Download Math Scope and Sequence

Foundational Mathematics
with Assessments
Understanding Whole Numbers 1
(with Assessments)
Understanding Whole Numbers 1:
Pretest
Understanding Whole Numbers: 0
through 10
Greater Than, Less Than, Equal To
Ordinal Numbers: First through Tenth
Understanding Place Value: Ones and
Tens
Comparing Whole Numbers: 10
through 99
Understanding Place Value: Hundreds
Understanding Addition and
Subtraction 1 (with Assessments)
Understanding Addition and
Subtraction 1: Pretest
Understanding Addition
Understanding Addition: Number Line
and Hundreds Chart
Finding the Missing Number in
Addition
Understanding Subtraction
Understanding Subtraction: Number
Line and Hundreds Chart
Finding the Missing Number in
Subtraction
Adding and Subtracting Whole
Numbers 1 (with Assessments)
Adding and Subtracting Whole
Numbers 1: Pretest
Adding 0 through 2: Addition Basic
Facts
Adding 3 through 9: Addition Basic
Facts
Adding Two 2-Digit Numbers: Sums
Less Than 100
Adding Three or Four Numbers
Subtraction Basic Facts
Subtracting a 1-Digit Number from a 2Digit Number
Subtracting Two 2-Digit Numbers
Adding Two 2-Digit Numbers: Sums
Greater Than 99
Understanding Whole Numbers 2
(with Assessments)
Understanding Whole Numbers 2:
Pretest
Understanding Place Value:
Thousands
Reading and Writing Numbers in Word
Form
Understanding Place Value: Millions,
Billions, and Beyond
Representing Millions and Billions
Understanding Addition
and Subtraction 2 (with
Assessments)
Understanding Addition
and Subtraction 2: Pretest
Addition and Subtraction
Fact Families
Checking Subtraction by
Addition
Using the Identity
Property of Addition
Using the Commutative
Property of Addition
Using the Associative
Property of Addition
Adding and Subtracting
Whole Numbers 2 (with
Assessments)
Adding and Subtracting
Whole Numbers 2: Pretest
Adding Multi-Digit
Numbers
Subtracting Multi-Digit
Numbers with Regrouping
Subtracting Multi-Digit
Numbers with Consecutive
Regrouping
Subtracting across Zeros
Solving Addition and
Subtraction Story Problems
Understanding
Multiplication (with
Assessments)
Understanding
Multiplication: Pretest
Understanding
Multiplication as Repeated
Addition
Understanding
Multiplication as an Array
Using the Identity
Property of Multiplication
Using the Commutative
Property of Multiplication
Using the Associative
Property of Multiplication
Using the Distributive
Property of Multiplication
over Addition
Finding the Missing
Number in Multiplication
Identifying Multiples
Finding Common
Multiples and the Least
Common Multiple
Multiplying Whole
Numbers (with
Assessments)
Multiplying Whole
Numbers: Pretest
-1-
Multiplying by 0 through 5:
Multiplication Basic Facts
Multiplying by 6 through 10:
Multiplication Basic Facts
Multiplying a 2-Digit Number by a 1Digit Number
Multiplying by a Multiple of 10 or 100
Multiplying a 3-Digit Number by a 1Digit Number
Multiplying a Multiple of 10 by a
Multiple of 10
Multiplying a 2-Digit Number by a 2Digit Number
Solving Multiplication Story Problems
Understanding Division (with
Assessments)
Understanding Division: Pretest
Understanding Division as Repeated
Subtraction
Understanding Division as Fair
Sharing
Multiplication and Division Fact
Families
Dividing Whole Numbers (with
Assessments)
Dividing Whole Numbers: Pretest
Division Basic Facts
Dividing by a 1-Digit Number
