Unit 1 Equations And Inequalities Algebra 1

Unit 1 Equations and InequalitiesAlgebra 1Unit Goals – Stage 1Number of Days:MS 29 days 9/5/17 – 10/13/17HS 29 days 9/5/17 – 10/13/17Unit Description: In this unit, students analyze and explain precisely the process of solving an equation. Students, through reasoning, develop fluencywriting, interpreting, and translating between various forms of linear equations and inequalities, including literal and absolute-value equations.Materials: algebra tiles, protractorStandards for MathematicalPracticeSMP 1 Make sense of problems andpersevere in solving them.SMP 2 Reason abstractly andquantitatively.SMP 3 Construct viable argumentsand critique the reasoning ofothers.SMP 4 Model with mathematics.SMP 5 Use appropriate toolsstrategically.SMP 6 Attend to precision.SMP 7 Look for and make use ofstructure.SMP 8 Look for and expressregularity in repeatedreasoning.Standards for MathematicalContent Clusters Addressed[m] A-CED.A Create equations thatdescribe numbers orrelationships.[m] A-REI.A Understand solvingequations as aprocess of reasoningand explain thereasoning.[m] A-REI.B Solve equations andinequalities in onevariable.Transfer GoalsStudents will be able to independently use their learning to Make sense of never-before-seen problems and persevere in solving them. Construct viable arguments and critique the reasoning of others.Making MeaningUNDERSTANDINGSESSENTIAL QUESTIONSStudents will understand that Students will keep considering Linear equations and inequalities in one variable can be used How can equations and inequalities beto represent real-world situations.used to model, analyze, and solvereal-world and mathematical problems? Solving equations is a process of reasoning in which each stepcan be justified using the equality of numbers asserted at the How can you justify a solution pathprevious step, starting from the assumption that the originalwhen solving equations andequation has a solution.inequalities? The process for solving equations with numeric coefficients How is solving linear equations in onecan be applied to solving equations with letter coefficients.variable with numeric coefficients andsolving linear equations in one variable The solution to a linear equation in one variable and a linearwith letter coefficients similar?inequality in one variable is the value(s) that, when substitutedinto the equation/inequality for the variable, results in a true How do you solve absolute valuenumber statement.equations and inequalities?AcquisitionKNOWLEDGESKILLSStudents will know Students will be skilled at and/or be able to The definition of academic vocabulary Explain solution steps for solving linear equations in onewords, such as extraneous solutionvariable.and literal equations. Create and solve linear equations and inequalities in onevariable to represent a situation. You can add, subtract, multiply, ordivide both sides of an equation by Solve linear equations in one variable with letter coefficientsthe same nonzero number and the(literal equations).two sides will remain equal. Rearrange formulas to highlight a quantity of interest. The solutions to equations and Solve absolute value equations and inequalities.inequalities can be represented on a Graph the solution(s) to absolute value equations andnumber line.inequalities and interpret them in context.LONG BEACH UNIFIED SCHOOL DISTRICT2017-20181Posted 9/13/17

Unit 1 Equations and InequalitiesAlgebra 1Assessed Grade Level StandardsStandards for Mathematical PracticeSMP 1Make sense of problems and persevere in solving them.SMP 2Reason abstractly and quantitatively.SMP 3Construct viable arguments and critique the reasoning of others.SMP 4Model with mathematics.SMP 5Use appropriate tools strategically.SMP 6Attend to precision.SMP 7Look for and make use of structure.SMP 8Look for and express regularity in repeated reasoning.Standards for Mathematical Content[m] A-CED.A Create equations that describe numbers or relationships. [Linear, quadratic, and exponential]A.CED.1 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Includeequations arising from linear and quadratic functions, and simple rational and exponential functions. CA A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrangeOhm’s law V IR to highlight resistance R. [m] A-REI.A Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as a general principle.]A.REI.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting fromthe assumption that the original equation has a solution. Construct a viable argument to justify a solution method.[m] A-REI.B Solve equations and inequalities in one variable. [Linear inequalities; literal equations that are linear in the variables being solvedfor; quadratics with real solutions.]A.REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.A.REI.3.1 Solve one variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in acontext. CAKey:[m] major clusters; [s] supporting clusters, [a] additional clusters Indicates a modeling standard linking mathematics to everyday life, work, and decision-makingCA Indicates a California-only standardLONG BEACH UNIFIED SCHOOL DISTRICT2017-20182Posted 9/13/17

