Grade Level: Grade 9 ( October 14-17, 2024 )

Subject: Mathematics
Topic: Joint Variation
Time Frame: 4 days
Objectives (Based on MELCs)
At the end of the lesson, students should be able to:
[1.] Define joint variation and express the relationship among quantities in joint variation form.
[2.] Write the mathematical equation representing joint variation.
[3.] Solve problems involving joint variation.
[4.] Apply joint variation in real-life situations.

Day 1: Introduction to Joint Variation

I. Objectives:
[1.] Define joint variation.
[2.] Express the mathematical model of joint variation.
[3.] Identify real-life situations that involve joint variation.
II. Content:
 Introduction to Joint Variation
 Mathematical Model of Joint Variation
 Real-life Examples of Joint Variation
III. Learning Resources:
 Textbook
 PowerPoint presentation
 MELCs-based materials
 Example word problems
IV. Procedures:
A. Review:
 Briefly recall direct and inverse variation learned in the previous lesson.
 Ask students to give examples of situations involving direct and inverse variation.
B. Motivation:
 Present a scenario: The volume of a rectangular prism varies jointly with its length, width, and height. Ask students how the variables are
related.
C. Lesson Proper:
[1.] Discussion:
o Define joint variation as a relationship where a quantity varies directly with two or more other quantities.
o Present the general form of a joint variation equation:
z=kxy, where zzz varies jointly with xxx and y, and k is the constant of variation.
[2.] Examples:
o Provide simple examples and demonstrate how to write the equation for joint variation.
[3.] Guided Practice:
o Solve a few examples as a class.
D. Assessment:
 A short worksheet where students will write equations for joint variation problems.
E. Assignment:
 Write 3 real-life examples of joint variation and explain how the variables are related.

Day 2: Solving Problems Involving Joint Variation

I. Objectives:
[1.] Solve problems involving joint variation.
[2.] Derive the constant of variation from given data.
[3.] Use the equation of joint variation to solve real-life problems.
II. Content:
 Solving Word Problems Involving Joint Variation
 Finding the Constant of Variation
III. Learning Resources:
 Sample word problems
 PowerPoint presentation
 Textbook exercises
IV. Procedures:
A. Review:
 Quick recall of the joint variation formula z=kxyz = kxyz=kxy.
B. Motivation:
 Present a real-life problem: The amount of money earned by a salesperson varies jointly with the number of items sold and the price per
item.
C. Lesson Proper:
[1.] Solving Problems:
o Teach students how to solve problems by substituting given values into the joint variation equation to find the constant kkk.
o Emphasize the step-by-step process of solving joint variation problems.
[2.] Examples:
o Provide a few guided examples and walk students through the process of finding the constant and solving for unknown
variables.
[3.] Independent Practice:
o Students will solve word problems on joint variation independently.
D. Assessment:
 Worksheet with several joint variation problems for students to solve.
E. Assignment:
 Students are tasked with creating their own word problem involving joint variation, which will be used in the next lesson.

Day 3: Applying Joint Variation in Word Problems

I. Objectives:
[1.] Apply the concept of joint variation to various word problems.
[2.] Analyze and solve real-life problems involving joint variation.
[3.] Check the reasonableness of solutions in practical situations.
II. Content:
 Application of Joint Variation in Real-life Situations
 Analyzing Word Problems
III. Learning Resources:
 Textbook
 Sample word problems (students' own examples)
 Practice worksheets
IV. Procedures:
A. Review:
 Recall the steps for solving joint variation problems.
B. Motivation:
 Present a student’s word problem from the previous assignment and solve it as a class.
C. Lesson Proper:
[1.] Discussion:
o Reiterate the concept of joint variation and its applications in practical problems.
o Teach students how to analyze a problem to decide what kind of variation is involved.
[2.] Problem-Solving Activity:
o Let students work in pairs to solve each other's word problems created during the previous assignment.
[3.] Class Discussion:
o Discuss solutions and strategies, and encourage students to explain how they approached the problem.
D. Assessment:
 Check students' work and provide feedback on their problem-solving methods.
E. Assignment:
 Prepare for a quiz on joint variation and bring in a real-life scenario that involves joint variation for class discussion.

Day 4: Quiz and Real-life Application of Joint Variation

I. Objectives:
[1.] Assess the students’ understanding of joint variation.
[2.] Apply the concept of joint variation to real-life situations.
[3.] Reflect on the importance of joint variation in various fields.
II. Content:
 Quiz on Joint Variation
 Application of Joint Variation in Various Fields
III. Learning Resources:
 Quiz sheets
 Real-life application problems
 Visual aids
IV. Procedures:
A. Review:
 Quick review of key points from the previous lessons, focusing on how to set up and solve joint variation problems.
B. Quiz:
 Administer a short quiz on joint variation, covering equation writing, solving for unknowns, and word problems.
C. Application:
[1.] Real-life Situations:
 o Discuss various fields where joint variation plays a key role, such as physics (force, mass, and acceleration), economics (supply,
demand, and price), and engineering (volume, height, and area).
o Present a few real-world problems and let students work in groups to solve them.
[2.] Group Activity:
o Each group presents their solution and explains the reasoning behind it.
D. Assessment:
 Group activity output and a reflection on how joint variation applies to their daily lives.
E. Reflection:
 Ask students to write a reflection on what they have learned about joint variation and its importance in real-life situations.