Dividing by a 2-Digit Number
Dividing Multiples of 100
Writing a Quotient as a Mixed Number
Solving Division Story Problems
Understanding Fractions (with
Assessments)
Understanding Fractions: Pretest
Understanding Fractions: Equal Parts
of an Object
Understanding Fractions: Equal Parts
of a Collection
Fraction Notation: Numerator and
Denominator
Proper Fractions and Improper
Fractions
Renaming Improper Fractions as
Whole or Mixed Numbers
Finding Equivalent Fractions
Simplifying Fractions
Working with Common Denominators
and the Least Common Denominator
Comparing Fractions
Ordering Fractions
Renaming Mixed Numbers as
Improper Fractions
Adding and Subtracting Fractions
(with Assessments)
Adding and Subtracting Fractions:
Pretest
Adding and Subtracting Fractions: Like
Denominators
Adding and Subtracting Fractions:
Unlike Denominators
Adding Mixed Numbers
Subtracting Mixed Numbers: Like
Denominators
Subtracting Mixed Numbers: Unlike
Denominators
Multiplying and Dividing Fractions
(with Assessments)
Multiplying and Dividing Fractions:
Pretest
Multiplying Two Fractions
Multiplying Whole Numbers and Mixed
Numbers
Dividing a Fraction by a Fraction
Dividing Fractions, Whole Numbers,
and Mixed Numbers
Finding the Reciprocal
Solving Fraction Story Problems
Understanding Decimals (with
Assessments)
Understanding Decimals: Pretest
Understanding Decimals: Tenths
Understanding Decimal Place Value:
Tenths and Hundredths
Understanding Decimal Place Value:
Thousandths and Ten-Thousandths
Relating Decimals, Fractions, and
Mixed Numbers
Comparing and Ordering Decimals
Performing Operations with
Decimals (with Assessments)
Performing Operations with Decimals:
Pretest
Adding and Subtracting Decimals
Multiplying Decimals
Multiplying Decimals by 10 or 100
Dividing Decimals
Dividing a 2-Digit Number by 10 or
100
Renaming a Fraction as a Decimal
Rounding Decimals
Solving Decimal Story Problems
Working with Percent (with
Assessments)
Working with Percent: Pretest
Understanding Percent
Relating Fractions, Decimals, and
Percents
Finding a Percent of a Whole Number
Finding a Percent of a Decimal
Number
Understanding Ratio and
Proportion (with Assessments)
Understanding Ratio and Proportion:
Pretest
Understanding Ratio
Equivalent Ratios
Understanding Proportion
Solving Proportions
Solving Ratio, Proportion,
and Percent Story Problems
Plane and Solid Figures
(with Assessments)
Plane and Solid Figures:
Pretest
Lines, Parts of Lines, and
Angles
Lines in a Plane
Introduction to Triangles
Introduction to
Quadrilaterals
Introduction to Circles
Exploring Congruent
Figures
Exploring Similar Figures
Line Symmetry in Plane
Figures
Introduction to Solid
Figures
Using Geometry (with
Assessments)
Using Geometry: Pretest
Area: Counting Square
Units
Calculating the Area of
Rectangles and Squares
Calculating the Area of
Triangles
Calculating the Volume of
a Rectangular Prism
Measurement (with
Assessments)
Measurement: Pretest
Measuring Length: Metric
Units
Measuring Length:
Customary Units
Telling Time to the Minute
Measuring Temperature:
Fahrenheit
Measuring Temperature:
Celsius
Solving Measurement
Story Problems
Math Fundamentals
95 Hours
671 Objectives
Skill Level: Basic
Target Audience; M, H,
PS
This beginning Math curriculum is
designed to provide instruction in
all the computation skills . from
counting through beginning
geometry.
