# Radnor High School - Radnor Township School District

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5121910-448945-21590-375285Radnor Middle SchoolCourse OverviewMathIntroduction to Algebra 1General InformationCredits: N/A Length: Full YearWeighted: N/A Format: Meets DailyPrerequisite: Pre-Algebra, Course 3 Grade: 8I. Course DescriptionThe goal of this course is to provide students with a foundation in the algebraic strand of mathematics through experiences with: understanding patterns, relations, and functions; representing and analyzing mathematical situations and structures using algebraic symbols; 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 a process for logical thought, and as a field of study. This approach to Algebra 1 is organized around families of functions, with special emphasis on linear functions. As students learn about each family of functions, they will learn to represent them in multiple ways: as verbal descriptions, equations, tables, and graphs. They will also learn to model real‐world situations using functions in order to solve problems arising from those situations.MAJOR UNITS OF STUDYMARKING PERIOD: 1Unit: Chapter 1 – Expressions, Equations, and FunctionsCommon Core StandardsInterpret 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. The graph of a function is the set of ordered pairs consisting of an input and the corresponding 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 a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.Describe qualitatively the functional relationship between two quantities by analyzing a 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 been described 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) and characteristics of linear functions.Student Objectives:Writing and evaluating algebraic expressionsUsing expressions to write equations and inequalitiesRepresenting functions as verbal rules, equations, tables and graphsMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets BStudy Guides (optional)Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIESEvaluate 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 GraphsASSIGNMENTSLesson Practice Sheets BAssociated 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 grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades. Lesson Assessment/QuizzesChapter TestsTerminologyVariable Algebraic expressionEvaluate and algebraic expression Power ExponentBaseOrder of operationsVerbal modelRateUnit rateEquationOpen sentenceSolution of an equation or inequalityFormulaFunctionInputOutputDomainRangeIndependent variableDependant variableMedia, Technology, Web ResourcesMcDougal Littell Algebra I Easy Planner DVD ROMMcDougal Littell Algebra I Power Presentations DVD ROMMcDougal Littell resourcesTeacher developed smart-board documentsScientific CalculatorMARKING PERIOD: 1/2Unit: Chapter 2 – Properties of Real NumbersCommon Core StandardsUse rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value 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 to continue on to get better approximationsApply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical 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 numbersApplying properties of real numbersClassifying and reasoning with real numbersMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets BStudy Guides (optional)Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIESUse Integers and Rational Numbers Add Real Numbers Subtract Real Numbers Multiply Real Numbers Apply the Distributive Property Divide Real Numbers Find Square Roots and Compare Real NumbersASSIGNMENTSLesson Practice Sheets BAssociated 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 grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades. Lesson Assessment/QuizzesChapter TestsTerminologyWhole numbersIntegersPositive IntegerNegative integerRational numberOppositesAbsolute valueConditional statementIf-then statementCounter exampleAdditive identityAdditive inverseMultiplicative identityEquivalent expressionsDistributive propertyTermCoefficientConstant termLike termsMultiplicative inverseSquare rootRadicandPerfect squareIrrational numberReal numbersMedia, Technology, Web ResourcesMcDougal Littell Algebra I Easy Planner DVD ROMMcDougal Littell Algebra I Power Presentations DVD ROMMcDougal Littell resourcesTeacher developed smart-board documentsScientific CalculatorMARKING PERIOD: 2Unit: Chapter 3 – Solving Linear EquationsCommon Core StandardsGive examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the 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 whose solutions require expanding expressions using the distributive property and collecting like terms.Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.Solve linear equations and inequalities in one variable, including equations with coefficients 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 variableSolving proportion and percent problemsRewriting equations in two or more variablesMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets BStudy Guides (optional)Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIESSolve One‐Step Equations Solve Two‐Step Equations Solve Multi‐Step Equations Solve Equations with Variables on Both Sides Write Ratios and Proportions Solve Proportions Using Cross Products Solve Percent Problems Rewrite Equations and Formulas ASSIGNMENTSLesson Practice Sheets BAssociated 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 grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades. Lesson Assessment/QuizzesChapter TestsTerminologyInverse operations, equivalent equations, identity, ratio, proportion, cross product, scale drawing, scale model, scale, literal equationMedia, Technology, Web ResourcesMcDougal Littell Algebra I Easy Planner DVD ROMMcDougal Littell Algebra I Power Presentations DVD ROMMcDougal Littell resourcesTeacher developed smart-board documentsScientific CalculatorMARKING PERIOD: 3Unit: Chapter 4 – Graphing Linear Equations and Functions Common Core StandardsCompare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its 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 a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.Describe qualitatively the functional relationship between two quantities by analyzing a 