Grade Level: Grade 9 ( October 21-25, 2024 )

Subject: Mathematics
Topic: Combined Variation
Time Frame: 4 days
Objectives (Based on MELCs)
At the end of the lesson, students should be able to:
[1.] Define combined variation and distinguish it from other types of variation.
[2.] Write and solve mathematical equations representing combined variation.
[3.] Solve word problems involving combined variation.
[4.] Apply knowledge of combined variation in real-life situations.

Day 1: Introduction to Combined Variation

I. Objectives:
[1.] Define combined variation.
[2.] Distinguish between joint, direct, inverse, and combined variation.
[3.] Express mathematical models of combined variation.
II. Content:
 Introduction to Combined Variation
 Differences between direct, inverse, joint, and combined variation
 Mathematical models of combined variation
III. Learning Resources:
 Textbook
 PowerPoint presentation
 Visual aids showing different types of variation
 MELCs-aligned materials
IV. Procedures:
A. Review:
 Review direct, inverse, and joint variation. Ask students to recall the key features of each type of variation.
B. Motivation:
 Show a real-life situation (e.g., pressure in a gas varies directly with temperature and inversely with volume).
C. Lesson Proper:
[1.] Discussion:
o Define combined variation as a relationship where a quantity varies directly with one or more variables and inversely with
another.
o Provide examples of combined variation.
o Present the general form:
z=kxywz = \frac{kxy}{w}z=wkxy
where z varies directly with x and y and inversely with w.
[2.] Examples:
o Show examples of combined variation equations and their solutions.
[3.] Guided Practice:
o Solve a simple combined variation problem with the class.
D. Assessment:
 Students will write equations for a few combined variation scenarios.
E. Assignment:
 Ask students to find three examples from real life or science where combined variation is applied.

Day 2: Solving Problems Involving Combined Variation

I. Objectives:
[1.] Solve problems involving combined variation.
[2.] Derive the constant of variation from given values.
[3.] Use the combined variation equation to solve for unknowns.
II. Content:
 Problem-solving involving combined variation
  Determining the constant of variation
III. Learning Resources:
 Textbook
 PowerPoint presentation
 Sample word problems
IV. Procedures:
A. Review:
 Quick recall of the combined variation formula z=kxyw
B. Motivation:
 Present a real-life problem involving combined variation (e.g., the amount of load a bridge can carry varies directly with its width and
strength of materials but inversely with its length).
C. Lesson Proper:
[1.] Solving Problems:
o Demonstrate how to identify and solve problems involving combined variation.
o Highlight the steps to find the constant of variation and use it to solve for unknown values.
[2.] Guided Practice:
o Solve sample problems as a class.
[3.] Independent Practice:
o Students will solve a few word problems independently.
D. Assessment:
 Check student work on the independent practice problems.
E. Assignment:
 Assign a set of word problems on combined variation for homework.

Day 3: Real-life Applications of Combined Variation

I. Objectives:
[1.] Analyze and solve real-life problems involving combined variation.
[2.] Apply the concepts of combined variation in practical situations.
[3.] Justify the solution steps and check the reasonableness of answers.
II. Content:
 Application of combined variation in real-life scenarios
 Problem-solving techniques
III. Learning Resources:
 Real-life application problems (physics, economics, etc.)
 Visual aids
 Textbook
IV. Procedures:
A. Review:
 Brief review of the process for solving combined variation problems.
B. Motivation:
 Present a real-world scenario, such as how the weight of a suspended object varies with the tension of the rope and inversely with the
height from which it is hanging.
C. Lesson Proper:
[1.] Problem-Solving:
o Teach students how to analyze real-world problems to identify variables related through combined variation.
o Solve an example problem together as a class.
[2.] Group Activity:
o Group students and provide them with a set of real-life problems to solve.
[3.] Class Discussion:
o Let groups present their solutions and reasoning.
D. Assessment:
 Check the group activity outputs and assess the students’ understanding.
E. Assignment:
 Ask students to bring a real-life situation that involves combined variation for the next class.

Day 4: Quiz and Real-life Problem-Solving on Combined Variation

I. Objectives:
[1.] Assess understanding of combined variation through a quiz.
[2.] Apply combined variation to real-life word problems.
[3.] Reflect on the importance of combined variation in everyday contexts.
II. Content:
 Quiz on combined variation
 Application of combined variation to real-world problems
III. Learning Resources:
  Quiz sheets
 Real-life application problems
IV. Procedures:
A. Review:
 A quick recap of combined variation concepts and formulas.
B. Quiz:
 Administer a quiz covering combined variation (writing equations, solving for unknowns, and word problems).
C. Application Activity:
[1.] Real-life Scenarios:
o Discuss fields where combined variation is crucial, such as physics, economics, engineering, and biology.
o Present additional real-world problems and let students work on solving them individually or in pairs.
[2.] Class Discussion:
o Discuss the real-world applications and how students approached solving the problems.
D. Assessment:
 Assess the students' problem-solving strategies and answers during the class discussion.
E. Reflection:
 Ask students to write a short reflection on how combined variation is used in the world around them and its importance.