Basic Number Ideas Beginning
-2-
(with or without assessment
test)
Whole Numbers 0-9
Counting Numbers
Whole Numbers 0-9 Review
Whole Numbers 10-99
Whole Numbers 100-999
Numbers 10-999 Review
Hundreds and Thousands
Millions/Billions and Trillions
Addition (with or without
assessment test)
Meaning of Addition
Addition Facts 1
Addition Facts 2
Addition Properties
Addition Skills 1
Addition Skills 2
Addition Skills 3
Addition Skills 4
Addition Review
Subtraction (with or without
assessment test)
Meaning of Subtraction
Subtraction Facts
Subtraction Skills 1
Subtraction Skills 2
Subtraction Skills 3
Subtraction Skills 4
Subtraction Review
Problem Solving 1
Multiplication (with or without
assessment test)
Meaning of Multiplication
Multiplication Facts 1
Multiplication Facts 2
Multiplication Properties 1
Multiplication Properties 2
Multiplication Skills 1
Multiplication Skills 2
Multiplication Skills 3
Multiplication Skills 4
Multiplication Review I
Multiplication Skills 5
Multiplication Skills 6
Multiplication Skills 7
Multiplication Review II
Problem Solving 2
Division
(with or without assessment
test)
Meaning of Division
Division Facts
Division Skills 1
Division Skills 2
Division Skills 3
Division Review I
Division Skills 4
Division Skills 5
Division Skills 6
Division Skills 7
Division Skills 8
Division Review II
Problem Solving 3
Fractions
(with or without assessment test)
Meaning of Fractions
Equivalent Fractions
Multiples and Common
Denominators
Comparing Fractions
Improper Fractions and
Mixed Numbers
Basic Terms Review
Adding and Subtracting Fractions 1
Adding and Subtracting Fractions 2
Adding Mixed Numbers
Subtracting Mixed Numbers 1
Subtracting Mixed Numbers 2
Adding and Subtracting
Fractions Review
Multiplying Fractions
Dividing Fractions 1
Dividing Fractions 2
Multiplying and Dividing Mixed
Numbers 1
Multiplying and Dividing Mixed
Numbers 2
Multiplication and Division Review
Problem Solving 4
Decimals
(with or without assessment test)
Decimal Fractions 1
Decimal Fractions 2
Adding and Subtracting Decimals
Multiplying Decimals
Dividing Decimals
Decimals Review
Problem Solving 5
Ratio/Proportion/Percent
(with or without assessment test)
Ratio Concepts
Proportion Concepts
Percent Concepts 1
Percent Concepts 2
Ratio/Proportion/Percent Review
Problem Solving 6
Geometry and
Measurement
(with or without assessment test)
Plane Figures 1
Plane Figures 2
Figure Comparison
Common 3-Dimensional Figures
Basic Figures Review
Linear Measurement
Area Measurement
Volume and Capacity Measurement
Measurement Review
Problem Solving 7
Math Problem
Solving
57 Hours
19 Objectives
Skill Level:
Basic - Advanced
Target Audience: M, H,
PS
This powerful math courseware
features nineteen interactive
scenarios that encourage
learners to explore and apply
mathematical concepts from
basic computation to advanced
algebra.
Math Fundamentals:
Math Problem Solving
Building a Highway
Smart Shopping
Car Costs
Running a Business
Beginning Algebra:
Math Problem Solving
Plan for a Fishing Trip
Tunnel through Bald
Mountain
Bean-Counting
Intermediate Algebra:
Math Problem Solving
Video Rental
Running a Race
Advanced Algebra:
Math Problem Solving
Car Rental
Building Boats
Saving the Birds
Geometry and
Measurement:
Math Problem Solving
Planning a Park
Shelf Space
Probability and
Statistics:
Math Problem Solving
The Fund Raiser
Making the Grade
Statistics for Quality
Data Skills:
Math Problem Solving
Growing Lilies
Planning a Playground
Applied Math
(with or without assessment
test)
14 Hours
24 Objectives
Skill Level: Basic
Target Audience: M, H, PS
Part of PLATO Workskills, this course teaches
the practical mathematics skills essential for
success in the modern workplace.
Time Applications
Clocks and Time Zones
Estimating
Math Conversions
Using Base, Rate, and Portion
Converting Linear Measurements
Converting Weight Measurements
Converting Volume Measurements
Using Linear Measurement Tools
Data Skills
35 Hours
84 Objectives
Skill Level: Intermediate
Target Audience: M, H, PS
Part of PLATO® WorkSkills, this curriculum
teaches both reading and math skills
essential to students. success in today.s
fast-paced workplace.
