Radnor Middle School
Course Overview
Math
Introduction to Algebra 1
General Information
Credits: N/A
Weighted: N/A
Prerequisite: Pre-Algebra, Course 3
Length: Full Year
Format: Meets Daily
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
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:
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
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
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
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
Grade 8
linear regression
interpolation
extrapolation
zero of a function
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 halfplanes.
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
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



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
Grade 8
Intro to Algebra
Last Modified
April 24, 2012