Math 9 tg draft 3.24. PDF

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TEACHING GUIDE Module 1: Quadratic Equations and Inequalities A. Learning Outcomes Content Standard: The learner demonstrates understanding of key concepts of quadratic equations, quadratic inequalities, and rational algebraic equations. Performance Standard: The learner is able to investigate thoro...

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Math 9 tg dra

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TEACHING GUIDE Module 1:

Quadratic Equations and Inequalities

A. Learning Outcomes Content Standard: The learner demonstrates understanding of key concepts of quadratic equations, quadratic inequalities, and rational algebraic equations. Performance Standard: The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life problems involving quadratic equations, quadratic inequalities, and rational algebraic equations and solve them using a variety of strategies. UNPACKING THE STANDARDS FOR UNDERSTANDING

DRAFT March 24, 2014 SUBJECT: Mathematics 9 QUARTER: First Quarter

LEARNING COMPETENCIES 1. Illustrate quadratic equations.

2. TOPIC: Quadratic Equations, Quadratic Inequalities, and Rational Algebraic Equations 3. LESSONS: 1. Illustrations of Quadratic Equations 2. Solving Quadratic Equations  Extracting Square Roots  Factoring  Completing the Square  Using the Quadratic Formula 3. Nature of Roots of Quadratic Equations 4. Sum and Product of Roots of Quadratic Equations 5. Equations Transformable to Quadratic Equations (Including Rational

Solve quadratic equations by: (a) extracting square roots; (b) factoring; (c) completing the square; and (d) using the quadratic formula.

Characterize the roots of a quadratic equation using the discriminant.

4. Describe the relationship between the coefficients and the roots of a quadratic equation. 5. Solve equations transformable to quadratic equations (including rational algebraic equations). 6. Solve problems involving quadratic equations and rational algebraic equations. 7. Illustrate quadratic inequalities. 8. Solve quadratic inequalities. 9. Solve problems involving quadratic inequalities.

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Algebraic Equations) 6. Applications of Quadratic Equations and Rational Algebraic Equations 7. Quadratic Inequalities ESSENTIAL UNDERSTANDING:

ESSENTIAL QUESTION:

MELVIN M. CALLANTA RICHARD F. DE VERA 

Students will understand that quadratic equations, quadratic inequalities, and rational algebraic equations are useful tools in solving real-life problems and in making decisions given certain constraints.

How do quadratic equations, quadratic inequalities, and rational algebraic equations facilitate finding solutions to real-life problems and making decisions?

 

TRANSFER GOAL:

WRITERS:

DRAFT March 24, 2014 Students will be able to apply the key concepts of quadratic equations, quadratic inequalities, and rational algebraic equations in formulating and solving real-life problems and in making decisions.

B. Planning for Assessment Product/Performance

The following are products and performances that students are expected to come up with in this module. a. Quadratic equations written in standard form b. Objects or situations in real life where quadratic equations, quadratic inequalities, and rational algebraic equations are illustrated c. Quadratic equations, quadratic inequalities, and rational algebraic equations that represent real life situations or objects d. Quadratic equations with 2 solutions, 1 solution, and no solution e. Solutions of quadratic equations which can be solved by extracting square roots, factoring, completing the square, and by using the quadratic formula f. A journal on how to determine quadratic equation given the roots, and the sum and product of roots g. Finding the quadratic equation given the sum and product of its roots h. Sketch plans or designs of objects that illustrate quadratic equations, quadratic inequalities, and rational algebraic equations i. Role playing a situation in real life where the concept of quadratic equation is applied

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j.