Reading Graphical Data
(with or without assessment test)
Reading Pie Charts
Introduction to Line Graphs
Reading Line Graphs
Introduction to Bar Graphs
Reading Bar Graphs
Introduction to Data in Tables
Reading Data in Tables
Introduction to Flowcharts
Computing Graphical Data
(with or without assessment test)
Graphing and Charting
Tables
Using Pictographs
Using Line Graphs
Using Bar Graphs
Using Pie Charts
Using Histograms
Reading Complex Charts and
Graphs
(with or without assessmenttest)
Reading Histograms
Reading Complex Tables
Reading Complex Flowcharts
Constructing Graphs and Charts
(with or without assessment test)
Constructing Line Graphs
Constructing Pie Charts
-3-
Constructing Bar Graphs
Constructing Histograms
Selecting Graphs and Charts
ALGEBRA 1 (part 1)
Basic Number Ideas
Odd and Even Numbers
Prime and Composite
Exponents: Exponential Form
Exponents: Product Rule
Exponents: Power Rule
The Additive Inverse of Integers
Adding Integers
Subtracting Integers
Multiplying Integers
Dividing Integers
Square Roots of Perfect Squares
Square Roots of Imperfect Squares
Multiplying Common Fractions
Adding and Subtracting Fractions
Adding and Subtracting Mixed
Numbers
Dividing Fractions
Multiplying and Dividing Mixed
Numbers
Using Basic Number Ideas
Mental Math with Whole Numbers
Mental Math with Fractions and
Percents
Math Sentences
Order of Operations
Expressions in 1 Variable
Expressions in 2 or More Variables
Determining the True Value of a
Statement
Adding Monomials
Subtracting Monomials
Multiplying Monomials
Dividing Monomials
Adding Binomials and Monomials
Subtracting Binomials and Monomials
Multiplying Binomials and Monomials
Dividing Binomials and Monomials
Linear Equations in 1 Variable:
Solving by Inspection
Linear Equations in 1 Variable:
Isolating the Variable
Linear Inequalities in 1 Variable, Part
1
Linear Inequalities in 1 Variable, Part
2
More Difficult Linear Inequalities in 1
Variable
Special Quadratic Equations, Part 1
Special Quadratic Equations, Part 2
Using Linear Equations to Solve
Problems
Using Quadratic Equations to Solve
Problems
Graphing Basics
Coordinate Plane
Identifying Points on a Coordinate Plane
Ordered Pairs as Solutions to a Linear
Equation
Graphing Linear Equations in
2 Variables
Solving and Graphing
Systems of Equations
Solving Problems with
Systems of Linear Equations
Equations and
Formulas
Literal equations
Adapting and Using Formulas
Special Topics
Visualizing Percents Less
than 1%
Converting Percents Less
Than 1% to Decimals
Converting a Decimal to a
Fraction of a Percent
Finding the Amount with
Percents Less than 1%
Visualizing Percents Greater
than 100%
Converting Percents Greater
than 100% to Decimals
Converting a Number Greater
than 1 to a Percent
Mean, Median, and Mode
Probability and Possible
Outcomes
Probability of an Event
Solving Problems with
Percents
Solving Problems with Mean,
Median, and Mode
Solving Problems with
Probability
Estimation Basics
Estimation by Clustering
Scaling and Proportion, Part
1
Scaling and Proportion, Part
2
Introduction to
Functions
Patterns and Sequences
Functions
Describing Functions with
Equations, Tables, and
Graphs
Linear Patterns
Graphs, Slopes and yIntercepts
Equations, Graphs, Slopes,
and y-Intercepts
Interpreting Graphs to Solve
Problems
ALGEBRA 1 (part 2)
Sets and Numbers
Additive Inverse of an Integer
Integer Sum
Integer Difference
Integer Product
Integer Quotient
Adding Fractions
-4-
Subtracting Fractions
Multiplicative Inverse of a Fraction
Product of Fractions
Quotient of Fractions
Basic Set Concepts: Elements in a
Set
Basic Set Concepts: Finite or Infinite
Basic Set Concepts: Subsets
Basic Set Concepts: Roster and Set builder
Forms
Union of Two Sets
Intersection of Two Sets
Positive and Negative Exponents
Integer Exponents and the Product Rule
Integer Exponents and the Quotient Rule
Integer Exponents and the Power Rule,
Part 1
Integer Exponents and the Power Rule,
Part 2
Square Roots of Integers
Multiplication Rule for Radicals
Division Rule for Radicals
Simplifying Radicals, Part 1
Simplifying Radicals, Part 2
Review: Fractions and Sets
Review: Exponents and Radicals
Polynomials and
Factoring
Classifying Polynomials
Additive Inverse of a Monomial
Monomial Sum
Monomial Difference
Monomial Product
Monomial Quotient
Binomial Sum
Additive Inverse of a Binomial
Binomial Difference
Value of a Polynomial
Polynomial Sum
Polynomial Difference
Product of a Monomial and
Polynomial
Simplifying Polynomial Expressions
Product of Polynomials
Quotient of a Monomial and
Polynomial
Quotient of a Binomial and
Polynomial
Greatest Common Factor of
Monomials
Monomial Factors of Polynomials
Binomial Factors of Polynomials, Part
1
