Download Whitman-Hanson Regional High School provides all students with a

Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective,
concerned citizens and contributing members of the global community.
Course Number
405/406/407
Title Algebra I (A, B, C)
Grade 9
# of Days 180
Course Description
This is the essential foundation for all following Mathematics courses and for the bulk of preparation for the
Grade 10 MCAS test. Algebra I will run the entire school year. Topics will include variables, solving equations
and inequalities, linear sentences, graphing and systems. Symbolism is used to express abstract ideas. Real life
applications will be included for all topics. This course addresses Whitman-Hanson Student Learning
Expectations 1-6.
Instructional Strategies
Instructional Strategies include but may not be limited to the following:
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Student Learning
Expectations
Whole class instruction
Individual work: homework, classwork, assessments
Group work: activities, problem solving
Experiments, demonstrations, investigations
Video presentations
Use of technology (graphing calculators and computers)
Projects
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Read, write and communicate effectively.
Utilize technologies appropriately and effectively.
Apply critical thinking skills.
Explore and express ideas creatively.
Participate in learning both individually and collaboratively.
Demonstrate personal, social, and civic responsibility.
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Part A Major Concepts
Tools of Algebra - Chapter 1
Variables
Topics
Student Expectations
Definition of Variable
Use of Variables in Expressions and Equations
Identify variables in expressions and equations
Translate verbal descriptions to algebraic expressions
Write algebraic expressions from tabular data
Order of Operations
Simplifying Expressions
Definition of Exponents
Evaluating Expressions with Parentheses &
Exponents
Apply Order of Operations to reduce to simplest form
Translate between exponential and repeated multiplication forms
Substitute and simplify expressions with parentheses and exponents
Exploring Real Numbers
Definitions of Number Sets
Identify or differentiate between naturals, wholes, integers, rationals,
irrationals and reals
Compare the values of two expressions
Use <, >, ≤, ≥, =, ≠ appropriately when comparing two real numbers
Define absolute value as the distance from zero on a number line
Simplify an absolute value expression ex: |-4| = 4
Inequality
Absolute Value
Operations on Real Numbers
Addition and Subtraction
Know and apply the identity element for addition and subtraction is zero
Find the additive identity (opposite) of a number
State the Inverse Property of Addition ex: a + -a = 0
Use the number line model to add or subtract real numbers
Use the tile model to add or subtract real numbers
Know and apply the identity element for multiplication and division is one
Find the multiplicative inverse (reciprocal) of a number
State the Inverse Property of Multiplication ex: a • 1/a = 1
Know and apply the Multiplication Property of 0 ex: a • 0 = 0
Know and apply the Multiplication Property of -1 ex: a • -1 = -a
Multiply and divide real numbers
Define a matrix by the number of rows and columns
Determine whether two matrices can be added or subtracted
Perform scalar multiplication on a matrix
Multiplication and Division
Matrices
Properties of Real Numbers
The Distributive Property
Use the Distributive Property to simplify expressions
Define and use coefficient, constant, term and like term appropriately
Identify and combine like terms (similar terms) with multiply variables and
exponents
Know and apply the Commutative Property of Addition ex: a + b = b + a
Know and apply the Commutative Property of Multiplication ex: a • b = b • a
Commutative Property
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Coordinate Plane Graphing
Major Concepts
Solving Equations - Chapter 2
One Step Equations
Associative Property
Know and apply the Associative Property of Addition
ex: (a + b) + c = a + (b + c)
Know and apply the Associative Property of Multiplication
ex: (a • b) • c = a • (b • c)
Definitions
Graphing
Scatter Plots
Identify x and y axes, the quadrants and the origin
Plot ordered pairs (coordinates)
Create appropriate horizontal and vertical scales to plot real data points
Determine positive, negative or no correlation of the scatter plot
Sketch the trend line (line of best fit) for correlated data
Student Expectations
Topics
Properties of Equality
Name and apply the addition, subtraction, multiplication and division