Formulating and solving real-life problems involving quadratic equations, quadratic inequalities, and rational algebraic equations k. Conducting a mathematical investigation on quadratic inequalities l. Graphing the solution set of quadratic inequalities formulated Assessment Map TYPE

KNOWLEDGE

PreAssessment/ Diagnostic

Pre-Test: Part I Identifying quadratic equations, quadratic inequalities, and rational algebraic equations

PROCESS/ SKILLS Pre-Test: Part I Solving quadratic equations, quadratic inequalities, and rational algebraic equations

UNDERSTANDING

PERFORMANCE

Pre-Test: Part I Solving problems involving quadratic equations, quadratic inequalities, and rational algebraic equations

Pre-Test: Part I Products and performances related to or involving quadratic equations, quadratic inequalities, rational algebraic equations, and other mathematics concepts

Describing the roots of quadratic equations

DRAFT March 24, 2014 Writing the quadratic equations given the roots

Solving equations transformable to quadratic equations

Pre-Test: Part II Situational Analysis Identifying the fixtures or furniture to be designed Determining the mathematics concepts or principles involved in the designs of the fixtures

Graphing the solution sets of quadratic inequalities Pre-Test: Part II Situational Analysis Illustrating every part or portion of the fixture including their measures Writing the expressions, equations, or inequalities that describe the situations or problems Solving 3 

 

Pre-Test: Part II Situational Analysis Explaining how to prepare the designs of the fixtures Solving real-life problems

Pre-Test: Part II Situational Analysis Making designs of fixtures Formulating equations, inequalities, and problems

Formative

Quiz: Lesson 1 Identifying quadratic equations Identifying situations that illustrate quadratic equations

equations and inequalities Quiz: Lesson 1 Representing situations by mathematical sentences Writing quadratic equations in standard form

ax 2  bx  c  0 and identifying the values of a, b, and c

Quiz: Lesson 1 Differentiating quadratic equations from linear equations Explaining how to write quadratic equations in standard form Justifying why quadratic equations can be written in standard form in two ways Formulating and describing a quadratic equation that represents a given situation

DRAFT March 24, 2014 Quiz: Lesson 2A Identifying quadratic equations that can be solved by extracting square roots

Quiz: Lesson 2A Solving quadratic equations by extracting square roots

Writing a quadratic equation that represents the area of the shaded region of a square. Finding the length of a side of a square using the quadratic equation formulated.

Quiz: Lesson 2B Identifying quadratic equations that

Quiz: Lesson 2B Solving quadratic equations by 4 

 

Quiz: Lesson 2A

Explaining how to solve quadratic equations by extracting square roots

Justifying why a quadratic equation has at most two roots Explaining why some quadratic equations can be solved easily by extracting square roots

Solving real-life problems involving quadratic equations Quiz: Lesson 2B Explaining how to solve quadratic equations by

can be solved by factoring

factoring

factoring

Writing a quadratic equation that represents the area of the shaded region of a rectangular figure.

Explaining why some quadratic equations may be solved more appropriately by factoring

Finding the length and the width of a figure using the quadratic equation formulated. Quiz: Lesson 2C Identifying quadratic equations that can be solved by completing the square

Quiz: Lesson 2C Solving quadratic equations by completing the square

Solving real-life problems involving quadratic equations

Quiz: Lesson 2C Explaining how to solve quadratic equations by completing the square

DRAFT March 24, 2014 Writing and solving a quadratic equation that represents the area of the shaded region of a rectangular figure. Finding the particular measure of a figure using the quadratic equation formulated. Quiz: Lesson 2D Determining the values of a, b, and c in a quadratic equation Identifying quadratic

Quiz: Lesson 2D Writing quadratic equations in the form

ax 2  bx  c  0 Solving quadratic 5 

 

Explaining why some quadratic equations may be solved appropriately by completing the square

Solving real-life problems involving quadratic equations

Quiz: Lesson 2D Explaining how to solve quadratic equations by using the quadratic formula Explaining why all quadratic equations

equations that can be solved by using the quadratic formula

equations by using the quadratic formula Writing and solving quadratic equations that represent some given situations

Quiz: Lesson 3 Determining the values of a, b, and c in a quadratic equation

can be solved by using the quadratic formula Solving real-life problems involving quadratic equations

Quiz: Lesson 3 Finding the value of the discriminant of a quadratic equation

Quiz: Lesson 3 Explaining how to determine the nature of the roots of quadratic equations

