INSET G2Math

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.

Rubrics Category 4 3 2 1 Demonstrate Demonstrate understanding Demonstrate Clarity of creativity and on creative little or no Not clear Presentation goes beyond thought and creativity requirement requirements A little Difficult to difficult to understand Detailed and understand Explanation Clear and several clear but includes components critical are missing components Accurate, written in Presented Written in precise incomplete, clear narrative narrative form relationship form and are No Conclusion and are to supported by conclusion clearly mathematical mathematical supported by evidence evidence mathematical maybe limited evidence Questions are clear and Questions greatly add to Questions are are difficult the reader’s Questions are Related somewhat to understanding clear and easy Question difficult to understand of the to understand understand or are not procedures present related to the presentation Complete, Neat and easy Neat but 3 or Messy and Organizational neat and easy to read, 1 or 2 4 items are more than 5 chart to read items missing missing 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

INTRODUCTION You 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.

INTRODUCTION 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  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?

INTERACTION On 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)

INTERACTION You may also ask the students to access the following websites to answer more activities on solving equations. www.algebralab.org/practice.aspx?File:word_linearequatio ns.AML www.Free- ed.net/sweethaven/Math/Algebra/Linearequation/Lineq One01_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 expr essed as Has differ ent namely

Integration Values 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 #1 Identify 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 #2 Supply 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 #3 Solve 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 #4 Solve 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

INSET G2Math

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