Rationale For Algebra 1A1/1A2 Instructional Guide
Rationale for Algebra 1A1/1A2 Instructional GuideOrganizational HighlightsA textbook is but one of the various resources that can be used to access the content standards. Through the Algebra Mandate, teacherswere given resources during LUCI training or Algebra Strategies training. These resources are available for teachers to use along withthe textbook.Recommended lessons from McDougal Littell, Algebra 1, Concepts & Skills, are listed for each of the content standards. CaliforniaContent Standards are listed in each section of the book. Individual lessons consist of assignment guides, assessment resources,problem solving exercises, teaching resources, and strategies for English Language Learners.Quarter OneModern applications of mathematics rely on solving systems of linear equations more than on any other single technique(Mathematics Framework for California Public Schools, p. 159) Thus, the first basic skills that must be learned in Algebra1 are those that relate to understanding linear equations. Thus, the first quarter goes back to seventh grade standards towork on algebraic properties and solving linear equations with one variable. This allows for students to take another look atthe basis for algebraic thinking and to solidify the skills necessary to be successful in Algebra.Quarter TwoThe second quarter continues to build upon linear equations, adding the dimensions of word problems and graphs. TheDesign Team felt it was important for students to master these standards before moving on to solving systems of equations.
Quarter ThreeIn the 3rd Quarter students continue to work on linear equations and inequalities, and absolute value equations andinequalities are added. The state has identified that the second major component of Algebra 1 is the application of linearequations and inequalities by beginning to solve systems of equations, which account for much of what is needed in highermathematics.Quarter FourThe fourth quarter addresses slope and other properties of graphs, preparing students for the first quarter of Algebra 1B1.Students continue to work on systems of equations and inequalities. Application is presented with rate and motionproblems. This lays the groundwork for the second year of this program.
LOS ANGELES UNIFIED SCHOOL DISTRICTAlgebra 1A1/1A2Mathematics Instructional Guide: Quarter OneALGEBRAIC EXPRESSIONSNUMBER SENSEStandards:* 1.01.1* 2.0* 4.024.0 – 25.3Dates**Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the fourbasic arithmetic operations where applicable.Students use properties of numbers to demonstrate whether assertions are true or falseStudents understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understandand use the rules of exponents.Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) 4(x-2) 12.Embedded StandardsStandard #1.0ConceptsMcDougal LittellAlgebraic properties; solving Sections: 1.1 – 1.6and applying linear equationsin one variable1.01.12.04.0The number line, realnumbers, algebraicpropertiesAdditional ResourcesSections: 2.1 – 2.8A S S E S S M E N TE N R I C H M E N T / R E T E A C H I N GKey: Power Standard* Assessed StandardStrikethrough: Topic not taught or assessed this quarter** Dates to be determined at school siteLAUSD Mathematics ProgramInstructional Guide, Algebra 1A1/1A2Quarter One, 2003-2004
LOS ANGELES UNIFIED SCHOOL DISTRICTAlgebra 1A1/1A2Mathematics Instructional Guide: Quarter TwoAPPLICATIONS OF LINEAR EQUATIONSStandards:* 5.0* 6.0* 7.024.0 – 25.3Dates**Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justificationfor each step.Students graph a linear equation and compute the x – and y – intercepts (e.g., graph 2x 6y 4). They are also able to sketch the region defined by linearinequality (e.g., sketch the region defined by 2x 6y 4).Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.Embedded StandardsStandard #5.0ConceptsSolving linear equations andword problemsMcDougal LittellSections: 3.1 – 3.9Additional Resources“Conveyor Belt”,Using SymbolicAlgebra to Represent and to SolveProblems ,Pathwise InstructionalGuide Two, ETS 20036.07.0Graph linear equationsVerify points on a lineSections: 4.1 – 4.7Exploring Relationships betweenSymbolic Expressions and Graphs,Pathwise Guide Four, ETS 2003A S S E S S M E N TE N R I C H M E N T / R E T E A C H I N GKey: Power Standard* Assessed StandardStrikethrough: Topic not taught or assessed this quarter** Dates to be determined at school siteLAUSD Mathematics ProgramInstructional Guide, Algebra 1A1/1A2Quarter Two, 2003-2004
