Radnor High School - Radnor Township School District

Radnor Middle SchoolCourse OverviewMathIntroduction to Algebra 1General InformationCredits: N/AWeighted: N/APrerequisite: Pre-Algebra, Course 3Length: Full YearFormat: Meets DailyGrade: 8I. Course DescriptionThe goal of this course is to provide students with a foundation in the algebraic strand ofmathematics through experiences with: understanding patterns, relations, and functions; representing and analyzing mathematical situations and structures using algebraicsymbols; using mathematical models to represent and understand quantitative relationships; analyzing change in various contexts.Mathematics itself will be looked at not just as calculation but also as a modeling language, as aprocess for logical thought, and as a field of study.This approach to Algebra 1 is organized around families of functions, with special emphasis onlinear functions. As students learn about each family of functions, they will learn to representthem in multiple ways: as verbal descriptions, equations, tables, and graphs. They will also learnto model real‐world situations using functions in order to solve problems arising from thosesituations.Grade 8Intro to AlgebraLast ModifiedApril 24, 2012

MAJOR UNITS OF STUDYMARKING PERIOD: 1Unit: Chapter 1 – Expressions, Equations, and FunctionsCommon Core Standards Interpret parts of an expression, such as terms, factors, and coefficients. Understand that a function is a rule that assigns to each input exactly one output. Thegraph of a function is the set of ordered pairs consisting of an input and thecorresponding output. Construct a function to model a linear relationship between two quantities.Determine the rate of change and initial value of the function from a description of arelationship or from two (x, y) values, including reading these from a table or from agraph. Interpret the rate of change and initial value of a linear function in terms of thesituation it models, and in terms of its graph or a table of values. Describe qualitatively the functional relationship between two quantities by analyzinga graph (e.g., where the function is increasing or decreasing, linear or nonlinear).Sketch a graph that exhibits the qualitative features of a function that has beendescribed verbally.Keystone Connections:A1.1.1.4 Use estimation strategies in problem solving situations.A1.1.2.1 Write, solve, and/or graph linear equations using various methods.A1.1.3.1 Write, solve, and/or graph linear inequalities using various methods.A1.2.1.1 Analyze and/or use patterns or relations.A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables.PA State Standards2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) andcharacteristics of linear functions.Student Objectives: Writing and evaluating algebraic expressions Using expressions to write equations and inequalities Representing functions as verbal rules, equations, tables and graphsMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets BGrade 8Intro to AlgebraLast ModifiedApril 24, 2012

Study Guides (optional) Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIES Evaluate Expressions Apply Order of Operations Write Expressions Write Equations and Inequalities Use a Problem Solving Plan Represent Functions as Rules and Tables Represent Functions as GraphsASSIGNMENTS Lesson Practice Sheets B Associated Chapter exercisesASSESSMENTSHomework will be assigned on a daily basis. Grades will be based on quizzes and tests.Additionally, teachers may use homework, group activities, and/or projects for gradingpurposes. The Radnor Middle School grading system and scale will be used to determine lettergrades. Lesson Assessment/Quizzes Chapter TestsTerminologyVariableAlgebraic expressionEvaluate and algebraic expressionPowerExponentBaseOrder of operationsVerbal modelRateUnit rateEquationOpen sentenceSolution of an equation or ependent variableDependant variableMedia, Technology, Web Resources McDougal Littell Algebra I Easy Planner DVD ROM McDougal Littell Algebra I Power Presentations DVD ROM McDougal Littell Classzone.com resourcesGrade 8Intro to AlgebraLast ModifiedApril 24, 2012

Teacher developed smart-board documentsScientific Calculatorwww.learningupgrade.comGrade 8Intro to AlgebraLast ModifiedApril 24, 2012

MARKING PERIOD: 1/2Unit: Chapter 2 – Properties of Real NumbersCommon Core Standards Use rational approximations of irrational numbers to compare the size of irrationalnumbers, locate them approximately on a number line diagram, and estimate thevalue of expressions (e.g., π2). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how tocontinue on to get better approximations Apply and extend previous understandings of addition and subtraction to add andsubtract rational numbers; represent addition and subtraction on a horizontal orvertical number line diagramKeystone Connections:A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals,percents, square roots, and exponents).PA State StandardsStudent Objectives: Performing operations with real numbers Applying properties of real numbers Classifying and reasoning with real numbersMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets B Study Guides (optional) Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIES Use Integers and Rational Numbers Add Real Numbers Subtract Real Numbers Multiply Real Numbers Apply the Distributive Property Divide Real NumbersGrade 8Intro to AlgebraLast ModifiedApril 24, 2012

