ࡱ>  IKbjbjVV ;<<"C&8Lce>OO"qqqLLL$E LLLLL qqtttLqqtLtttq@;ht50ettt\LLtLLLLL  tLLLeLLLLLLLLLLLLL :  Linear Equations Unit: Solving Linear Equations (A 2-week unit lesson plan) Soo Han EDCI 5464 Curriculum Unit Project Table of Contents Day 1: 3.1 Solving Equations Using Addition and Subtraction ---------------------------------------------------------------------- 3 3.2 Solving Equations Using Multiplication and Division ------------------------------------------------------------------- 4 Day 2: 3.3 Solving Multi-Step Equations ----------------------------------------------------------------------------------------------- 4 Day 3: Quiz 3.4 Solving Equations with Variables on Both Sides-------------------------------------------------------------------------- 4, 5 Day 4: 3.5 Linear Equations and Problem Solving 3.6 Solving Decimal Equations-------------------------------------------------------------------------------------------------- 5, 6 Day 5: 3.6 Solving Decimal Equations Quiz 3.7 Formulas and Functions ----------------------------------------------------------------------------------------------------- 6, 7 Day 6: 3.8 Rates, Ratios, and Percents Review ----------------------------------------------------------------------------------------------------------------------------- 7, 8 Day 7: Test --------------------------------------------------------------------------------------------------------------------------------- 8 Day 1 : 3.1 Solving Equations Using Addition and Subtraction, 3.2 Solving Equations Using Multiplication and Division Virginia Standards of Learning (SOL Algebra I)Student ExperiencesBlooms TaxonomyReadiness LevelLearning StylesMultiple IntelligenceA.1 The student will solve multistep linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable, and apply these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions. A.3 The student will justify steps used in simplifying expressions and solving equations and inequalities. Justifications will include the use of concrete objects; pictorial representations; and the properties of real numbers, equality, and inequality.Students will learn solving equation by related to real-life problems such as finding a record temperature change, computer time, city parks, restoring movies, thunderstorms, and bald eagle. Students will learn solve linear equations using addition, subtraction, multiplication, and division. They will use linear equations to solve real-life problems and geometric problems.Students will recognize and define equivalent, inverse operations Students identify and list equivalent, inverse operation, solution step, and linear equation Students will identify and distinguish addition property of equality and inequality Concrete: Students will understand the instructions that are detailed with clear, concise, and sequential (step by step add, subtract, multiply, and divide each side) directions. Formal: Students will be responsible for establishing the goal of this lesson and timeline for completion of this assignment.Learning Alone: Students are given time to work on problems on their own Mobility: This lesson is good for those who are most comfortable when they sit quietly and do work. Sound: Students will receive verbal recognition for satisfactory completion of the questions by a teacher.Visual/Spatial: Students who learns best through a visual/spatial intelligence will have to rely upon their abilities to visualize the equivalent by using real transformations or power point presentation Verbal: Students who are comfortable explaining their ideas in words will have ample to solve equations by +, -, *, / Day 2 : 3.3 Solving Multi-Step Equations Virginia Standards of Learning (SOL Algebra I)Student ExperiencesBlooms TaxonomyReadiness LevelLearning StylesMultiple IntelligenceA.1 The student will solve multistep linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable, and apply these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions.Students will use two or more transformations to solve an equation. Students will use multi-step equations to solve real-life problems. Student will know how to use TI-83 calculator at the end of the lesson.Students will discover and examine to solve multi-step equations using the solve feature of a graphing calculator Students will design multi-step equations. Students summarize solution step, and linear equation Students modify on their own solving multi-step equationsConcrete: Students will understand the process of solving multi-steps of equation given a clear, concise, and sequential directions Formal: Students will be assigned as group to discover and examine and conclude the multi-step equations. They will orient questions to draw a conclusion by thinking abstractlyWorking in groups: This activity will benefit those who are peer-oriented learners. (Optional) Working Alone: This activity will benefit students who work on problems using calculator on their own. Mobility: This lesson allows students to use calculator frequently so that they can understand using it. Light: Students work best in low-light.Verbal/Linguistic: Students whose intelligence is centered upon verbal/linguistic tendencies will have the opportunity to present their findings (the model) to the classmates. Body/Kinesthetic: Students will use body/kinesthetic intelligence to construct and solve equation by using TI-83 calculator. They comprehend main