LOS ANGELES UNIFIED SCHOOL DISTRICTAlgebra 1A1/1A2Mathematics Instructional Guide: Quarter ThreeABSOLUTE VALUESYSTEMS OF LINEAR EQUATIONSLINEAR INEQUALITIESStandards:* 3.0* 5.0* 6.0* 7.0* 9.024.0 – 25.3Dates**Students solve equations and inequalities involving absolute values.Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justificationfor each step.Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x 6y 4 ). They are also able to sketch the region defined by linearinequality ( e.g., sketch the region defined by 2x 6y 4 ).Students verify that a point lies on a line, given the equation of the line. Students are able to derive the equation of a line by using the point-slope formula.Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve asystem of two linear inequalities in two variables and to sketch the solutions sets.Embedded StandardsStandard #5.06.0ConceptsSolving problems with linearequationsMcDougal LittellSections: 3.6 – 3.97.05.0Point slope formula andequationsWord problemsReview section: 4.7Sections: 5.1 – 5.53.05.06.0Solve and graph linearinequalitiesAbsolute value in equationsand inequalitiesSections: 6.1 – 6.89.0Solving linear systems ofequationsSections: 7.1 – 7.6Additional ResourcesA S S E S S M E N TE N R I C H M E N T / R E T E A C H I N GKey: Power Standard* Assessed StandardStrikethrough: Topic not taught or assessed this quarter** Dates to be determined at school siteLAUSD Mathematics ProgramInstructional Guide, Algebra 1A1/1A2Quarter Three, 2003-2004
LOS ANGELES UNIFIED SCHOOL DISTRICTAlgebra 1A1/1A2Mathematics Instructional Guide: Quarter FourSYSTEMS OF EQUATIONSCOORDINATE GEOMETRYRATE PROBLEMSStandards:* 3.0* 5.0* 6.0* 7.0* 8.0* 9.0* 15.024.0 – 25.3Dates**Students solve equations and inequalities involving absolute value.Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and providejustification for each step.Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x 6y 4 ). They are also able to sketch the region defined by linearinequality (e.g., sketch the region defined by 2x 6y 4 ).Students verify that a point lies on a line, given the equation of the line. Students are able to derive the equation of a line by using the point-slope formula.Students understand the concepts of parallel line and perpendicular lines and how those slopes are related. Students are able to find the equation of a lineperpendicular to a given line that passes through a given point.Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve asystem of two linear inequalities in two variables and to sketch the solutions sets.Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.Embedded StandardsStandard #7.08.0ConceptsSlope; perpendicular andparallel linesMcDougal LittellReview sections: 5.1 – 5.63.05.06.0Absolute value equations and Review sections: 6.6 – 6.8inequalities; solving andgraphing inequalities9.0Systems of inequalitiesReview section: 7.615.0Applications of equations torate problemsSections: 3.7, 3.8, 5.5Additional ResourcesAnalyzing Graphs andInterpreting Slopes,PathwiseInstructional Tools Guide One,ETS 2003A S S E S S M E N TE N R I C H M E N T / R E T E A C H I N GKey: Power Standard* Assessed StandardStrikethrough: Topic not taught or assessed this quarter** Dates to be determined at school siteLAUSD Mathematics ProgramInstructional Guide, Algebra 1A1/1A2Quarter Four, 2003-2004
Through the Algebra Mandate, teachers were given resources during LUCI training or Algebra Strategies training. These resources are available for teachers to use along with the textbook. Recommended lessons from McDougal Littell, Algebra 1, Concepts & Skills, are listed for each of the content standards. California
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