Grade Level: Grade 10 ( October 14-24, 2024 )

Subject: Mathematics
Topic: Chords, Arcs, and Central Angles
Time Frame: 7 days
Objectives (Based on MELCs)
At the end of the lesson, students should be able to:
[1.] Define and identify chords, arcs, and central angles of a circle.
[2.] Differentiate between major and minor arcs.
[3.] Solve for unknown measures of chords, arcs, and central angles.
[4.] Apply properties of arcs, chords, and central angles to solve real-life problems.

Day 1: Introduction to Circles, Chords, and Arcs

I. Objectives:
[1.] Define a circle, chord, and arc.
[2.] Identify chords and arcs in given circle diagrams.
[3.] Differentiate between major and minor arcs.
II. Content:
 Definition and basic concepts of circles, chords, and arcs
 Major and minor arcs
III. Learning Resources:
 Textbook
 Circle diagrams (visual aids)
 PowerPoint presentation
 MELCs-aligned materials
IV. Procedures:
A. Review:
 Quick recall of basic geometric terms (e.g., radius, diameter, circumference).
B. Motivation:
 Present a real-life example, such as a bicycle wheel, and ask students where they can see arcs and chords.
C. Lesson Proper:
[1.] Discussion:
o Define a circle, chord, and arc, showing clear diagrams.
o Explain the difference between a major and a minor arc using circle diagrams.
[2.] Examples:
o Show examples of circles with marked chords and arcs.
o Ask students to identify whether an arc is major or minor.
[3.] Guided Practice:
o Provide students with practice problems involving identifying chords and arcs.
D. Assessment:
 Short quiz where students will identify chords and arcs in given diagrams.
E. Assignment:
 Draw a circle and label two chords and their corresponding major and minor arcs.

Day 2: Central Angles and Their Relationship with Arcs

I. Objectives:
[1.] Define a central angle and understand its relationship with arcs.
 [2.] Relate the measure of a central angle to the measure of the arc it intercepts.
II. Content:
 Definition of a central angle
 Relationship between a central angle and its intercepted arc
III. Learning Resources:
[1.] Circle diagrams with central What is the definition of a polygon?
A. A closed plane figure made of line segments C. A solid shape
B. A figure with curved lines D. A figure with no angles
2. How are polygons classified?
A. According to the number of sides and angles C. By their size
B. By their color D. By the material they are made of
3. What do you call a polygon with four equal sides and four right angles?
A. Rectangle C. Rhombus
B. Parallelogram D. Square
4. Which of the following polygons has five sides?
A. Hexagon C. Heptagon
B. Pentagon D. Octagon
5. What is a regular polygon?
A. A polygon with unequal sides  Present the scenario of a pizza slice as a representation of
a central angle and its intercepted arc.
B. A polygon with equal sides and angles
C. Lesson Proper:
 Textbook [1.] Discussion:
 PowerPoint presentation
IV. Procedures:
[B.] Define a central angle as an angle whose vertexA
A. Review: polygon with curved sides
 Review definitions of chords and arcs. C. A polygon with unequal angles
B. Motivation:
6. How many sides does an octagon have?
A. 6 C. 8
B. 7 D. 9
o What is the center of the circle.
[7.] Explain that the measure of a centraleach interior angle in a regular hexagon?
E.[A.] 90° G. 120°
F. 108° H. 135°
7.[8.] Which of the following is an irregular polygon?
[A.] A polygon with all sides and angles equal to B. A circle
A. A polygon with unequal sides and/or angles C. A square
8.[9.] What do you call a three-sided polygon with equal sides?
A. Isosceles triangle C. Equilateral triangle
B. Scalene triangle D. Right triangle

9. How is the number of interior angles in a polygon determined?

A.[B.] By doubling the number of sides C. It is the same as the number of sides
B. By adding the number of sides D. By subtracting the number of sides from 180°
10. What is the sum of the interior angles of a pentagon?
A. 360° C. 720°
B. 540° D. 900°
11. How can you describe a regular decagon?
A. It has ten sides of different lengths C. It is a circle
B. It has ten sides of equal length and equal D. It has six sides
angles
o What is the measure of the arc it intercepts.
[2.] Examples:
 o Provide examples of central angles and the corresponding arc measures.
[3.] Guided Practice:
o Have students practice determining the measure of arcs using the measure of central angles.
D. Assessment:
 Worksheet where students solve for unknown arc measures given central angles.
E. Assignment:
[12.] Draw a circle, markeach interior angle in a central angle, and calculate the measure of its intercepted arc.regular octagon?