properties to solve equations
Determine the inverse operation for a given equation
Recognize division, and multiplication by the reciprocal, as equivalent steps
Use inverse operations to solve equations using real numbers
Inverse Operations
Two-Step Equations
Isolate the Variable Term, then Isolate the Variable
Use Algebra tiles to solve two-step equations
Use inverse operations in the correct order to solve equations using real
numbers
Multi-Step Equations
Simplifying before Solving
Combine like terms before solving the equation
Use the Distributive Property to eliminate grouping symbols before solving
Multiply to eliminate fractions from all terms before solving
Multiply to eliminate decimals from all terms before solving
Variables on Both Sides
Equations with a Single Solution
Identities-Equations with Many Solutions
Equations with No Solution
Solving Equations with Matrices on Both Sides
Combine like terms: variable terms on one side, numbers on the other
Recognize solutions of identities as 5=5 or any a=a
Recognize equations with no solution when 4 = 8 or any a = b
Solve equations made from corresponding elements from each matrix
Equations and Problem
Solving
Defining One Variable in Terms of Another
Define a variable and use it to write other algebra expressions for parts in the
problem
Write and solve equations using several terms and only one variable
Define a variable and increase it for consecutive integers, consecutive odd o
even integers, consecutive multiples
Make a table to organize data for rate, time and distance and use the table to
write an equation
Consecutive Number Problems
Distance-Rate-Time Problems (Uniform Motion)
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Formulas
Transforming Literal Equations
Use properties of equality to rewrite a literal equation in terms of a different
variable
Measures of Central Tendency
Mean, Median, Mode and Range
Differentiate between mean, median and mode
Calculate the mean, median, mode and range
Create a one or two-sided stem and leaf plot from a set of data
Determine the mean, median, mode and range from a stem and leaf plot
Student Expectations
Stem and Leaf Plots
Major Concepts
Solving Inequalities - Chapter
3
Inequalities and their Graphs
Solving Inequalities Using
Addition and Subtraction
Solving Inequalities Using
Multiplication and Division
Topics
Finding Solutions
Determine a solution to an inequality by inspection or evaluation
Graph the solution to an inequality on a number line with open/closed circles
and arrows
Addition Property of Inequality
Use the Addition Property of Inequality to solve inequalities
Subtraction Property of Inequality
Use the Subtraction Property of Inequality to solve inequalities
Multiplication Property of Inequality for c>0
Apply the Multiplication Property of Inequality for c>0 by multiplying both
sides of the inequality by a positive number
Apply the Multiplication Property of Inequality for c<0 by multiplying both
sides of the inequality by a negative number and reversing the inequality sign
Multiplication Property of Inequality for c<0
Division Property of Inequality
Apply the Division Property of Inequality for c>0 and c<0 by dividing both
sides of the inequality by c and leaving the inequality alone or reversing it
respectively.
Solving Multi-Step Inequalities
Simplifying before Solving
Combine like terms before solving the equation
Use the Distributive Property to eliminate grouping symbols before solving
Collect variables on one side of the inequality and numbers on the other
before solving
Compound Inequalities
Writing a Compound Inequality
Write a compound inequality from a number line graph of one segment with
two endpoints or two sections with arrows heading in opposite directions
Know that solutions to the inequality must make both inequalities true
Know that the solution on the graph will be one segment
Know that solutions to the inequality can make either inequality true
Know that the solution on the graph will be two rays heading in opposite
directions
Compound Inequalities Joined by "and"
Compound Inequalities Joined by "or"
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Absolute Value Equations and
Inequalities
Solving Absolute Value Equations
Calculate two correct answers to an absolute value equation (|a| = b) by
creating two equations joined by "or" ( a = b or a = -b )
Rewrite and absolute value inequality using "and" with < or ≤ and using "or"
with > and ≥
Calculate two correct answers to an absolute value inequality by creating two
equations joined by "or" or "and"
Given |a| > b use a > b or a < -b
Given |a| < b use a < b and a > -b leading to -b < a < b