Binomial Factors of Polynomials, Part
2
Factoring the Difference of Squares
Factoring Perfect Square Trinomials
Factoring Trinomials, Part 1
Factoring Trinomials, Part 2
Review: Polynomials and Factoring
Equations and
Inequalities
Simple Equations in 1 Variable:
Using Inspection
Simple Equations in 1 Variable:
Isolating the Variable
More Difficult Linear Equations in 1
Variable
Absolute Value of a Number
Equations with Absolute Values
Graphing a Solution Set on a Number
Line
Solving and Graphing Equations in 1
Variable
Solving Problems with Linear
Equations in 1 Variable
Linear Inequalities in 1 Variable, Part
1
Linear Inequalities in 1
Variable, Part 2
Linear Inequalities in 1
Variable, Part 3
Solving Simple Quadratic Equations
Solving Quadratic Equations by
Factoring, Part 1
Solving Quadratic Equations by
Factoring, Part 2
Solving Quadratic Equations by
Factoring, Part 3
Quadratic Formula
Solving Problems With the
Quadratic Equations
Review: Equations and Inequalities
Algebra 2 (part 1)
Rational Expressions
Evaluating Rational Expressions
Restrictions on Rational Expressions
Equivalent Forms of Rational
Expressions
Simplifying Rational Expressions
Sum of Rational Expressions, Part 1
Difference of Rational Expressions:
Part 1
Product of Rational Expressions
Quotient of Rational Expressions
Common Denominators of Rational
Expressions
Sum of Rational Expressions: Part 2
Difference of Rational Expressions:
Part 2
Review: Rational Expressions
Graphs and Linear
Equations
The Coordinate
Graphing Ordered Pairs
Solutions of Linear
Equation as Ordered Pairs
Graphing a Linear Equation in 2 Variables
Graphing Linear Inequality in 2 Variables
Slope of a Line from 2 Points
The y-Intercept of a Line
Using the Slope and yIntercept to Graph a Line
Finding the Slope and yIntercept from an Equation
Writing Equations in SlopeIntercept Form
Identifying Graphs from Their
Equations
Parallel Lines and Their
Slopes
Perpendicular Lines and
Their Slopes
Equations of Parallel or
Perpendicular
Lines
Review: Graphs
Linear Systems of
Equations and
Inequalities
Solving Linear Systems of
Equations:
Graphs
Classifying Linear Systems
Solving Linear Systems of
Inequalities: Graphs
Solving Linear Systems of
Equations: Substitution
Solving Linear Systems of
Equations: Addition
Solving Linear Systems of
Equations: Matrices 1
Solving Linear Systems of
Equations:
Matrices 2
Solving Problems with Linear
Systems
Review: Linear Systems
Probability
Chance Experiments and
Probability
Determining the Probability of
an Event
Multiplication Principle of
Counting
Review: Probability
Vectors
Introduction to Vectors
Vector Addition
Algebra 2 (part 2)
Numbers and Their
Properties
Rules for Exponents and
Radicals
Rationalizing the
Denominator in
Rational Expressions
Applying Rules for Exponents
and Radicals
Scientific Notation
Simplifying Algebraic
Expressions
Multiplying Algebraic
Expressions
-5-
Factoring Algebraic Expressions
Factoring Sums and Differences of
Perfect Cubes
Factoring or Using Quadratic
Formulas
Rational Expressions: Simplify
Rational Expressions: Add and
Subtract
Rational Expressions: Multiply and
Divide
Special Equations and
Inequalities
Evaluating Expressions With
Absolute Value
Absolute Value, Inequalities, and
Interval Notation
Graphing Linear Inequalities in 1
Variable
Graphing with Restrictions on the
Variable
Graphing Solution Sets of Associated
Inequalities
Coordinates and Curves
Calculating the Slope of a Line
Point-Slope and Slope-Intercept
Forms of Equations
Equation of a Line Given a Point and
Parallel Line
Equation of a Line Given a Point and
Perpendicular Line
Perpendicular Bisector of a Line
Segment
Distance between 2 Points
Distance between a Point and a Line
Distance and Circles
Parabola and Its Intercepts
Parabola and Its Vertex
Ellipse
Hyperbola
Equations of Ellipses and Hyperbolas
Functions and Their
Graphs
Defining a Function with Its
Rule
Finding Values of a Function
Using Its Rule
Equations and Graphs of
Functions, Part 1
Equations and Graphs of
Functions, Part 2
Functional Values
Composite Functions
Domain Values of Composite
Functions
Inverse of a Function
Determining if a Function Has an
Inverse
Solving Problems with Linear Functions
Solving Problems with Quadratic
Functions
Beginning Algebra
Exponential and
Logarithmic Functions
Properties of Exponential Functions
Properties of Logarithmic
Functions
Recognizing Graphs of Types of
Functions
Solving Problems: Exponential and
Logarithmic
Exponential Growth
Exponential Decay
Pre-Algebra
23 Hours
177 Objectives
Skill Level: Intermediate
Target Audience: M, H, PS
This curriculum provides students with the
foundation skills they.ll need to understand and
apply algebraic concepts.