Describing the roots of a quadratic equation

Applying the concept of discriminant of quadratic equations in solving real-life problems

DRAFT March 24, 2014 Writing a quadratic equation that represents a given situation

Quiz: Lesson 4 Determining the values of a, b, and c in a quadratic equation

Quiz: Lesson 4 Finding the sum and the product of roots of quadratic equations

Quiz: Lesson 4 Explaining how to determine the sum and the product of the roots of quadratic equations

Finding the roots of quadratic equation

Explaining how to find the roots of quadratic equation

ax 2  bx  c  0 using the values of a, b, and c

ax 2  bx  c  0 using the values of a, b, and c

Writing the quadratic equation given the roots

Explaining how to determine the quadratic equation given the roots

Writing a quadratic equation that represents a given situation

Using the sum and the product of roots of quadratic equations in solving real-life problems

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Quiz: Lesson 5 Identifying quadratic equations that can be written in the form

Quiz: Lesson 5 Transforming equations to quadratic equations in the form

Quiz: Lesson 5 Explaining how to transform equations to quadratic equations in the form

ax 2  bx  c  0

ax 2  bx  c  0

ax 2  bx  c  0

Identifying rational algebraic equations that are transformable to quadratic equations

Finding the solutions of equations transformable to quadratic equations in the form

Explaining how to solve equations transformable to quadratic equations in the form

ax 2  bx  c  0 including rational algebraic equations

Solving equations with extraneous solutions or roots

ax 2  bx  c  0

Solving problems involving equations transformable to quadratic equations in the form

DRAFT March 24, 2014 ax 2  bx  c  0 including rational algebraic equations

Quiz: Lesson 6 Identifying the information given in real-life problems involving quadratic equations

Quiz: Lesson 6 Solving quadratic equations and rational algebraic equations as illustrated in some real-life problems

Quiz: Lesson 6 Solving real-life problems involving quadratic equations and rational algebraic equations

Quiz: Lesson 7 Identifying quadratic inequalities

Quiz: Lesson 7 Finding the solution set of quadratic inequalities

Quiz: Lesson 7 Explaining how to find the solution set of quadratic inequalities

Graphing the solution set of quadratic inequalities

Explaining how to graph the solution set of quadratic inequalities

Determining whether a point is a solution to a given inequality

Describing the solution set of quadratic inequalities and

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their graphs Determining the quadratic inequality that is described by a graph

Explaining how to determine the quadratic inequality that is described by a graph Solving real-life problems involving quadratic inequalities

Summative

Post-Test: Part I Identifying quadratic equations, quadratic inequalities, and rational algebraic equations

Post-Test: Part I Solving quadratic equations, quadratic inequalities, and rational algebraic equations

Post-Test: Part I Solving problems involving quadratic equations, quadratic inequalities, and rational algebraic equations

Post-Test: Part I Products and performances related to or involving quadratic equations, quadratic inequalities, rational algebraic equations, and other mathematics concepts

DRAFT March 24, 2014 Describing the roots of quadratic equations Writing the quadratic equations given the roots

Solving equations transformable to quadratic equations Graphing the solution sets of quadratic inequalities

Post-Test: Part II Situational Analysis Identifying the locations of establishments, roads, and pathways to be included in the ground plan of the proposed shopping

Post-Test: Part II Situational Analysis Writing the expressions, equations, or inequalities that describe the situations or problems

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Post-Test: Part II Situational Analysis Explaining how to prepare the ground plan of the proposed shopping complex

Post-Test: Part II Situational Analysis Making a ground plan of the proposed shopping complex

Solving real-life problems

Formulating equations, inequalities, and problems

complex Determining the mathematics concepts or principles involved in the ground plan SelfAssessment

Solving equations and inequalities

Journal Writing: Expressing understanding of quadratic equations, quadratic inequalities, and rational algebraic equations and their solutions or roots Expressing understanding on finding solutions of quadratic equations, quadratic inequalities, and rational algebraic equations

Assessment Matrix (Summative Test) Levels of What will I assess? Assessment The learner demonstrates understanding of key concepts of quadratic Knowledge equations, quadratic 15% inequalities, and rational algebraic equations.

