggested that the teacher drill a small hole in the centre of the protractors large enough to pass the cotton through. Each group makes a clinometer. Using the list of students made to measure angles. Explain how it is done.


The clinometer allows the students to measure the angle ABC. They are then able to calculate the angle BAC. The students can then be sent to a few places around the school to practise measuring such angles. Usually it is best for one person to hold the clinometer in such a way that his or her eye looks along the ruler to the top of the object concerned, and a team member reads off the angle. Students should take turns doing this. The aim, here, is to become proficient at taking angles so that this is not an issue during Session 2. For each measurement, the students should sketch a diagram. Session 2 In this session the students learn how to measure the height of one or more suitable objects, carry out the activity, and write up a poster explaining how this procedure is carried out. Each student will need to measure the distance between his or her feet and eyes. Imagine the tall object to be measured is a building.

40

Students measure the distance d from the base of the tree. They use the clinometer to find the angle θ. Using tan they can fi nd h (because h = d x tan(θ)). And, of course, they need to add on the distance between their feet and e yes at t he end. Before the teacher sends the groups out, go through two practice examples using imaginary figures. Once you are sure the groups understand the process get each group to take the necessary measurements and calculate the heights concerned. Each group should make tree measurements of the angle concerned (each at a different distance); one for each member of the group. On their return to class, lest the activity be quickly forgotten, get each student to make a small poster that fully describes how a clinometer is made and how it was used for making the relevant measurements just completed.

Session 3 In this session the students are given an insight into how trigonometry might be used, under the appropriate circumstances, to measure the height of the moon. But first the students nee d to be reminded what ‘latitude’ means, and what the moon rising or setting over the horizon means. Get the students to draw a circle representing the earth. Get them to mark a point P on the earth and imagine they are standing at this point. Now they draw a tangent through that point. The tangent is basically the horizon at P. When the moon is above this line it is above the horizon and visible from P. When it crosses the line it is either rising or setting. When it is below the line it is not visible from P. Get the student to find, using an atlas, four countries at a latitude of 20 degrees, two in the southern hemisphere and two in the northern. If you are at latitude 60 degrees, where might you be? What is the weather likely to be at a latitude 0 degree? Why? If you are at a latitude of 90 degrees, where are you? Students complete this session by making a poster explaining what it means when the moon passes over the horizon, what latitude means with some examples, how the calculation was made, and some interesting facts associated with this problem. F. Finding Practical Applications of concepts and All groups must explain their work and share insights about the activity given to them. skills in daily living 41

G. Making Generalizations The teacher will summarize the lesson for the week. and Abstractions H. Evaluating Learning The teacher will give a 30-point quiz. I. Additional activities for The students are tasked to answer their Problem Sets about Solving problems involving trigonometric functions. application or remediation V. REMARKS VI. RE FLECTION

42


LESSON

School


Grade Level

11

Teacher


Learning Area

Core Track



Quarter

2nd



II . CONTENT

III.

Session 2

2 hours 2 hours The learners shall be able to determine key concepts of circular functions, trigonometric identities, inverse trigonometric functions, and the polar coordinate system The learners shall be able to f ormulate and solve accurately situational problems involving appropriate trigonometric functions The learners shall be able to: illustrate the domain and range of th e inverse trigonometric functions. STEM_PC11T-IIh-1 evaluate an inverse trigonometric expression. STEM_PC11T-IIh-2 Trigonometry: a. Angles and Angular Measure, b. The Unit Circle, C. Circular Functions, d. Properties of Sine and Cosine, e. Fundamental Identities, f. Sum and difference Identities, g. Double-angle and Half-Angle Identities, h. Inverse Circular Functions, i. Equations involving Circular Functions, j. Application of Circular Functions and k. The Polar Coordinate System 



LEARNING

RESOURCES

A. References


Pre-Calculus for Senior High School Students White board and white board marker Projector Illustration Board Chalk

I V. PROCEDURES

43

JUST ALONG THE 4 CORNERS The teacher prepares question about the domain and range of circular functions. To begin the activity, teacher places one of the index cards face down on each student's desk. Instruct students to look at their cards privately to find out if their role in the game is that of a Player or a Fibber. Tell students to not reveal their roles to their classmates. Run through a couple of practice questions before beginning the game. Pose the first question and four possible responses. Ask A. Reviewing previous lesson students which response they think is the correct one. Have students who think the correct answer is A stand by the A sign. Students or presenting the new topic who think the correct answer is B, C, or D gather near their respective signs. BELIEVE IT OR NOT: IT’S

Here's the catch! Students who hold the Player cards go to their appropriate corners while students who hold the Fibber cards are free to go to an y corner. The Fibber's movements are intended to throw off the other students. Perhaps some of the brightest students are Fibbers and some players will be tempted to follow those students to the wrong corners. Doing this encourages students to think for themselves, not just follow the flock. B. Establishing a purpose for a The class will consider the reverse process of getting the circular function values of a given angle. lesson C. Presenting the Lesson The teacher will present the lesson about the Inverse Circular Functions. The teacher will discuss the following: 1. Inverse Sine Function D. Discussing the concepts 2. Inverse cosine Function 3. Inverse tangent Function 4. Inverse Secant, Cosecant and Cotangent Functions E. Developing Mastery Same groupings, the teacher will give problems to each group and they must have a correct and unified answer about the discussion. F. Finding Practical Applications of concepts and The students will discuss their work. skills in daily living G. Making Generalizations The teacher will summarize the lesson for the week. and Abstractions H. Evaluating Learning The teacher will give a 30-point quiz. I. Additional activities for The students are tasked to answer their Problem Sets about Solving problems involving trigonometric functions. application or remediation V. REMARKS VI. RE FLECTION

44

45

Pre-Calculus: Daily Lesson Log

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