Basic Number Ideas -PreAlgebra (with or without
assessment test)
Odd/Even/Prime/Composite
Numbers
Exponents - Pre-Algebra
Adding and Subtracting Integers
Multiplying and Dividing Integers
Square Roots - Pre-Algebra
Common Fractions
Using Basic Number Ideas
Math Sentences, Part 1 (with or
without assessment test)
Variables
Monomials
Binomials
Linear Equations: 1 Variable
Linear Inequalities: 1 Variable
Special Quadratic Equations
Using Math Sentences, Part 1
Math Sentences, Part 2
(with or without assessment test)
Coordinate Plane
Linear Equations: 2 Variables
Systems of Equations - Pre-Algebra
Using Math Sentences, Part 2
Special Topics
(with or without assessment test)
Percents, Part 1
Percents, Part 2
Mean, Median, and Mode
Probability - Pre-Algebra
Using Special Topics
36 Hours
282 Objectives
Skill Level:
Intermediate
Target Audience: M, H,
PS
Building on the information
presented in
Pre-Algebra, these courses
continue students. ntroduction to
algebra with instruction for sets
and numbers, polynomials and
factoring, and math sentences,
following up with application
exercises.
Sets and Numbers (with
or without assessment
test)
Integer Sum
Integer Difference
Integer Product and
Quotient
Fractional Numbers: Add &
Subtract
Fractional Numbers:
Multiply &
Divide
Basic Set Concepts
Set Union and Intersection
Exponents - Beginning
Algebra
Quotient and Power
Square Roots - Beginning
Algebra
Roots and Radicals
Review: Sets and Numbers
Polynomials and
Factoring (with or
without assessment
test)
Monomial Sum and
Difference
Monomial Product and
Quotient
Binomial Sum and
Difference
Polynomial Sum and
Difference
Polynomial Product
Polynomial Quotient
Common Factors
Factoring II
Factoring Special Cases
Factoring Trinomials I
Factoring Trinomials II
Review:
Polynomials/Factoring
-6-
Math Sentences
(with or without assessment test)
Simple Equations
Solving Equations
Absolute Value
Graphing
Word Problems I
Inequalities I
Inequalities II
Simple Quadratics
Quadratic Equations
Quadratic Formula
Word Problems II
Review: Math Sentences
Intermediate Algebra
20 Hours
140 Objectives
Skill Level: Intermediate
Target Audience: M, H, PS
Starting where Beginning Algebra left off,
this curriculum provides instruction in the
core algebra topics usually required to
fulfill high school course requirements.
Rational Expressions (with or
without assessment test)
Evaluating
Equivalent Forms
Rational Sum and Difference
Rational Product and Quotient
Unlike Denominators
Review: Rational Expression
Graphs (with or without
assessment test)
Points in a Plane
Linear Equations and Inequalities
Slope and Y-Intercept
Slope - Intercept Form
Parallel and Perpendicular Lines Intermediate
Review: Graphs
Linear Systems of
Equations and Inequalities (with or
without assessment test)
Linear Systems
Systems - Substitute
Systems - Addition
Word Problems
Review: Linear Systems
Probability
(with or without assessment test)
Probability I
Probability II
Review: Probability
Advanced Algebra
27 Hours
75 Objectives
Skill Levels: Advanced
Target Audience: H, PS
This college-level course prepares students for
the high-technology jobs of today.