Day 3: Properties of Chords

I. Objectives:
[1.] Identify properties of chords in a circle.
[2.] Apply the properties of chords to solve geometric problems.
II. Content:
 Properties of chords (e.g., congruent chords, perpendicular bisectors)
III. Learning Resources:
 Visual aids
 Textbook
 Example problems
IV. Procedures:
A. Review:
 Review chord definitions and central angles.
B. Motivation:
[A.] Present
E.[B.] 90° G. 120°
F. 108° H. 135°
12.[13.] Which polygon is named based on the number of vertices?
A. Hexagon C. Pentagon
B. Heptagon D. All of the above
13.[14.] How do you find the sum of the interior angles of a polygon?
A. Multiply the number of sides by 90°
B. Multiply the number of sides by 180°
C. Subtract 2 from the number of sides and multiply by 180°
D. Divide the number of sides by 2
14. What is the definition of an archery target as an example of equilateral polygon?
A. A polygon with all sides and angles equal chords forming
 A polygon with all sides equal but different regions in a circle.
C. Lesson Proper:
[1.] Discussion:
o Introduce the key properties of chords (e.g., congruent chords have congruent arcs).
o Explain the perpendicular bisector property of chords.
[2.] Examples:
o Provide problems that involve applying the properties of chords to find unknown values.
[3.] Guided Practice:
o Let students solve problems involving the properties of chords.
D. Assessment:
 Quiz on identifying and using chord properties.
E. Assignment:
 Practice problems on applying the properties of chords.

Day 4: Solving for Unknowns Involving Chords and Arcs

I. Objectives:
[1.] Solve for unknown chord lengths or arc measures using known properties.
[2.] Apply algebraic methods to solve geometric problems involving chords and arcs.
II. Content:
 Solving problems with unknown chord lengths or arc measures
III. Learning Resources:
 Practice worksheets
 Textbook
IV. Procedures:
A. Review:
 Review properties of chords and their relationship to arcs.
B. Motivation:
 Present a bridge's structure and how its support system relates to chords in a circle.
C. Lesson Proper:
[1.] Problem-Solving:
o Walk students through the process of solving problems that involve finding unknown chord lengths or arc measures.
[2.] Guided Practice:
o Solve a few examples together as a class.
[3.] Independent Practice:
o Let students practice solving similar problems.
D. Assessment:
 Worksheet where students solve for unknowns involving chords and arcs.
E. Assignment:
 Additional practice problems involving the relationships between chords and arcs.

Day 5: Arc Length and Central Angles

I. Objectives:
[1.] Calculate the length of an arc given the radius and central angle.
[2.] Use the formula for arc length in solving problems.
II. Content:
 Arc length formula: Arc Length=θ360∘×2πr\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi rArc Length=360∘θ×2πr
III. Learning Resources:
 Formula sheet
 Practice problems
 Visual aids
IV. Procedures:
A. Review:
 Recall how to find the measure of an arc using central angles.
B. Motivation:
 Present a curved path in a park as an arc, and ask students how to determine its length.
C. Lesson Proper:
[1.] Discussion:
o Introduce the formula for finding the length of an arc.
o Explain how the central angle influences the length of the arc.
[2.] Examples:
o Solve a few examples of arc length calculation using the formula.
[3.] Guided Practice:
o Let students calculate the arc length in practice problems.
D. Assessment:
 Worksheet where students compute the arc length of different circle segments.
E. Assignment:
 Find the arc length of a circle segment given a central angle and radius.

Day 6: Solving Real-life Problems Involving Chords and Arcs

I. Objectives:
[1.] Solve real-life problems involving chords, arcs, and central angles.
[2.] Apply geometric principles to practical scenarios.
II. Content:
 Real-life application of chords, arcs, and central angles
III. Learning Resources:
 Real-world problems
 Textbook
IV. Procedures:
A. Review:
 Review arc length formula and properties of chords.
B. Motivation:
 Show how architects use chords and arcs in designing structures.
C. Lesson Proper:
[1.] Problem-Solving:
o Guide students through solving real-life problems involving chords, arcs, and central angles (e.g., bridge construction,
roundabouts).
[2.] Group Activity:
 o Divide students into groups and provide each group with a real-world problem to solve.
D. Assessment:
 Group output on solving the given problem.
E. Assignment:
 Research how arcs and chords are used in different fields (architecture, engineering, etc.).

Day 7: Quiz on Chords, Arcs, and Central Angles

I. Objectives:
[A.] Assess students’ understanding of chords, arcs, and central angles.
[1.] Evaluate problem-solving skills.
II. Content:
 Comprehensive quiz on chords, arcs, and central angles
III. Learning Resources:
 Quiz sheets
IV. Procedures:
A. Review:
 Quick review of key points from previous lessons.
B. Quiz:
 Administer a quiz covering the identification of chords and arcs, solving for unknowns, and applying the properties of arcs, chords, and
central angles.
C. Reflection:
 After the quiz, ask students to reflect on what topics they found challenging and how they can improve.

Grade Level: Grade 11 ( October 14-24, 2024 )

Subject: Mathematics
Topic: Domain and Range of a Rational Function
Time Frame: 7 days
Objectives (Based on MELCs)
At the end of the lesson, the learners should be able to:
[1.] Define rational functions and identify their key components.
[2.] Determine the domain of rational functions.
[3.] Determine the range of rational functions.
[4.] Solve problems involving the domain and range of rational functions.
[5.] Apply concepts of domain and range in real-world scenarios.