objective lesson through direct use of technology such as calculator Day 3 : 3.4 Solving Equations with Variables on Both Sides Virginia Standards of Learning (SOL Algebra I)Student ExperiencesBlooms TaxonomyReadiness LevelLearning StylesMultiple IntelligenceA.3 The student will justify steps used in simplifying expressions and solving equations and inequalities. Justifications will include the use of concrete objects; pictorial representations; and the properties of real numbers, equality, and inequality.Students will use algebra tiles to model and solve equations with a variable on both sides. Students will use two or more transformations to solve an equation. Students will use multi-step equations to solve real-life problems, such as finding the temperature inside the Earth Ex. 7 in the textbook.Students will identify the term identity Students will predict the result of one side of equation. Students will collect variables on one side of an equation. Students will apply and use equations to solve real-life problemsConcrete: Students will learn the process of solving equations by clear explanation and visual and detail steps of process. Formal: Students develop describing in words abstractly the process how to solve a multi-step linear equation.Working in groups: This activity will benefit students who are peer-oriented learners as well as auditory learners through group work. Interpersonal and interpersonal intelligence: Students will rely on intrapersonal and interpersonal intelligence to delegate and to cooperate with each other to reach the objective of this activity.Visual/Spatial: Students who learn best through visual /spatial intelligence will have to rely on their abilities to visualize the construction of building algebra tile model to solve equation. Verbal/Linguistic: Students are centered on verbal/linguistic will have ample opportunity to present their finding from activity. Kinesthetic; Students are able to use algebra tile to manipulate materials. Day 4 : 3.5 Linear Equations and Problem Solving, 3.6 Solving Decimal Equations Virginia Standards of Learning (SOL Algebra I)Student ExperiencesBlooms TaxonomyReadiness LevelLearning StylesMultiple IntelligenceA.1 The student will solve multistep linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable, and apply these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions. A.3 The student will justify steps used in simplifying expressions and solving equations and inequalities. Justifications will include the use of concrete objects; pictorial representations; and the properties of real numbers, equality, and inequality.Students will use a diagram to help understand real-life problems, such as planning where bicyclists should meet in Ex. 22 in the textbook. Students can use verbal models with other problem solving strategies such as drawing a diagram Students will use tables and graphs to check the answers. Students will learn to solve linear equations graphically on a graphing calculatorStudents will recall using verbal model to solve real-life problem. Students will draw a diagram to help understand real-life problems. Students will use tables and graphs to check your answerConcrete: Students work with an actual drawing a diagram with clear and sequential instruction physically. Formal: Students who can visualize and predict before drawing a diagram to solve equations.Working in groups: This activity will benefit students who are peer-oriented learners as well as auditory learners through group work. Mobility: This group work allows students to draw and compare and differentiate the diagram to conclude solving equations. Working Alone: Students will work alone using TI-83 calculator individually and comfortably.Verbal/Linguistic: Students are centered on verbal/linguistic will have ample opportunity to present their finding from activity. Logical: This process of the drawing diagram is very ordered and concise. Kinesthetic: Students move around somewhat drawing diagrams. It shows that allowing students to use their hands and to learn by drawing. Day 5 : 3.6 Solving Decimal Equations, 3.7 Formulas and Functions Virginia Standards of Learning (SOL Algebra I)Student ExperiencesBlooms TaxonomyReadiness LevelLearning StylesMultiple IntelligenceA.1 The student will solve multistep linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable, and apply these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions. Students will find exact approximate solutions of equations that contain decimals. Students will solve real-life problems that use decimals such as calculating sales tax in Ex. 5 from textbook. They will solve a formula such as area, temperature conversion, interest, distance formulas for one of its variables and rewrite an equation in function formStudents will identify found-off error. Students will show and calculate exact and approximate solutions of equations that contain decimals Students will connect to solve real-life problems that use decimals. Students will discover a formula for one of its variables. Students will conclude and rewrite an equation in function formConcrete: Students manipulate formulas by step by step with detailed directions. Formal: Students are determined what steps are useful and apply which formulas for understanding and reasoning.Working in groups: This activity helps students teach directly and indirectly using different formula and