Group 2 Ms. Patricia Flores

Ms. Janice Cruz

Toni Limuco

Robert Mendoza

Isabel Granado

Jocelyn dela Peña

Ma. Jhoana Bulos

Norlito Medollar

Doris Villaflores

Lorna Valencia

LINEAR EQUATIONS in one variable

Time Frame: 10 days

STAGE 1

Content standard The learner demonstrates understanding of

the key concepts of first-degree equations in

one variable.

PERFORMANCE standard

The learner models situations using oral,

written, graphical and algebraic methods to

solve problems involving first degree

equations and inequalities in one variable.

Essential Understanding

Real life problems where certain quantities

are unknown can be solved using first degree

equations and inequalities in one variable.

Essential questions

How can we use first degree equations and

inequalities in one variable to solve real life

problems where certain quantities are

unknown?

knowledge The students will know: mathematical expressions, first degree equations and inequalities in one variable first degree equations and inequalities in one variable properties of first degree equations and inequalities in one variable applications of first degree equations and inequalities in one variable

skills The students will be able to: Differentiate mathematical expressions from equations and equalities.Identify an describe first-degree equations and inequalities in one variable. Give examples of first degree equations and inequalities in one variable Describes situation using first degree equations and inequalities in one variable Enumerate and explain the different properties of first degree equations and inequalities Give illustrative examples of each property Apply the properties of equations and equalities in solving first degree equations in one variable Verify and explain the solution to problems involving first degree equations and inequalities in one variable Extend, pause, and solve related problems in real life

PRIOR KNOWLEDGE Unknown quantities or variables can be represented only by x or y. Variable has a fixed value. Linear equation cannot be apply in real life. In solving equations, variables are always on the left side. The use of properties of equalities and the use of relationship symbols ( or )

TRANSFER GOAL

Use linear equations in one variable to solve real-life problems.

Specifically:To model relationship between physical quantities and real life situations

STAGE 2

performance TASK

To apply your knowledge involving linear equations in one variable,

you are to play the role of a teacher. You are tasked to investigate the

relationship between the physical quantities that are found in the

environment or find real word problems that models a linear equation.

You are tasked to write the corresponding equations and related

questions to the problem. Write your explanation. You are to organize

your work on a chart or poster which shall include the

problem/situation that you investigated, your observations, the

corresponding linear equation/model, related questions, explanations

and reflection. Your presentation will be judged by your classmates.

RubricsCategory 4 3 2 1

Clarity of Presentation

Demonstrate creativity and goes beyond requirement

Demonstrate understanding on creative thought and requirements

Demonstrate little or no creativity

Not clear

Explanation Detailed and clear

Clear

A little difficult to understand but includes critical components

Difficult to understand and several components are missing

Conclusion

Accurate, written in precise narrative form and are clearly supported by mathematical evidence

Written in clear narrative form and are supported by mathematical evidence

Presented incomplete, relationship to mathematical evidence maybe limited

No conclusion

Related Question

Questions are clear and greatly add to the reader’s understanding of the procedures related to the presentation

Questions are clear and easy to understand

Questions are somewhat difficult to understand

Questions are difficult to understand or are not present

Organizational chart

Complete, neat and easy to read

Neat and easy to read, 1 or 2 items missing

Neat but 3 or 4 items are missing

Messy and more than 5 items missing

Facets of understanding

Explanation

How to solve physical quantities that are found in the environment

or real word problem that models linear equations

Interpretation

By recording an observation in a chart and writing the

findings and conclusion

Application

Variety of techniques in solving real life problems involving

linear equations

Self – knowledge

Solve problem through the idea of linear equations in one

variable

STAGE 3

INTRODUCTIONYou are a farmer and supplier of rice in your

community. If the approximate numbers of

families is above 45 and each family needs a

cavan of rice per month, how many cavans of

rice are needed for 2 months? 5 months? One

year? What do you think will happen if the

number of families increases by 2 per year.

Complete the table to show the demands of rice.

Year No. of Families No. of Demands per Year

2010 45 2011 2012 2013 2014

INTRODUCTION

INTRODUCTION

Based on the given information on the table, form an equation. How can you construct an equation to get the number of demands for the succeeding years? How can we use the first degree equation in one variable to solve real life problems where certain quantities are unknown?