Solving Absolute Value Inequalities
Applying Absolute Value in Quality Control situations
Major Concepts
Topics
Solving and Applying Proportions - Chapter 4
Ratio and Proportion
Definitions
Unit Analysis
Solving Proportions
Write an absolute value inequality to describe an acceptable tolerance
Student Expectations
Define terms such as: ratio, proportion, unit analysis, unit rate, means and
extremes of a proportion, cross products
Find the unit rate
Convert from one set of units to another by multiplying by conversion factors
Solve a proportion by cross multiplying and setting cross products equal
Solve a proportion by multiplying a binomial by a monomial
Proportions and Similar
Figures
Similar Figures
Define similar figures as those with the same shape but different size, the
angle measures are equal and the sides are proportional
Use the ~ symbol for similar figures ex: Δ ABC ~ Δ DEF
Use similar figures to determine indirect measurement
Use scale and a drawing to determine actual size
Proportions and Percent
Equations
Applying Proportions to Percent Problems
Use part/whole = n/100 to solve percent problems
Change the % to a #/100 to solve part/whole problems
Translate verbal descriptions to algebraic percent equations and solve
Solve percent equations with percents greater than 100% or less than 1%
Use fractional quantities to estimate percents ex: 32% ≈ ⅓ 32% of 18 ≈ 6
Writing Percent Equations
Estimating with Percents
Percent of Change
Percent of Change
Calculate the percent increase
Calculate the percent decrease
Determine the greatest possible error or a measuring unit
Calculate the percent error
Applying Ratios to Probability
Definitions
Define: probability, outcome, sample space, event, theoretical probability,
complement of an event, experimental probability, P(A), P(not A)
Change decimal results to percentage results when calculating probability
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Theoretical Probability
Determine the theoretical probability by finding the number of possible
favorable outcomes / the sample space
Determine the complement of an event ex: P(not event) = 1 - P(event)
Determine the experimental probability by counting the number of times a
favorable event happens / the number of times the experiment was done
Explain that experimental probability will be closer to theoretical probability
when the amount of data is large
Experimental Probability
Law of Large Numbers
Probability of Compound
Events
Independent Events
Define independent events as events that do not influence one another ex:
drawing cards with replacement
Apply P(A and B) = P(A) • P(B) to determine probability
Define dependent events as events that influence one another because the
occurrence of one event affects the probability of the other ex: drawing
cards without replacement
Dependent Events
Part B Major Concepts
Graphs and Functions - Chapter 5
Relating Graphs to Events
Story Graphs
Relations and Functions
Apply P(A then B) = P(A) • P(B after A) to determine probability
Student Expectations
Topics
Using labels and the horizontal and vertical scale, describe the changes in a
graph with a story
Given a story, sketch a graph with appropriate changes for each part of the
story
Definitions
Define relation, domain, range, function, function rule, function notation,
vertical line test
Determine whether a relation is a function by the vertical line test
Determine whether a relation is a function by examining tables and mapping
diagrams
Evaluate a function by substituting and solving for f(n)
Find the range given the domain
Functions
Function Rules, Tables and
Graphs
Independent vs. Dependent Variables
Differentiate between independent and dependent variables as input and
output
Differentiate between independent and dependent variables as x and y
values
Differentiate between independent and dependent variables on the horizonta
and vertical axes
Show an algebraic, graphic, numeric and verbal display of a function ex: f(x
= 2x + 4, a linear graph, a table of values and a verbal description for each
function
The Rule of Four
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Writing a Function Rule
Writing a Rule from a Table
Writing a Rule from a Verbal Description
Write a rule from a table that is a linear or a simple quadratic (f(x) = x^2 + c)
Write a rule from a verbal description that is a linear or a simple quadratic
(f(x) = x^2 + c)
Write a rule from a graph that is a linear or simple quadratic (f(x) = x^2 + c)
Writing a Rule from a Graph
Direct Variation
Definitions
Direct Variation Equation
Define direct variation, constant of variation
Determine if an equation is a direct variation in the form y = kx