which formula to apply by verbal discussion the procedures and reasoning of getting answers. Light: This activity benefits those who work best in high-level light. Intrapersonal: Students analyze procedures of solving equations by using different formula and come up with their own answers. Verbal/Linguistic: Students are centered on verbal/linguistic will have ample opportunity to present their finding from activity. Visual: Students need to see the steps of solving equations by sharing their ideas and writing step-by-step during group work. Day 6 : 3.8 Rates, Ratios, and Percents, Review Virginia Standards of Learning (SOL Algebra I)Student ExperiencesBlooms TaxonomyReadiness LevelLearning StylesMultiple IntelligenceA.3 The student will justify steps used in simplifying expressions and solving equations and inequalities. Justifications will include the use of concrete objects; pictorial representations; and the properties of real numbers, equality, and inequality.Students will use rates and ratios to model and solve real-life problems such as applying unit analysis. Students will use ratios to write an equation. Students will form a group and discuss to find rectangle whose length-to-width ratios are equal to the golden ratio.Students will identify rate a per b is a/b and unit rate. Students will use and explain percents to model and solve real-life problems Students apply rates, ratios, and percents and use equations solving skills to solve problems. Concrete: Students solve equations based on drawing and step-by-step procedural process of solving equations. Formal: Students solve equation using higher math logically and rationally.Self-Motivated: Students who are self-motivated will do best with the lesson. They are persistent doing multi-step solving equations. Structure: Students who are structured would apply solving equations mathematically.Logical: Mathematics is used in equations. Visual: Procedural steps of solving equation are shown. Verbal: Writing steps of solving equations are very visual structure of doing maths. Day 7 : Test Virginia Standards of Learning (SOL Algebra I)Student ExperiencesBlooms TaxonomyReadiness LevelLearning StylesMultiple IntelligenceA.1 and A.3. Students will test on based on Chapter 3.Students will recall linear equation and multi-steps of solving equations and apply formulas to solve equations. Students analyze which ways are useful for solving linear equation. Concrete: Students solve equations based on drawing diagrams and writing steps of solving equations. Formal: Students solve equations using higher math. Structure: Solving Equation mathematically is involved in high amount of structure. Self-Motivated: Students will who are self-motivated will do best with test and homework.Visual: Pictures and diagrams are used extensively in problems. Logical: Equations are used extensively. Algebra I County (Local) Standards  Benchmark 3.a Essential Justify Steps Used to Simplify and Solve Equations and Inequalities The student will justify steps used in simplifying expressions and solving equations and inequalities. Justifications will include the use of concrete objects; pictorial representations; and the properties of real numbers, equality, and inequality. POS Correlation: A.1.1 Reporting Categories: Included: MTH.ALGI: Blueprint Algebra I Test/Equations and Inequalities Indicator 3.a.1 Essential Simplify and solve equations and inequalities with number properties Simplify expressions and solve equations and inequalities, using the commutative, associative, and distributive properties. POS Correlation: A.1.1.1, A.1.1.5, A.2.1.3, A.2.1.5 Indicator 3.a.2 Essential Simplify and solve equations and inequalities with order of operations Simplify expressions and solve equations and inequalities, using the order of operations. POS Correlation: A.1.1.5 Indicator 3.a.3 Essential Solve equations by using properties of numbers Solve equations, using the addition, multiplication, closure, identity, and inverse properties. POS Correlation: A.2.1.3 Indicator 3.a.4 Essential Solve equations by using properties of equality Solve equations, using the reflexive, symmetric, transitive, and substitution properties of equality. POS Correlation: A.2.1.3 Indicator 3.a.5 Essential Create representations for solving equations and inequalities Create and interpret pictorial representations for simplifying expressions and solving equations and inequalities. POS Correlation: A.1.1.5, A.2.1.3, A.2.1.5 Indicator 3.a.6 Expected  Justify steps in solving equations and inequalities Justify the steps in solving equations and inequalities by using concrete objects, pictorial representations, and the properties of operations on real numbers. POS Correlation: A.2.1.3 and A.2.1.5 Indicator 3.a.7 Extended Honors/GT Solve absolute value equations in one variable algebraically Solve absolute value equations in one variable algebraically. Use properties of equality to solve one step, two-step, and multi-step equations in one variable. Use properties of equality and the distributive property to solve equations with variables on both sides. Write ratios and proportions. Solve proportions using cross products. Solve percent problems, such as finding the percent of a number, a base, and part of a base. Rewrite equations in function form. Solve formula and literal equations for a given variable.     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