Radnor Middle School Course Overview. Math Introduction to Algebra 1. Prerequisite: Pre-Algebra, Course 3 Grade: 8

Transcription

1 Radnor Middle School Course Overview Math Introduction to Algebra 1 General Information Credits: N/A Length: Full Year Weighted: N/A Format: Meets Daily Prerequisite: Pre-Algebra, Course 3 Grade: 8 I. Course Description The 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.

2 MAJOR UNITS OF STUDY MARKING PERIOD: 1 Unit: Chapter 1 Expressions, Equations, and Functions Common 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. 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: A Use estimation strategies in problem solving situations. A Write, solve, and/or graph linear equations using various methods. A Write, solve, and/or graph linear inequalities using various methods. A Analyze and/or use patterns or relations. A Interpret and/or use linear functions and their equations, graphs, or tables. PA State Standards 2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) and characteristics 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 graphs Materials &Texts Algebra 1 Larson series McDougal, Littell & Co ed.

3 Study Guides (optional) Lesson Note Taking Guides (optional) Activities, Assignments, & Assessments ACTIVITIES 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 Graphs ASSIGNMENTS Associated Chapter exercises ASSESSMENTS Homework 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/Quizzes Chapter Tests Terminology Variable Algebraic expression Evaluate and algebraic expression Power Exponent Base Order of operations Verbal model Rate Unit rate Equation Open sentence Solution of an equation or inequality Formula Function Input Output Domain Range Independent variable Dependant variable Media, Technology, Web Resources McDougal Littell Algebra I Easy Planner DVD ROM McDougal Littell Algebra I Power Presentations DVD ROM McDougal Littell Classzone.com resources

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5 MARKING PERIOD: 1/2 Unit: Chapter 2 Properties of Real Numbers Common Core Standards Use 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 approximations Apply 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 diagram Keystone Connections: A Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents). PA State Standards Student Objectives: Performing operations with real numbers Applying properties of real numbers Classifying and reasoning with real numbers Materials &Texts Algebra 1 Larson series McDougal, Littell & Co ed. Study Guides (optional) Lesson Note Taking Guides (optional) Activities, Assignments, & Assessments ACTIVITIES Use Integers and Rational Numbers Add Real Numbers Subtract Real Numbers Multiply Real Numbers Apply the Distributive Property Divide Real Numbers

6 Find Square Roots and Compare Real Numbers ASSIGNMENTS Associated Chapter exercises ASSESSMENTS Homework 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/Quizzes Chapter Tests Terminology Whole numbers Integers Positive Integer Negative integer Rational number Opposites Absolute value Conditional statement If-then statement Counter example Additive identity Additive inverse Multiplicative identity Equivalent expressions Distributive property Term Coefficient Constant term Like terms Multiplicative inverse Square root Radicand Perfect square Irrational number Real numbers Media, 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

7 MARKING PERIOD: 2 Unit: Chapter 3 Solving Linear Equations Common Core Standards Give 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: A Write, solve, and/or graph linear equations using various methods. PA State Standards Student Objectives: Solving equations in one variable Solving proportion and percent problems Rewriting equations in two or more variables Materials &Texts Algebra 1 Larson series McDougal, Littell & Co ed. Study Guides (optional) Lesson Note Taking Guides (optional) Activities, Assignments, & Assessments ACTIVITIES Solve One Step Equations Solve Two Step Equations Solve Multi Step Equations Solve Equations with Variables on Both Sides

8 Write Ratios and Proportions Solve Proportions Using Cross Products Solve Percent Problems Rewrite Equations and Formulas ASSIGNMENTS Associated Chapter exercises ASSESSMENTS Homework 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/Quizzes Chapter Tests Terminology Inverse operations, equivalent equations, identity, ratio, proportion, cross product, scale drawing, scale model, scale, literal equation Media, 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

9 MARKING PERIOD: 3 Unit: Chapter 4 Graphing Linear Equations and Functions Common Core Standards Compare 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: A Analyze and/or use patterns or relations. A Interpret and/or use linear functions and their equations, graphs, or tables. A Describe, compute, and/or use the rate of change (slope) of a line. PA State Standards 2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) and characteristics of linear functions 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 problems Materials &Texts Algebra 1 Larson series McDougal, Littell & Co ed. Study Guides (optional)

10 Lesson Note Taking Guides (optional) Activities, Assignments, & Assessments ACTIVITIES Plot 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 ASSIGNMENTS Associated Chapter exercises ASSESSMENTS Homework 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/Quizzes Chapter Tests Terminology Quadrant solution of an equation in two variables graph of an equation in two variables linear equation standard form of a linear equation linear function x-intercept y-intercept slope rate of change slope-intercept form parallel direct variation constant of variation function notation family of functions parent linear function

11 Media, 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

12 MARKING PERIOD: 3/4 Unit: Chapter 5 Writing Linear Equations Common Core Standards 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. 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: A Analyze and/or interpret data on a scatter plot. PA State Standards 2.6.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:

13 Writing linear equations in a variety of forms Using linear models to solve problems Modeling data with a line of fit Materials &Texts Algebra 1 Larson series McDougal, Littell & Co ed. Study Guides (optional) Lesson Note Taking Guides (optional) Activities, Assignments, & Assessments ACTIVITIES Write 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 ASSIGNMENTS Associated Chapter exercises ASSESSMENTS Homework 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/Quizzes Chapter Tests Terminology Point-slope form Converse Perpendicular scatter plot positive correlation negative correlation relatively no correlation line of fit best fitting line linear regression interpolation extrapolation zero of a function

14 Media, 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

15 MARKING PERIOD: 4 Unit: Chapter 6 Solving and Graphing Linear Inequalities Common Core Standards Graph 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 halfplanes. Keystone Connections: A Write, solve, and/or graph linear inequalities using various methods. PA State Standards 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. Student Objectives: Applying properties of inequalities Using statements with and/or Graphing inequalities Materials &Texts Algebra 1 Larson series McDougal, Littell & Co ed. Study Guides (optional) Lesson Note Taking Guides (optional) Activities, Assignments, & Assessments ACTIVITIES Solve Inequalities Using Addition and Subtraction Solve Inequalities Using Multiplication and Division

16 Solve Multi Step Inequalities Solve Compound Inequalities Solve Absolute Value Equations Solve Absolute Value Inequalities Graph Linear Inequalities in Two Variables ASSIGNMENTS Associated Chapter exercises ASSESSMENTS Homework 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/Quizzes Chapter Tests Terminology Graph of an inequality equivalent inequality compound inequality absolute value equation absolute deviation linear inequality in two variables solution of an inequality in two variables graph of an inequality in two variables half-plane Media, 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