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 been described 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) and characteristics 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 methodsRecognizing how linear equations and functions affect their graphsUsing graphs of linear equations and functions to solve real world problemsMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets BStudy Guides (optional)Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIESPlot Points in a Coordinate Plane Graph Linear Equations Graph Using Intercepts Find Slope and Rate of Change Graph Using Slope‐Intercept Form Model Direct Variations Graph Linear Functions ASSIGNMENTSLesson Practice Sheets BAssociated 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 grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades. Lesson Assessment/QuizzesChapter TestsTerminologyQuadrantsolution of an equation in two variablesgraph of an equation in two variableslinear equationstandard form of a linear equationlinear function x-intercepty-interceptsloperate of changeslope-intercept formparalleldirect variationconstant of variationfunction notationfamily of functionsparent linear functionMedia, Technology, Web ResourcesMcDougal Littell Algebra I Easy Planner DVD ROMMcDougal Littell Algebra I Power Presentations DVD ROMMcDougal Littell resourcesTeacher developed smart-board documentsScientific CalculatorMARKING PERIOD: 3/4Unit: Chapter 5 – Writing Linear EquationsCommon Core StandardsDescribe qualitatively the functional relationship between two quantities by analyzing a 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 been described verbally.Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.Keystone Connections:A1.2.2.2 Analyze and/or interpret data on a scatter plot.PA State Standards2.6.A1.C. Select or calculate the appropriate measure of central tendency, calculate and apply the interquartile range for one-variable data, and construct a line of best fit and calculate its equation for two-variable data.2.6.A1.E. Make predictions based on lines of best fit or draw conclusions on the value of a variable in a population based on the results of a sample.2.8.A1.B. Evaluate and simplify not understood algebraic expressions, for example: sums of polynomials, products/quotients of exponential terms and product of a binomial times a trinomial; and solve and graph linear equations and inequalities.2.8.A1.E. Use combinations of symbols and numbers to create expressions, equations, and inequalities in two or more variables, systems of equations, and inequalities, and functional relationships that model problem situations.2.8.A1.F. Interpret the results of solving equations, inequalities, systems of equations, and systems of inequalities in the context of the situation that motivated the model.2.9.A1.A. Use algebraic techniques to determine if two lines are parallel and / or perpendicular.Student Objectives:Writing linear equations in a variety of formsUsing linear models to solve problemsModeling data with a line of fitMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets BStudy Guides (optional)Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIESWrite Linear Equations in Slope‐Intercept Form Use Linear Equations in Slope‐Intercept Form Write Linear Equations in Point‐Slope Form Write Linear Equations in Standard Form Write Equations of Parallel and Perpendicular Lines Fit a Line to Data Predict with Linear Models ASSIGNMENTSLesson Practice Sheets BAssociated 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 grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades. Lesson Assessment/QuizzesChapter TestsTerminologyPoint-slope formConversePerpendicularscatter plotpositive correlationnegative correlationrelatively no correlationline of fitbest fitting linelinear regressioninterpolationextrapolationzero of a functionMedia, Technology, Web ResourcesMcDougal Littell Algebra I Easy Planner DVD ROMMcDougal Littell Algebra I Power Presentations DVD ROMMcDougal Littell resourcesTeacher developed smart-board documentsScientific CalculatorMARKING PERIOD: 4Unit: Chapter 6 – Solving and Graphing Linear Inequalities Common Core StandardsGraph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.Keystone Connections:A1.1.3.1 Write, solve, and/or graph linear inequalities using various methods.PA State Standards2.8.A1.B. Evaluate and simplify not understood algebraic expressions, for example: sums of polynomials, products/quotients of exponential terms and product of a binomial times a trinomial; and solve and graph linear equations and inequalities.2.8.A1.E. Use combinations of symbols and numbers to create expressions, equations, and inequalities in two or more variables, systems of equations, and inequalities, and functional relationships that model problem situations.2.8.A1.F. Interpret the results of solving equations, inequalities, systems of equations, and systems of inequalities in the context of the situation that motivated the model.Student Objectives:Applying properties of inequalitiesUsing statements with and/orGraphing inequalitiesMaterials &TextsAlgebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed. Lesson Practice Sheets BStudy Guides (optional)Lesson Note Taking Guides (optional)Activities, Assignments, & AssessmentsACTIVITIESSolve Inequalities Using Addition and SubtractionSolve Inequalities Using Multiplication and DivisionSolve Multi‐Step InequalitiesSolve Compound InequalitiesSolve Absolute Value EquationsSolve Absolute Value Inequalities Graph Linear Inequalities in Two Variables ASSIGNMENTSLesson Practice Sheets BAssociated 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 grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades. Lesson Assessment/QuizzesChapter TestsTerminologyGraph of an inequalityequivalent inequalitycompound inequalityabsolute value equationabsolute deviationlinear inequality in two variablessolution of an inequality in two variablesgraph of an inequality in two variableshalf-planeMedia, Technology, Web ResourcesMcDougal Littell Algebra I Easy Planner DVD ROMMcDougal Littell Algebra I Power Presentations DVD ROMMcDougal Littell resourcesTeacher developed smart-board documentsScientific Calculator ................
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