radnor high school · 2012. 9. 3. · mcdougal littell algebra i power presentations dvd rom...
TRANSCRIPT
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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.
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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: 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 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.‐ 2007 ed.
Lesson Practice Sheets B
MAJOR UNITS OF STUDY
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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
Lesson Practice Sheets B
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
Grade 8 Intro to Algebra Last Modified
April 24, 2012
Teacher developed smart-board documents
Scientific Calculator
www.learningupgrade.com
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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: A1.1.1.1 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.‐ 2007 ed.
Lesson Practice Sheets B
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
Grade 8 Intro to Algebra Last Modified
April 24, 2012
Find Square Roots and Compare Real Numbers ASSIGNMENTS
Lesson Practice Sheets B
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
www.learningupgrade.com
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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: A1.1.2.1 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.‐ 2007 ed.
Lesson Practice Sheets B
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
Grade 8 Intro to Algebra Last Modified
April 24, 2012
Write Ratios and Proportions
Solve Proportions Using Cross Products
Solve Percent Problems
Rewrite Equations and Formulas ASSIGNMENTS
Lesson Practice Sheets B
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
www.learningupgrade.com
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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: 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 Standards 2.8.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 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.‐ 2007 ed.
Lesson Practice Sheets B
Study Guides (optional)
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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
Lesson Practice Sheets B
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
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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
www.learningupgrade.com
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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: A1.2.2.2 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:
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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.‐ 2007 ed.
Lesson Practice Sheets B
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
Lesson Practice Sheets B
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
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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
www.learningupgrade.com
Grade 8 Intro to Algebra Last Modified
April 24, 2012
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 half-planes.
Keystone Connections: A1.1.3.1 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.‐ 2007 ed.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
Solve Inequalities Using Addition and Subtraction
Solve Inequalities Using Multiplication and Division
Grade 8 Intro to Algebra Last Modified
April 24, 2012
Solve Multi‐Step Inequalities
Solve Compound Inequalities
Solve Absolute Value Equations
Solve Absolute Value Inequalities
Graph Linear Inequalities in Two Variables ASSIGNMENTS
Lesson Practice Sheets B
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
www.learningupgrade.com