Day 1: Introduction to Rational Functions

I. Objectives:
[1.] Define rational functions.
[2.] Identify the numerator and denominator in rational functions.
[3.] Simplify rational functions.
II. Content:
 Definition of rational functions
 Identifying parts of rational functions
 Simplifying rational expressions
III. Learning Resources:
 Textbook
 PowerPoint presentation
 Graphing calculators (optional)
 MELCs-aligned materials
IV. Procedures:
A. Review:
 Review basic functions, including polynomial and linear functions.
B. Motivation:
 Present a scenario like calculating speed (distance/time), which is a rational function.
C. Lesson Proper:
[1.] Discussion:
[B.] Define rational functions as the quotient of two polynomials.A polygon with all angles equal but different sides
B. A polygon with all sides and angles different
15. How many sides does a heptagon have?
A.[C.] 5 C. 7
B. 6 D. 8
16.[15.] What is a polygon with seven sides called?
 A. Pentagon C. Heptagon
B. Hexagon D. Octagon
17.[16.] What is the measure of each interior angle in a regular pentagon?
A. 90° C. 120°
B. 108° D. 135°
18.[17.] How do you identify an irregular polygon?
A. By checking if all sides and angles are equal
B. By looking at its color
C. By checking if it has straight sides
D. By seeing if it has unequal sides and/or angles
19. Which of the following is a regular polygon?
A. A square

o Explain the difference between a rational expression and a rational function.

o Show how to simplify rational functions by factoring.
[2.] Examples:
o Provide examples of rational functions and ask students to simplify them.
[3.] Guided Practice:
o Have students simplify rational functions.
D. Assessment:
 Short quiz on identifying and simplifying rational functions.
E. Assignment:
 Simplify three given rational functions.

Day 2: Determining the Domain of Rational Functions

I. Objectives:
[1.] Define the domain of a function.
[2.] Identify restrictions on the domain of a rational function.
[3.] Solve for the domain of given rational functions.
II. Content:
 Definition of domain
 Restrictions on the domain (denominator cannot be zero)
 Solving for the domain
III. Learning Resources:
 Rational function diagrams
 Textbook
 Graphing calculators
IV. Procedures:
A. Review:
 Quick recall of simplifying rational functions.
B. Motivation:
 Present a practical problem, such as dividing resources (e.g., water consumption), and ask when the situation becomes undefined.
C. Lesson Proper:
[1.] Discussion:
o Define the domain as the set of all possible inputs (values of xxx) that make the function valid.
o Explain that the denominator cannot be zero in rational functions.
o Show how to find the values of xxx that make the denominator zero and exclude them from the domain.
[2.] Examples:
o Solve for the domain of several rational functions.
[3.] Guided Practice:
o Let students find the domain of given rational functions.
D. Assessment:
 Worksheet where students solve for the domain of various rational functions.
E. Assignment:
 Find the domain of three more rational functions.

Day 3: Determining the Domain of More Complex Rational Functions

I. Objectives:
[1.] Determine the domain of more complex rational functions.
[2.] Apply the process of finding the domain to functions with higher-degree polynomials.
II. Content:
 Solving for the domain of complex rational functions
 Functions with higher-degree polynomials
III. Learning Resources:
 Textbook
 Graphing calculators
IV. Procedures:
A. Review:
 Review the process of finding the domain of basic rational functions.
B. Motivation:
 Discuss how complex systems (e.g., multiple pipelines) can be represented by rational functions and how understanding their domain is
essential.
C. Lesson Proper:
[1.] Discussion:
o Walk students through more complex examples, including higher-degree polynomials in the numerator and denominator.
o Emphasize the importance of factoring and simplifying the expression to find the domain.
[2.] Examples:
o Provide complex examples and find the domain step by step.
[3.] Guided Practice:
o Have students practice with more challenging rational functions.
D. Assessment:
 Worksheet on solving the domain of complex rational functions.
E. Assignment:
 Solve for the domain of three challenging rational functions.

Day 4: Introduction to the Range of Rational Functions

I. Objectives:
[1.] Define the range of a function.
[2.] Understand how the range differs from the domain.
[3.] Identify the range of simple rational functions.
II. Content:
 Definition of range
 Identifying the range of rational functions
III. Learning Resources:
 Graphs of rational functions
 Textbook
 Graphing calculators
IV. Procedures:
A. Review:
 Review the domain of rational functions.
B. Motivation:
 Present a graph showing how output values (range) can vary based on input values (domain).
C. Lesson Proper:
[1.] Discussion:
o Define the range as the set of all possible output values of the function.
o Explain how to determine the range by analyzing the behavior of the rational function’s graph.
[2.] Examples:
o Provide simple rational functions and identify their range from their graph.
[3.] Guided Practice:
o Use graphing calculators or graphing tools to explore the range of rational functions.
D. Assessment:
 Short quiz on identifying the range of simple rational functions.
E. Assignment:
 Find the range of two rational functions by sketching their graphs.