Find Square Roots and Compare Real NumbersASSIGNMENTS Lesson Practice Sheets B Associated Chapter exercisesASSESSMENTSHomework will be assigned on a daily basis. Grades will be based on quizzes and tests.Additionally, teachers may use homework, group activities, and/or projects for gradingpurposes. The Radnor Middle School grading system and scale will be used to determine lettergrades. Lesson Assessment/Quizzes Chapter TestsTerminologyWhole numbersIntegersPositive IntegerNegative integerRational numberOppositesAbsolute valueConditional statementIf-then statementCounter exampleAdditive identityAdditive inverseMultiplicative identityEquivalent expressionsDistributive propertyTermCoefficientConstant termLike termsMultiplicative inverseSquare rootRadicandPerfect squareIrrational numberReal numbersMedia, Technology, Web Resources McDougal Littell Algebra I Easy Planner DVD ROM McDougal Littell Algebra I Power Presentations DVD ROM McDougal Littell Classzone.com resources Teacher developed smart-board documents Scientific Calculator www.learningupgrade.comGrade 8Intro to AlgebraLast ModifiedApril 24, 2012

MARKING PERIOD: 2Unit: Chapter 3 – Solving Linear EquationsCommon Core Standards Give examples of linear equations in one variable with one solution, infinitely manysolutions, or no solutions. Show which of these possibilities is the case by successivelytransforming the given equation into simpler forms, until an equivalent equation ofthe form x a, a a, or a b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whosesolutions require expanding expressions using the distributive property and collectinglike terms. Rearrange formulas to highlight a quantity of interest, using the same reasoning as insolving equations. For example, rearrange Ohm’s law V IR to highlight resistance R. Solve linear equations and inequalities in one variable, including equations withcoefficients represented by letters.Keystone Connections:A1.1.2.1 Write, solve, and/or graph linear equations using various methods.PA State StandardsStudent Objectives: Solving equations in one variable Solving proportion and percent problems Rewriting equations in two or more variablesMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets B Study Guides (optional) Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIES Solve One‐Step Equations Solve Two‐Step Equations Solve Multi‐Step Equations Solve Equations with Variables on Both SidesGrade 8Intro to AlgebraLast ModifiedApril 24, 2012

Write Ratios and ProportionsSolve Proportions Using Cross ProductsSolve Percent ProblemsRewrite Equations and FormulasASSIGNMENTS Lesson Practice Sheets B Associated Chapter exercisesASSESSMENTSHomework will be assigned on a daily basis. Grades will be based on quizzes and tests.Additionally, teachers may use homework, group activities, and/or projects for gradingpurposes. The Radnor Middle School grading system and scale will be used to determine lettergrades. Lesson Assessment/Quizzes Chapter TestsTerminologyInverse operations, equivalent equations, identity, ratio, proportion, cross product, scaledrawing, scale model, scale, literal equationMedia, Technology, Web Resources McDougal Littell Algebra I Easy Planner DVD ROM McDougal Littell Algebra I Power Presentations DVD ROM McDougal Littell Classzone.com resources Teacher developed smart-board documents Scientific Calculator www.learningupgrade.comGrade 8Intro to AlgebraLast ModifiedApril 24, 2012

MARKING PERIOD: 3Unit: Chapter 4 – Graphing Linear Equations and FunctionsCommon Core Standards Compare properties of two functions each represented in a different way(algebraically, graphically, numerically in tables, or by verbal descriptions). Forexample, given a linear function represented by a table of values and a linear functionrepresented by an algebraic expression, determine which function has the greater rateof change. Interpret the equation y mx b as defining a linear function, whose graph is astraight line; give examples of functions that are not linear. For example, the functionA s2 giving the area of a square as a function of its side length is not linear becauseits graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Construct a function to model a linear relationship between two quantities.Determine the rate of change and initial value of the function from a description of arelationship or from two (x, y) values, including reading these from a table or from agraph. Interpret the rate of change and initial value of a linear function in terms of thesituation it models, and in terms of its graph or a table of values. Describe qualitatively the functional relationship between two quantities by analyzinga graph (e.g., where the function is increasing or decreasing, linear or nonlinear).Sketch a graph that exhibits the qualitative features of a function that has beendescribed verbally.Keystone Connections:A1.2.1.1 Analyze and/or use patterns or relations.A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables.A1.2.2.1 Describe, compute, and/or use the rate of change (slope) of a line.PA State Standards2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) andcharacteristics of linear functions.2.11.A1.B. Describe rates of change as modeled by linear equations.Student Objectives: Graphing linear equations and functions using a variety of methods Recognizing how linear equations and functions affect their graphs Using graphs of linear equations and functions to solve real world problemsMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets B Study Guides (optional)Grade 8Intro to AlgebraLast ModifiedApril 24, 2012