How will I assess? Paper and Pencil Test

How Will I Score?

DRAFT March 24, 2014 Illustrate quadratic equations.

Process/Skills 25%

Understanding 30%

Solve quadratic equations by: (a) extracting square roots; (b) factoring; (c) completing the square; (d) using the quadratic formula. Characterize the roots of a quadratic equation using the discriminant. Describe the relationship between the coefficients and the roots of a quadratic equation. 9 

 

Part I items 1, 2, 3, 8, 12, and 15

1 point for every correct response

Part II item 3

Part I items 4, 5, 6, 7, 9, 10, 11, 13, 14, and 16 Part II items 5 and 6 Part I items 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28 Part II items 1 and 6

1 point for every correct response

1 point for every correct response

Rubric for explanation Criteria: Clear Coherent Justified Rubric on Problem Solving

Solve equations transformable to quadratic equations (including rational algebraic equations). Solve problems involving quadratic equations and rational algebraic equations. Illustrates quadratic inequalities. Solve quadratic inequalities. Solve problems involving quadratic inequalities.

DRAFT March 24, 2014 Product/ Performance 30%

The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life problems involving quadratic equations, quadratic inequalities, and rational algebraic equations and solve them using a variety of strategies.

Part II items 2 and 4

Rubric on Design (Ground Plan) Criteria: 1. Content 2. Clarity of Presentation 3. Accuracy of Measurements

Rubric for Equations Formulated and Solved Rubric on Problem Posing/Formulation Criteria: Relevant Authentic Creative Clear Insightful

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C. Planning for Teaching-Learning Introduction: This module covers key concepts of quadratic equations, quadratic inequalities, and rational algebraic expressions. It is divided into seven lessons namely: Illustrations of Quadratic Equations, Solving Quadratic Equations, Nature of Roots of Quadratic Equations, Sum and Product of Roots of Quadratic Equations, Transforming Equations to Quadratic Equations (including Rational Algebraic Equations), Applications of Quadratic Equations, and Rational Algebraic Equations, and Quadratic Inequalities. In Lesson 1 of this module, the students will identify and describe quadratic equations and illustrate these using appropriate representations. They will also formulate quadratic equations as illustrated in some real-life situations. Lesson 2 is divided into four sub-lessons. In this lesson, the students will be given the opportunity to learn the different methods of solving quadratic equations namely: extracting square roots, factoring, completing the square, and using the quadratic formula. They will also determine the method that is more appropriate to use in solving quadratic equations.

DRAFT March 24, 2014 After the students have learned to solve quadratic equations, the next thing that they will do is to determine the nature of the roots of these equations using the value of the discriminant. This topic will be covered in Lesson 3.

In Lesson 4, the students will learn about the relationships among the

values of a, b, and c in a quadratic equation ax 2  bx  c  0 , where a ≠ 0, and its roots. In this lesson, the students should be able to come up with the quadratic equation given the roots or vice-versa.

One of the important lessons that students need to learn is that some equations can be transformed to quadratic equations in the form ax 2  bx  c  0 , a ≠ 0. Some examples of these kinds of equations are rational algebraic equations. The students should be able to identify and solve these equations in Lesson 5. In Lesson 6, the students will find out the vast applications of quadratic equations as they solve real-life problems involving these. Moreover, they will be given the chance to formulate real-life problems involving quadratic equations and solve these using the appropriate methods. Another interesting mathematics concept that the students will learn in this module is quadratic inequality. This is the content of Lesson 7. In this lesson, the students will determine the solution set of quadratic inequalities algebraically and graphically. The students will also be given the opportunity to use graphing materials, tools, or computer software like GeoGebra in finding the solution set of quadratic inequalities.

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In all the lessons, the students are given the opportunity to use their prior knowledge and skills ...