Find the constant of variation (k)
Write the equation of direct variation given a point
Use a table to determine the constant of variation k = y/x
Describing Number Patterns
Definitions
Define inductive reasoning, conjecture, sequence, term, arithmetic sequence
common difference, input, output
Use inductive reasoning to extend number patterns to the next 4 terms
Use the common difference in A(n) = a + (n - 1) d to extend the pattern to
the nth term of an arithmetic sequence
Student Expectations
Extend Number Patterns
Arithmetic Sequences
Major Concepts
Linear Equations and Their Graphs - Chapter 6
Rate of Change and Slope
Definitions
Topics
Define rate of change, slope, positive slope, negative slope, zero slope,
undefined slope
Find the rate of change using a table
Find the rate of change using two points on a graph
Find the slope using two given points or two points on a graph
Find the slope of a horizontal line using two points or memorization
State the slope of a vertical line is undefined
Calculating Slope
Slope-Intercept Form
Definitions
y-intercept
Slope-Intercept Form
Define y-intercept, slope-intercept form
Find the y-intercept by looking at a graph
Find the slope and y-intercept by looking at the equation y = mx + b
Write an equation in slope-intercept form given the slope and the y-intercept
Write an equation in slope-intercept form from a graph
Graph an equation in slope-intercept form
Standard Form
Definitions
x and y-intercepts
Define standard form of a linear equation, x-intercept
Find x-intercept by making y=0 and solving for x
Find y-intercept by making x=0 and solving for y
Graph a line using the x and y-intercepts
Graph a horizontal line by keeping the y value constant
Graph a vertical line by keeping the x value constant
Transform an equation in slope-intercept form to standard form through
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algebra
Point-Slope From and Writing
Linear Equations
Parallel & Perpendicular Lines
Definitions
Define point-slope form
Point-Slope Form
Graph a line in point-slope form
Write the equation of a line in point-slope form given a point and a slope
Write the equation of a line in point-slope form given two points
Write the equation of a line in point-slope form given a table of data
Definitions
Define parallel lines, perpendicular lines, negative reciprocal slope, right
angle
Determine whether two lines are parallel given any form of the linear
equations
Write the equation of a line through a given point, parallel to another line
Find the slope of a line perpendicular to a given line
Write the equation of a line through a given point, perpendicular to a given
line
Parallel Lines
Perpendicular Lines
Scatter Plots & Equations of
Lines
Absolute Value Equations
Definitions
Define line of best fit, correlation coefficient
Trend Lines or Lines of Best Fit
Draw a trend line (line of best fit) from a scatter plot
Use points on the trend line to estimate the equation of the line
Use a graphing calculator to find the equation of a line of best fit
Use a graphing calculator to find the correlation coefficient, r
Definitions
Absolute Value Equations
Define absolute value equation, translation
Graph the absolute value equation with a vertical translation
Graph the absolute value equation with a horizontal translation
Write the equation of an absolute value function using horizontal and/or
vertical translations to y = |x|
Student Expectations
Major Concepts
Topics
Systems of Equations and Inequalities - Chapter 7
Solving Systems by Graphing Definitions
Solving Systems by Graphing
Define system of equations, solution of a system of equations
Manually graph two lines and find any points of intersection
Use Technology to graph two lines and find any points of intersection
Identify a system with one solution
Identify a system with no solution
Identify a system with an infinite number of solutions
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Solving Systems Using
Substitution
Substitution Method
Use the Substitution Method to find any solutions when the coefficient where
you substitute is 1
Use the Substitution Method to find any solutions when the coefficient where
you substitute is not 1
Solving Systems Using
Elimination
Elimination Method
Use the Elimination Method and addition to solve a system where one pair o
like terms are opposites.
Use the Elimination Method and subtraction to solve a system where one
pair of like terms are the same.
Use the Elimination Method after multiplying one equation to get a pair of
opposites.
Use the Elimination Method after multiplying two equations to get a pair of
opposites.