Day 5: Finding the Range of Rational Functions Analytically

I. Objectives:
[1.] Determine the range of rational functions without graphing.
[2.] Use algebraic methods to solve for the range of a rational function.
II. Content:
 Analytically determining the range of rational functions
III. Learning Resources:
 Textbook
 Practice problems
IV. Procedures:
A. Review:
 Review the concept of the range of rational functions.
B. Motivation:
 Discuss how understanding the range can help in optimizing functions in fields such as economics or engineering.
C. Lesson Proper:
[1.] Discussion:
o Introduce methods for determining the range algebraically by setting the function equal to yyy and solving for xxx.
o Explain how asymptotes affect the range.
[2.] Examples:
o Work through several examples of finding the range algebraically.
[3.] Guided Practice:
o Have students solve for the range of given rational functions without graphing.
D. Assessment:
 Worksheet on finding the range of rational functions analytically.
E. Assignment:
 Solve for the range of three rational functions using algebraic methods.

Day 6: Solving Problems Involving Domain and Range

I. Objectives:
[1.] Apply knowledge of domain and range to solve word problems.
[2.] Interpret real-life scenarios involving rational functions.
II. Content:
 Word problems involving rational functions
 Application of domain and range in real-life situations
III. Learning Resources:
 Textbook
 Word problems handouts
IV. Procedures:
A. Review:
 Review the process of determining the domain and range of rational functions.
B. Motivation:
 Present a practical problem, such as calculating rates of change in physics or economics, which can be modeled by rational functions.
C. Lesson Proper:
[1.] Problem-Solving:
o Walk students through solving real-world problems using rational functions.
o Focus on interpreting the domain and range in context.
[2.] Group Activity:
o Divide students into groups and give each group a word problem to solve using rational functions.
D. Assessment:
 Group output on solving the given problem.
E. Assignment:
 Solve two-word problems involving rational functions.

Day 7: Comprehensive Review of Domain and Range

I. Objectives:
[1.] Review all concepts of domain and range in rational functions.
[2.] Practice solving problems involving the domain and range of rational functions.
II. Content:
 Review of domain and range concepts
 Practice problems
III. Learning Resources:
 Textbook
 Review worksheet
IV. Procedures:
A. Review:
 Quick review of the main points from previous lessons.
B. Activity:
 Pair students up for peer teaching, where they will explain the concepts of domain and range to each other.
C. Practice:
[A.] Provide a comprehensive worksheet rectangle with a mix of problems on domain and range.unequal sides
D. Assessment:
 Worksheet output.
E. Assignment:
  Complete unfinished review exercises.

Grade Level: Grade 11 ( October 14-24, 2024 )

Subject: Applied Economics
Topic: Market Price
Time Frame: 8 days
Objectives (Based on MELCs)
At the end of the lesson, the learners should be able to:
[1.] Define market price and explain its significance in economics.
[2.] Describe how supply and demand affect market price.
[3.] Identify factors that influence market price.
[4.] Analyze real-world scenarios to determine market price changes.
[5.] Apply knowledge of market price to evaluate market conditions.

Day 1: Introduction to Market Price

I. Objectives:
[1.] Define market price and understand its components.
[2.] Explain the significance of market price in economics.
II. Content:
 Definition of market price
 Components of market price
III. Learning Resources:
 Textbook
 PowerPoint presentation
 Whiteboard and markers
IV. Procedures:
A. Review:
 Discuss previous lessons on basic economic concepts.
B. Motivation:
[B.] Present a scenario related to purchasing goods at A triangle with two equal sides
B. A pentagon with different prices.side lengths
C. Lesson Proper:
[1.] Discussion:
[18.] Define market price asWhat is the price at which goods are boughtprimary difference between regular and soldirregular
polygons?
C. The number of sides
D. The measurement of sides and angles
E. The color and shape
F. The area and perimeter
20. What is the term for a polygon with eight sides?
A. Heptagon C. Nonagon
B. Octagon D. Decagon
21.[19.] Which of the following best describes a quadrilateral?
A. A polygon with three sides C. A polygon with five sides
B. A polygon with four sides D. A polygon with six sides
22. What is the measure of each interior angle in the marketplace.a regular decagon?
o Discuss factors that contribute to determining market price.
[2.] Examples:
[B.] Provide examples
A.[C.] 108° C. 135°
B. 120° D. 144°
Part II: True or False (26-35)
23. A polygon is a closed-plane figure with curved sides.
A.[D.] True B. False
24.[20.] A regular polygon has all sides and angles equal.
A. True B. False
25.[21.] A hexagon has six sides and six interior angles.
 A. True B. False
26.[22.] An irregular polygon has sides and angles that are not equal.
A. True B. False
27.[23.] The sum of the interior angles of a triangle is 360°.
A. True B. False
28.[24.] A regular hexagon has interior angles measuring 120° each.
A. True B. False
29.[25.] A decagon has ten sides.
A. True B. False
30.[26.] The sum of the interior angles of a regular octagon is 1080°.
A. True B. False
o A polygon with sides of different market prices for the same product in various markets.
[3.] Guided Practice:
[27.] Group discussion on how prices vary inlengths and angles of different scenariosmeasures is irregular.
D. Assessment:
 Exit ticket asking students to define market price in their own words.
[A.] True C. False
31.[28.] A square is a type of rectangle.
A. True B. False

Part III: Identification (36-40)

36. What is the term for a polygon with ten sides?


37. What do you call a four-sided polygon with equal sides and angles?


38. What is the sum of the interior angles of a hexagon?



39. What do you call a polygon with seven sides?



40. What is the name for a polygon with nine sides?



Part IV: Matching Type (41-45)

Match the descriptions in Column A with their corresponding terms in Column B.

