Unit 1, Review – Transitioning from Previous Mathematics
Instructional Resources: Prentice Hall: Algebra 1
Concept
Transitioning from Seventh
grade mathematics to
Algebra 1
• Read, compare and order real
numbers
• Add, subtract, multiply and
divide rational numbers and
take positive rational numbers
to whole-number powers
• Multiply, divide and simplify
rational numbers by using
exponent rules
• Work with rates, ratios and
percents to solve problems
Textbook Connections
California Standards Key Concepts Book: Algebra
1 P6 – P66
Topic 1: Working with Fractions: P6-P25
Topic 2: Rates, Ratios and Percents: P26-P41
Topic 3: Integers: P42-P66
Vocabulary
Absolute value
Decimal
Difference
Equivalent fractions
Evaluate (an expression)
Fraction
Greatest common factor (GCF)
Improper fraction
Integer
Mixed number
Opposite
Order of operations
Percent
Product
Quotient
Rate
Ratio
Simplest form (of a fraction)
Sum
Variable
Variable expression
105
Unit 1, Concept 2 – Solutions of Linear Sentences in One Variable
Instructional Resources: Prentice Hall: Algebra 1
Standards:
1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including
closure properties for the four basic arithmetic operations where applicable.
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents.
4.0 Students simplify expressions before solving linear equations and inequalities in one variable
Concept
(and related skills)
Understand the connections
from arithmetic to algebra
• Understand the meaning of
variables and variable
expressions
• Apply the concept of absolute
value to simple equations
• Solve simple equations using
mental math
• Simplify numerical expressions
using the properties of real
numbers including the
distributive property
• Evaluate variable expressions
• Translate phrases into algebraic
expressions
Textbook Connections
Lessons
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-9
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
Symbols and Expressions
The Commutative and Identity Properties
Exponential Notation
The Associative Property
The Distributive Property of Multiplication over
Addition
Writing Expressions
Solving Equations: An Introduction
Using Formulas
Integers and the Number Line
Rational Numbers
Addition of Rational Numbers
Subtraction of Rational Numbers
Multiplication of Rational Numbers
Division of Rational Numbers
Using the Distributive Property
Inverse of a Sum and Simplifying
Vocabulary
Absolute value
Base
Closure property
Coefficient
Distributive property
Equation
Exponent
Inequality
Integer
Like terms
Numerical expression
Opposite
Order of operations
Power
Real number
Reciprocal
Solution
Term
Variable
Variable expression
106
Unit 1, Concept 3 – Solutions of Linear Sentences in One Variable
Instructional Resources: Prentice Hall: Algebra 1
Standards:
4.0 Students simplify expressions before solving linear equations and inequalities in one variable
5.0 Students solve multistep problems, including word problems involving linear equations and linear inequalities
in one variable and provide justification for reach step
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
Concept
(and related skills)
Understand and solve
equations in one
variable (including
absolute value)
• Solve linear equations
in one variable
(including proportions)
• Graph solutions to
equations on a number
line
o Solve application
problems
Textbook Connections
Vocabulary
Lessons
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
3-9
9-3
The Addition Property of Equality
The Multiplication Property of Equality
Using the Properties Together
Expressions and Equations
More on Solving Equations
Clearing an Equation of Fractions or Decimals
Formulas
Solving Equations Involving Absolute Value
Proportions
Equations and Absolute Value
Absolute value
Absolute value equation
Equivalent equations
Formula
Identity
Inverse operations
Linear equation
Properties of equality
Rounding error
107
Unit 2, Concept 1 – Solutions and Graphs of Linear Sentences in One and Two Variables
Instructional Resources: Prentice Hall: Algebra 1
Standards:
6.0 Students graph a linear equation and compute the x- and y-intercepts. They are also able to sketch the region defined by
linear inequality.
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using
the point-slope formula.
8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find
the equation of a line perpendicular to a given line that passes through a given point.