Applications of Linear
Systems
Writing Systems of Linear Equations
Write a system of linear equations from a verbal description and solve
Linear Inequalities
Definitions
Graphing Linear Inequalities
Define linear inequality, solutions of an inequality
Use dotted or solid lines and shading to represent the solution to a linear
inequality
Transform the given inequality if necessary to facilitate graphing
Check a point on the graph to verify the solution
Systems of Linear Inequalities
Solving by Graphing
Graph the linear inequalities on the same coordinate plane and indicate any
solution
Write a system of linear inequalities from a verbal description and solve by
graphing
Student Expectations
Writing Systems of Linear Inequalities
Part C Major Concepts
Exponents and Exponential Functions - Chapter 8
Types of Exponents
Zero Exponent
Negative Exponent
Topics
Know that every nonzero number raised to the zero power is one ex: a0 = 1
Know that every nonzero number raised to a negative exponent is one over
that number raised to the positive of that exponent ex: a-n = (1/an)
Simplify expressions involving exponents
Recognize scientific notation
Manually Convert between scientific notation and standard notation
Order numbers written in scientific notation
Scientific Notation
Properties of Exponents
Multiply two numbers with the same base ex: am • an = an+m
Raise a number with an exponent to a power ex: (am)n = am•n
Multiplication Properties of Exponents
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Raise a product to a power ex: (ab)m = am • bm
Divide powers with the same base ex: (am/an) = am-n
Raise a quotient to a power ex: (a/b)m = (am/bm)
Division Properties of Exponents
Geometric Sequences
Definition
Calculate the common ratio of a geometric sequence
Determine whether a sequence is arithmetic, geometric or neither
Determine the first term, common ratio, and term number of a rule
Create a rule given a geometric sequence: A(n) = a • r n-1
Rules
Exponential Functions
Identify that an exponential function is in the form y = a • bx
Generate tabular data from exponential functions
Graph exponential functions utilizing tabular data
Identify exponential growth functions in the form y = a • b x when a>0 and b>1
Definition
Graphing
Exponential Growth
Identify the growth factor from the function (b)
Use functions to reflect compound interest with varying interest periods
Identify exponential decay functions in the form y = a • bx when a>0 and
0<b<1
Exponential Decay
Major Concepts
Polynomials and Factoring - Chapter 9
Adding/Subtracting
Definitions
Polynomials
Identify the decay factor from the function (b)
Student Expectations
Topics
Identify and differentiate between a mono-, bi-, tri-, and poly-nomials
Determine degrees of polynomials
Write polynomials in Standard Form
Simplify polynomials by combining like terms
Adding and Subtracting Polynomials
Multiplying Polynomials
Multiplying a Monomial and a Trinomial
Multiplying a Binomial and a Trinomial
Multiplying a Binomial and a Binomial
Alternative Methods of Multiplying Polynomials
Factoring Polynomials
Finding the Greatest Common Factor (GCF)
Factoring out a Monomial
Factoring ax2 + bx + c where a = 1
Factoring ax2 + bx + c where a ≠ 1
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Multiply polynomials using the Distributive Property
Multiply polynomials using the vertical or horizontal method
Multiply using the Distributive Property
Multiply using First Outside Inside Last (FOIL) method
Identifying special cases with squares and differences of squares
Multiply polynomials using the area model
Multiply polynomials using algebra tiles
Find GCF using prime factorization or common factors
Use the GCF to factor out a monomial from a polynomial
Factor a trinomial into two binomials
Factor a trinomial into two binomials
Identify perfect square polynomials and factor them
ex: a2 + 2ab + b2 = (a + b)2 and a2 − 2ab + b2 = (a − b)2
3rd Degree Polynomials with Four Terms
Major Concepts
Topics
Quadratic Equations and Functions - Chapter 10
Square Roots
Working with Square Roots
Factor four term polynomials by grouping
Student Expectations
Standard Form
Quadratic Function
Quadratic Equation
Convert quadratic functions into Standard Form ex: y = ax2 + bx + c
Convert quadratic equations into Standard Form ex: ax2 + bx + c = 0
Graphing Quadratic Equations
Definitions
Define and label a parabola, axis of symmetry, vertex, and the maximum or
minimum point of a parabola
Create a table of values to graph a parabola from a quadratic equation
Use x= −b/2a to find the axis of symmetry of a parabola
Creating Coordinate Tables
Finding the Axis of Symmetry
State the square root of a number (and whether it is rational or irrational)
Know the perfect squares from 0-400
Solving Quadratic Equations
Various Methods to Solve Quadratic Equations
Solve quadratic equations by graphing (creating parabolas)
Solve quadratic equations by using algebra and square roots
Solve quadratic equations by factoring polynomials
Solve quadratic equations by completing the square
Solve quadratic equations by using the Quadratic Formula
Utilize the discriminant to determine whether there are two, one or no
solutions to a quadratic equation
Linear, Quadratic and
Exponential Models
Choosing a Model from Graphs, Data and Verbal
Descriptions
Identify and differentiate between the following types of functions:
Linear, Quadratic and Exponential
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