Column A: 44. A polygon with four sides and unequal sides and
41. A polygon with six sides angles
42. A polygon with eight sides 45. A polygon with equal sides and angles
43. A polygon with five sides
Column B: D. Irregular polygon
A. Square E. Assignment:Pentagon
B. Hexagon F. Octagon
C. Regular polygon

Part V: Short Answer (46-50)

 Explain the difference between a Research and find the market price of a specific product.

Day 2: Supply and Demand Basics

I. Objectives:
[46.] regular and an irregular polygon.


47. How can you determine the measure of each interior angle in a regular polygon?


48. Why is a triangle considered a polygon, and what are its properties?


49. Describe the lawsproperties of supply and demanda regular hexagon.

[1.] Explain how supply and demand interact to determine market price.
II. Content:
 Laws of supply and demand
 Market equilibrium
III. Learning Resources:
 Graphs showing supply and demand curves
 Textbook
IV. Procedures:
A. Review:
 Recap definitions of supply and demand from previous lessons.
B. Motivation:
 Pose a question: "Why do prices go up when there is a shortage of a product?"
C. Lesson Proper:
[1.] Discussion:
o Explain the laws of supply and demand and how they affect market price.
o Introduce the concept of market equilibrium.
[2.] Examples:
o Graph the supply and demand curves and identify the equilibrium price.
[3.] Guided Practice:
o Have students practice plotting supply and demand curves.
D. Assessment:
 Quick quiz on supply and demand concepts.
E. Assignment:
 Write a paragraph explaining how supply and demand affect market price.

Day 3: Factors Influencing Market Price

I. Objectives:
[1.] Identify key factors that influence market price.
[2.] Discuss how external factors can cause shifts in supply and demand.
II. Content:
 Factors affecting supply (cost of production, technology)
 Factors affecting demand (consumer preferences, income)
III. Learning Resources:
 Case studies
 Charts and graphs
IV. Procedures:
A. Review:
 Review concepts of supply and demand.
B. Motivation:
 Discuss recent news articles about price changes in goods (e.g., fuel prices).
C. Lesson Proper:
[1.] Discussion:
o Identify and explain factors that affect supply and demand and their impact on market price.
[2.] Examples:
o Provide case studies showing how various factors influenced market prices of common goods.
[3.] Guided Practice:
o Analyze a case study as a class.
D. Assessment:
 Worksheet identifying factors influencing market prices of various products.
E. Assignment:
 Research a recent event that affected market price and summarize it.

Day 4: Market Price in Real-World Scenarios

I. Objectives:
[1.] Analyze real-world scenarios involving changes in market price.
[2.] Discuss the implications of fluctuating market prices.
II. Content:
 Case studies on price fluctuations
 Impact of price changes on consumers and producers
III. Learning Resources:
 Current events articles
 Videos demonstrating price changes
IV. Procedures:
A. Review:
 Review the importance of understanding market price.
B. Motivation:
 Show a video about a recent price surge (e.g., during a natural disaster).
C. Lesson Proper:
[1.] Discussion:
o Analyze how price changes affect consumer behavior and producer decisions.
[2.] Examples:
o Discuss several real-world examples of market price fluctuations.
[3.] Guided Practice:
o Work in groups to analyze a specific market price scenario.
D. Assessment:
 Group presentations on their market price analysis.
E. Assignment:
 Write a reflection on how market price affects their daily lives.

Day 5: Government Intervention and Market Price

I. Objectives:
[1.] Explain how government policies can influence market price.
[2.] Discuss price controls (ceilings and floors) and their impacts.
II. Content:
 Government intervention in markets
 Price ceilings and price floors
III. Learning Resources:
 Textbook
 Articles on government price controls
IV. Procedures:
A. Review:
 Review previous lessons on market price.
B. Motivation:
 Discuss examples of government intervention in the economy.
C. Lesson Proper:
[1.] Discussion:
o Explain price controls and their intended effects.
[2.] Examples:
o Discuss historical examples of price ceilings (rent control) and price floors (minimum wage).
[3.] Guided Practice:
o Analyze the effects of a hypothetical price control on a market.
D. Assessment:
  Quiz on government interventions in the market.
E. Assignment:
 Write a short essay on the pros and cons of government price controls.