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
Concept
(and related skills)
Understand and graph
linear equations in one and
two variables using a
variety of techniques
• Verify that a point lies on,
above, or below a line
• Evaluate the slope of a line
• Graph a linear function by
plotting points, using
intercepts,
and using the slope and
y-intercept
• Sketch the region defined
by a linear inequality
• Identify characteristics of
parallel and perpendicular
lines
Textbook Connections
Vocabulary
Lessons
7-1
7-2
7-3
7-4
7-5
7-8
Graphing Ordered Pairs
Graphing Equations
Linear Equations and Their Graphs
Slope
Equations and Slope
Parallel and Perpendicular Lines (the part of this section
pertaining to characteristics of parallel and perpendicular
lines)
9-5 Inequalities in Two Variables
Direct variation
Function notation
Linear equation
Linear inequality in two variables
Ordered pair
Slope
Slope-intercept form
x - intercept
y - intercept
114
Unit 2, Concept 2 – Solutions and Graphs of Linear Sentences in One and Two Variables
Instructional Resources: Prentice Hall: Algebra 1
Standards:
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using
the point-slope formula.
8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find
the equation of a line perpendicular to a given line that passes through a given point.
Concept
(and related skills)
Understand and derive
linear equations using a
variety of techniques
Textbook Connections
Vocabulary
Lessons
7-6 Finding the Equation of a Line
7-7 Fitting Equations to Data
Derive the equation of a line 7-8 Parallel and Perpendicular Lines (the part of this section
• given the slope and a point
pertaining to writing equations of lines)
on a line
• given 2 points on the line
• parallel or perpendicular to
a given line through a
given point
Linear model
Perpendicular
Point-slope form
Rate of change
Standard form
115
Unit 2, Concept 3 – Solutions and Graphs of Linear Sentences in One and Two Variables
Instructional Resources: Prentice Hall: Algebra 1
Standards:
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents
3.0 Students solve equations and inequalities involving absolute values.
4.0 Students simplify expressions before solving linear equations and inequalities in one variable
5.0 Students solve multistep problems, including word problems involving linear equations and linear inequalities in one
variable and provide justification for reach step
Concept
(and related skills)
Understand and solve
inequalities in one
variable (including
absolute value)
• Solve inequalities in
one variable
• Solve linear absolute
value inequalities
• Graph inequality
solutions (including
absolute value) on a
number line
Textbook Connections
Vocabulary
Lessons
4-1 Inequalities and Their Graphs
4-2 The Addition Property of Inequalities
4-3 The Multiplication Property of Inequalities
4-4 Using the Properties Together
4-5 Using Inequalities
9-4 Inequalities and Absolute Value
Absolute-value inequality
Addition property of inequality
Compound inequality
Division property of inequality
Graph of an inequality
Linear inequality in two variables
Multiplication property of inequality
Subtraction property of inequality
116
Unit 3, Concept 1 – Solutions and Graphs of Linear Sentences in One and Two Variables
Instructional Resources: Prentice Hall: Algebra 1
Standards:
9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer
graphically. Students are able to solve a system of two linear inequalities in tow variables and to sketch the solution sets.
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
Concept
(and related skills)
Understand and solve
systems of linear equations
and linear inequalities
graphically and
algebraically
• Solve systems of
equations
by graphing
• Solve systems
of linear inequalities
by graphing
• Solve systems of two
linear equations using
substitution
and elimination
• Solve application
problems using the above
techniques
Textbook Connections
Vocabulary
Lessons
8-1
8-2
8-3
8-4
9-6
Solving Systems of Equations by Graphing
The Substitution Method
The Addition Method
Using Systems of Equations
Graphing Systems of Linear Inequalities
Linear combination
Point of intersection
Solution of a linear system
Solution of a system of linear
Inequalities
System of linear equations
System of linear inequality
123
Unit 3, Concept 2 – Quadratic Equations and Functions
Instructional Resources: Prentice Hall: Algebra 1
Standards:
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising
to a fractional power. They understand and use the rules of exponents
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
19.0 Students know the quadratic formula and are familiar with its proof by completing the square.
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
21.0 Students graph quadratic functions and know that their roots are the x-intercepts.
23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
Concept
(and related skills)
Textbook Connections
Understand how to solve
Lessons
quadratic equations and how to
interpret the graphs of quadratic
functions
13-1 Introduction to Quadratic Equations
13-2 More Solving Quadratic Equations
• Solve quadratic
13-4 The Quadratic Formula
equations by
1) graphing (x intercepts)
2) finding square roots
3) using the quadratic formula
• Relate the graph of a quadratic
function to its related quadratic
equation
• Solve application problems
using the above techniques
Vocabulary
Axis of symmetry
Discriminant
Parabola
Perfect square
Quadratic equation
Quadratic formula
Quadratic function
Radical expression
Radicand
Real root
Roots of a quadratic equation
Square root
Vertex
Zeros
124
Unit 4, Concept 1 – Quadratic Equations and Function; Operations on Polynomials
Instructional Resources: Prentice Hall: Algebra 1
Standards:
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents
10.0 Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including
word problems, by using these techniques.
11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a
common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of
binomials.
14.0 Students solve a quadratic equation by factoring or completing the square.
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
Concept
(and related skills)
Understand monomials
and polynomials and
perform operations on
them (including factoring)
and apply to solutions of
quadratic equations.
• Perform arithmetic
operations on and with
polynomials
• Factor 2nd and 3rd degree
polynomials over the
integers
• Use the zero-product rule
and factoring as well as
completing the square to
solve simple quadratics
Solve application problems
using the above techniques
Textbook Connections
Vocabulary
Lessons
5-1
5-2
5-3
5-5
5-6
5-7
5-8
5-9
5-10
5-11
6-1
6-2
6-3
6-4
6-5
6-6
6-7
6-8
13-3
Exponents
More with Exponents
Multiplying and Dividing Monomials
Polynomials
More on Polynomials
Addition of Polynomials
Subtraction of Polynomials
Multiplication of Monomials and Binomials
Multiplying Binomials: Special Products
Multiplying Polynomials
Factoring Polynomials
Difference of Two Squares
Trinomial Squares
Factoring x2 + bx + c
Factoring ax2 + bx +c
Factoring by Grouping
Factoring: A General Strategy
Solving Equations by Factoring
Solving by Completing the Square
Binomial
Completing the square
Degree of a monomial
Degree of a polynomial
Factor completely
Factored form
Factor a trinomial
Monomial
Perfect square trinomial
Polynomial
Prime polynomial
Standard form
Trinomial
Zero-product property
130
Unit 4, Concept 2 – Operations with Rational Expressions and Rational Equations
Instructional Resources: Prentice Hall: Algebra 1
Standards:
10.0 Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including
word problems, by using these techniques
12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest
terms.
13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and
conceptually challenging problems by using these techniques.
Concept
(and related skills)
Understand the algebra of
rational expressions
• Simplify rational
expressions
• Perform arithmetic
operations on and with
rational expressions
Textbook Connections
Vocabulary
Lessons
10-1
10-2
10-3
10-4
10-5
Simplifying Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions
Addition and Subtraction: Like Denominators
Addition and Subtraction: Unlike Denominators
Least common denominator
Rational expression
Rational number
131
Unit 4, Concept 3 – Operations with Rational Expressions and Rational Equations
Instructional Resources: Prentice Hall: Algebra 1
Standards:
11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a
common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of
binomials.
12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest
terms.
13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and
conceptually challenging problems by using these techniques.
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give
pertinent information about given relations and functions.
Concept
(and related skills)
Understand and solve
rational equations
in one variable
Textbook Connections
Vocabulary
Lesson
Rational equation
10-6 Solving Rational Equations
• Solve rational equations
• Solve applications
problems using the above
techniques
132