INTERACTIONOn Properties of Equality

Say: Earlier, you were able to represent and solve the

unknown by using linear equation in one variable. For

further understanding of the topic, ask: What is

equilibrium? Solicit students’ answers.

Discuss the different properties of equality. Illustrate

each through examples and mathematical models. Use

a number line or algebra tiles whenever necessary.

Emphasize the said properties are used to simplify and

solve mathematical equations.

INTERACTION Let the students answer Activity # 1.

Ask them to choose a partner and discuss their work.

Let them work on Activity # 2.

You may also ask the students to access the website

for their independent study on the properties of

equality.

http://www.mathwarehouse.com

Topic on Properties of Equality and Exercises

Let the students have a journal and answer the

question: “When do we say that equality exists between

men?”

INTERACTION On Solving Linear Equations

Say: In the activities that we have done, we

understand/realize the importance of having equality among

men, object, and things. Then ask: Given an equation, when

do we apply APE, SPE, MPE, and DPE. Tell the students that in

the next activity they will apply the different properties in

solving equation in one variable.

Ask the students to perform Activity # 3. Allow them to

work for 10 – 15 minutes. Ask them to get a partner, to take

turn in showing and explaining their work in front of the class

and write at least two comments on their partner’s work.

INTERACTION

Discuss the reason why zero should not be

used as a multiplier [or a divisor] in

transforming equations. Differentiate between

the terms undefined and indeterminate.

INTERACTION

Review PEMDAS. Have students

remember the order of operations in a

multi-operation expression or equation.

INTERACTION Let the students work by group in answering Activity #4. Let them explain their work on the board. Ask the students to give procedure in solving mathematical equations. Relate the steps to the different properties of equality. Emphasize the importance of reading a word problem carefully. List down the related terms of operations like addition, subtraction, multiplication and division. Word problems are difficult for many beginning algebra students. It is important for students to realize that when they need to apply mathematics to real life problems, they must isolate or identify relevant data from extraneous data. Emphasize that sometimes there are not enough facts available to solve a given problem. Let them work on Activity 5. (Word problem)

INTERACTIONYou may also ask the students to access the following

websites to answer more activities on solving

equations.

www.algebralab.org/practice.aspx?File:word_linearequat

ions.AML

www.Free-ed.net/sweethaven/Math/Algebra/Linearequat

ion/LineqOne01_LE.asp

Let the student do the Performance Task.

Integration Summarize what you have learned about linear equations and inequalities by doing the activity below. Give the students 3 to 5 minutes and ask some students to present and explain their answers to the class.

Concept Map

Can be expressed as

Has different

namely

IntegrationValues Integration Ask them to answer the following questions in a Journal to process the learning experience of the students. What knowledge and skills did you learn from the lesson that you can use in real life? What are the attitudes of men that can be developed in the study of first degree equations in one variable? How can you use your knowledge of linear equations to lessen/eliminate corruption in our government?

closure Linear equations can be expressed either in verbal or

mathematical manner. Properties serve as a guide in

solving equations. After performing the activity, we can

say that linear equations can help in solving problems

in real life. As we continue the lessons, you can see

more applications in our everyday life.

Thank you

ACTIVITY #1Identify the property used in each equation.

1. If x = 7 and y = 7, then x = y.

2. If x = 5, then x + 3 = 5 + 3.

3. If 4x = 5, then 4x/4 = 5/4.

4. If 5x = 7, then 7 = 5x.

5. If x + 10 = 5, then x + 10 – 10 = 5 – 10.

Back

ACTIVITY #2Supply the appropriate equation indicated by the given property..

1. If x = 3 and x + y = 4, then ________________ (Substitution)

2. (x + y) + z = _____________________ (Associative)

3. If m = n and m = 3, then ___________________ (Transitive)

4. If x + 3 = 8, then ________________________ (Addition PE)

5. If 4x = 8, then __________________________ (Division PE)

Back

ACTIVITY #3Solve the following equations.

1. x + 6 = 3

2. x – 8 = 15

3. -3x = 12

4. 1/3 x = 9

5. x + 4 = - 15

Back

ACTIVITY #4Solve the following equations.

1. 2x + 6 = x - 2

2. 2(x – 1) = 3(x – 2) + 7

3. 3x + 4 = 12 + 5(x – 4)

4. ½ (x + 4) = (x + 5)

5. 2/3x + 4 = ½ (x – 3)

Back