Day 6: Evaluating Market Conditions

I. Objectives:
[1.] Apply knowledge of market price to evaluate market conditions.
[2.] Analyze current market trends.
II. Content:


50. How does understanding the properties of polygons help in real-life applications?


Answer Key
Part I: Multiple Choice
1. A
2. A
3. D
4. B
5. B
6. C
7. C
8. B
9. C
10. C
11. B
12. B
13. D
14. D
15. C
16. A
17. C
18. C
19. B
20. D
21. A
22. B
23. B
24. B
25. D
Part II: True or False 26. B
27. A
28. A
29. A
30. B
31. A
32. A
33. B
34. A
35. A
Part III: Identification 36. Decagon
37. Square
38. 720°
39. Heptagon
40. Nonagon
Part IV: Matching Type 41. B
42. F
43. E
44. D
45. C
Part V: Short Answer 46. A regular polygon has all sides and angles equal, while an irregular polygon has sides and
angles that are not equal.
47. The measure of each interior angle in a regular polygon can be determined by dividing the sum of the interior
angles by the number of sides. The sum can be found using the formula (n−2)×180∘(n - 2) \times 180^\
circ(n−2)×180∘, where nnn is the number of sides.
48. A triangle is considered a polygon because it is a closed-plane figure made of three line segments. Its properties
include having three sides, three vertices, and the sum of its interior angles is always 180°.
49. A regular hexagon has six equal sides and six equal interior angles, each measuring 120°. It is both equilateral
and equiangular.
50. Understanding the properties of polygons helps in real-life applications such as architecture, design, and
engineering, where accurate measurements and understanding of shapes are essential for constructing
structures and creating designs.

Table of Specification for Grade 7 Mathematics (Matatag Curriculum, Quarter 1)

No. of %
Content Areas Remembering Understanding Applying Analyzing Evaluating Creating Total
Items Weight
1. Identification of
10 4 4 2 10 20%
Polygons
- Types of polygons 5 3 2 5 10%
- Regular vs. Irregular
5 1 2 2 5 10%
polygons
2. Properties of Polygons 15 3 4 4 3 1 15 30%
- Number of sides 5 2 2 1 5 10%
- Sum of interior angles 5 1 2 1 1 5 10%
- Sum of exterior angles 5 2 2 1 5 10%
3. Determining Measures
15 2 4 5 3 1 15 30%
of Angles and Sides
- Measure of interior
7 1 2 2 2 7 14%
angles
- Measure of exterior
5 1 1 2 1 5 10%
angles
 No. of %
Content Areas Remembering Understanding Applying Analyzing Evaluating Creating Total
Items Weight
- Number of sides of
3 1 1 1 3 6%
polygons
4. Application of
Measures of Angles and 10 1 3 4 2 10 20%
Sides
- Problem-solving
5 1 2 1 1 5 10%
involving angle measures
- Solving for unknown
5 1 3 1 5 10%
sides

Computation & Item Distribution

 Total number of items: 50
 Total percentage: 100%
 Distribution by cognitive levels (based on Bloom’s Taxonomy):
o Remembering: 10 items (20%)
o Understanding: 15 items (30%)
o Applying: 15 items (30%)
o Analyzing: 8 items (16%)
o Evaluating market conditions using supply and demand analysis: 2 items (4%)
 Understanding market trends
III. Learning Resources:
 Market reports
 Graphs and charts
IV. Procedures:
A. Review:
 Review factors influencing market prices.
B. Motivation:
 Present a recent market report for analysis.
C. Lesson Proper:
[1.] Discussion:
o Teach students how to analyze market conditions using supply and demand.
[2.] Examples:
o Analyze current market trends together.
[3.] Guided Practice:
o Have students evaluate a market report in groups.
D. Assessment:
 Group activity to present findings from market analysis.
E. Assignment:
 Write a report analyzing a chosen market trend.

Day 7: Group Project Preparation

I. Objectives:
[1.] Prepare for a group project on market price analysis.
[2.] Develop teamwork and research skills.
II. Content:
 Project guidelines and expectations
III. Learning Resources:
 Project rubric
 Research materials
IV. Procedures:
A. Review:
 Discuss the objectives of the group project.
B. Motivation:
 Explain the importance of collaboration and research skills in economics.
C. Lesson Proper:
 [1.] Discussion:
o Outline the project requirements and deadlines.
[2.] Group Work:
o Allow time for groups to brainstorm and plan their projects.
[3.] Guided Practice:
o Provide guidance on research methods.
D. Assessment:
 Teacher observation of group collaboration.
E. Assignment:
 Continue working on group projects at home.

Day 8: Group Project Presentation and Reflection

I. Objectives:
[1.] Present group projects on market price analysis.
[2.] Reflect on what was learned throughout the unit.
II. Content:
 Group presentations
 Reflection on market price concepts
III. Learning Resources:
 Project presentations
 Feedback forms
IV. Procedures:
A. Review:
 Quick recap of key concepts learned in the unit.
B. Motivation:
 Emphasize the importance of sharing knowledge with peers.
C. Lesson Proper:
[1.] Presentations:
o Each group presents their project to the class.
[2.] Feedback:
o Peers provide constructive feedback on each presentation.
[3.] Reflection:
o Conduct a class discussion on key takeaways from the unit.
D. Assessment:
 Evaluate group presentations based on the rubric.
E. Assignment:
 Write a reflection on the importance of understanding market price in economics.
o Creating: 0 items (0%)