Unit 1 Equations and InequalitiesAlgebra 1Evidence of Learning – Stage 2Assessment EvidenceUnit AssessmentClaim 1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.Concepts and skills that may be assessed in Claim1:A-CED.A The student creates equations and inequalities in one variable, including ones with absolute value, and uses them to solve problems. The student rearranges formulas to highlight a quantity of interest.A-REI.A The student constructs a viable argument to justify a solution method when solving linear equations in one variable. The student clearly and precisely constructs viable arguments to support their own reasoning and critique the reasoning of others.A-REI.B The student solves linear equations and inequalities in one variable with numeric coefficients. The student solves linear equations in one variable with letter coefficients (literal equations). The student solves one variable equations and inequalities involving absolute value, graphs the solutions, and interprets them in a context.Claim 2: Students can solve a range of wellposed problems in pure and appliedmathematics, making productive use ofknowledge and problem-solving strategies.Standard clusters that may be assessed inClaim 2: A-CED.A A-REI.BClaim 3: The student can clearly and preciselyconstruct viable arguments to support their ownreasoning and critique the reasoning of others.Standard clusters that may be assessed inClaim 3: A-REI.AOther EvidenceFormative Assessment Opportunities Informal teacher observations Checking for understanding using active participation strategies Exit slips/summaries Tasks Claim 4: The student can analyze complex,real-world scenarios and can construct and usemathematical models to interpret and solveproblems.Standard clusters that may be assessed inClaim 4: A-CED.A A-REI.A A-REI.BModeling Lessons (SMP 4)Formative Assessment Lessons (FAL)Quizzes / Chapter TestsSBAC Interim Assessment BlocksAccess Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum DocumentsLONG BEACH UNIFIED SCHOOL DISTRICT2017-20183Posted 9/13/17

Unit 1 Equations and InequalitiesAlgebra 1Learning Plan – Stage 3DaysLearning TargetI will explore solvingequations byparticipating in theOpening Task.1 dayI will reviewequations by 4-5daysSuggested Sequence of Key Learning Events and InstructionBig Ideas Math Algebra 1Expectations(Explorations and Lessons)OPENING TASK – Mystery LettersThis Opening Task can be done as a Solo-TeamTeach activity. First have students workindependently, and then have students share theirreasoning about the task with their team. Afterworking together, facilitate a class discussion aboutthe task utilizing Talk Moves. This task provides youwith information about what the students know aboutsolving equations from previous grades and is agateway into the entire unit on equations andinequalities. Solving simple equations, multi-step equations, andequations with variables on both sides of the equalsign. Creating equations to describe numbers orrelationships in a context. (SMP 2) Constructing a viable argument to justify mysolution method. (SMP 3) Answering questions such as o How do you solve simple and multi-stepequations?o How do you solve equations with variables onboth sides of the equal side?o Synergy Item Bank: Item ID 50537, 50645LONG BEACH UNIFIED SCHOOL DISTRICT2017-20184 Section 1.1 Section 1.2 Section 1.3Supplemental ResourcesConceptual Understanding: Mystery LettersConceptual Understanding: Create an Equation Givena Solution Set TaskProcedural Skills andFluency: Equations with Variableson Both Sides Solo-TeamTeach Multi-Step EquationsCarousel Solving Multi-Step LinearEquations Tic-Tac-Toe Khan Academy: Solvingequations with oneunknownPosted 9/13/17

Unit 1 Equations and InequalitiesAlgebra 1Learning Plan – Stage 3DaysLearning TargetI will solve linearequations in onevariable by 6-7daysSuggested Sequence of Key Learning Events and InstructionBig Ideas Math Algebra 1Expectations(Explorations and Lessons)Creating and solving absolute value equations. Section 1.4Graphing and interpreting the solutions of absolute Section 1.5value equations in the context of the situation. STEM Video: Dead(SMP 2)ReckoningSolving literal equations, including formulas tohighlight a quantity of interest. (SMP 7, SMP 8)Constructing a viable argument to justify mysolution method. (SMP 3)Answering questions such as o How do you solve an absolute value equation?o Compare and contrast solving equations withnumeric coefficients to equations with variablecoefficients.o Synergy Item Bank: Item ID 54482, 54974,57317, 69159, 64305, 76195, 76657, 76663Supplemental ResourcesConceptual Understanding: Absolute Value EquationsScenarios Absolute Value EquationsTaskProcedural Skills andFluency: Equations and FormulasTask Literal Equations Tic-TacToe Khan Academy: Solvingabsolute value equationsApplication: Building Financial Literacy:Dinner at Pepe’s Fantasy Football Task Pen Pal Task STEM Video PerformanceTask: Dead Reckoning2-3daysI will check myunderstanding ofsolving equationsby participating inthe FAL.FORMATIVE ASSESSMENT LESSON Building and Solving Complex Equations(SMP 1, 5, 6, 7, 8)LONG BEACH UNIFIED SCHOOL DISTRICT2017-20185Posted 9/13/17