Numbers and Their Properties
(with or without assessment test)
Exponents and Radicals
Algebraic Operations
Factoring
Algebraic Fractions
Equations and Inequalities
(with or without assessment test)
Intervals, Distance and Absolute
Values
Inequalities
Coordinates and Curves
(with or without assessment test)
Lines and Slopes
Parallel and Perpendicular Lines Advanced
Distance and Circles
Parabolas
Ellipses and Hyperbolas
Functions and Their
Graphs (with or without
assessment test)
Definitions of Functions
Graphs of Functions
More on Graphing Functions
Composite and Inverse Functions
Applications of Functions
Exponential Functions
(with or without assessment test)
Exponential and Logarithmic
Functions
Exponential Growth and Decay
Geometry and
Measurement 1
10 Hours
78 Objectives
Skill Level: Intermediate
Target Audience: M, H, PS
This curriculum offers students a
powerful introduction to basic
geometric and measurement concepts.
Geometry
(with or without assessment test)
Special Angles, Part 1
Special Angles, Part 2
Circles/Arcs/Circumferences
The Pythagorean Theorem 1
Using Geometry
Measurement
(with or without
assessment test)
Metric Measurement
Area, Part 1
Area, Part 2
Volume
Using Measurement
Geometry and
Measurement 2
45 Hours
156 Objectives
Skill Level:
Intermediate
Target Audience: M, H,
PS
This curriculum provides
instruction
required in most high school-level
geometry courses.
Introduction to
Geometry
(with or without
assessment test)
Postulates and Theorems
Points, Lines and Planes
Intersecting Lines and
Planes
Congruent Angles
Supplementary and
Complementary Angles
Two of a Kind
Triangles and Lines
(with or without
assessment test)
Congruent Triangles, Part 1
Congruent Triangles, Part 2
Congruent Triangle
Problems
Angles in Pairs
Transitive Properties of
Lines
The Sum of the Angles in a
Triangle
The Pythagorean Theorem
2
Solving Right Triangle
Problems
30-60 Right Triangles
Proportionality
A Sense of Proportion
Not Everything is Created
Equal
Polygons
(with or without
assessment test)
Introduction to Polygons
-7-
Summing up Angles
Angles in Regular Polygons
Parallelograms: Part 1
Parallelograms: Part 2
Rhombuses and Trapezoids
Transformations, Symmetry, and
Area (with or without assessment
test)
Symmetry
Translations
Rotations
Area of Right Triangles and
Parallelograms
Area of Any Triangle
Area of Trapezoids and
Rhombuses
Circles
(with or without assessment test)
Introduction to Circles
Tangents
Arcs and Chords
Inscribed Angles
Circles and Angles
Circles and Segments
Measuring Circumference
The Length of Arcs
The Area of Circles
Solids and Coordinate
Geometry (with or without
assessment test)
Prisms
Area and Volume of Cylinders
Area and Volume of Cones
The Distance Formula
Slope
Coordinates in Three Dimensions
Trigonometry
16 Hours
36 Objectives
Skill Level: Advanced
Target Audience: H, PS
This college-level curriculum provides
students with the skills necessary to understand
concepts such as right angle trigonometry,
circular functions, trigonometric identities, and
equations.
Trigonometric Functions
(with or without assessment test)
Right Angle Trigonometry
Radian Measure
Circular Functions
Three More Trigonometric
Functions
Graphing Trigonometric Functions
Trigonometric Identities
and Equations
(with or without assessment test)
Trigonometric Identities of a
Single Variable
Trigonometric Identities II
Trigonometric Equations
Inverse Trigonometric Functions
Law of Sines and Cosines
Polar Coordinates
Calculus 1
38 Hours
135 Objectives
Skill Level: Advanced
Target Audience: H, PS
An introduction to the fundamentals of
differential and integral calculus, this
curriculum provides a foundation for
further study in calculus, or in other fields
where a knowledge of calculus is required.
Limits I
Introduction to Limits - Tutorial
Introduction to Limits - Exercises
Limits of Rational and
Transcendental Functions- Tutorial
Limits of Rational and
Transcendental FunctionsExercises
Limits at Infinity - Tutorial
Limits at Infinity - Exercises
Limits II
Definition and Proofs of LimitsTutorial
Definition and Proofs of LimitsExercises
Use of Limit Theorems- Tutorial
Use of Limit Theorems- Exercises
Continuity - Tutorial
Continuity . Exercises
The Derivative
Derivative: Approximating Rates
and Definition - Tutorial
Derivative: Approximating Rates
and Definition - Exercises
Derivative: Instantaneous Rates Tutorial
Derivative: Instantaneous Rates .
Exercises
Techniques of
Differentiation
Differentiation of Polynomials and
Rational Functions - Tutorial
Differentiation of Polynomials and
Rational Functions - Exercises
Uses of the First DerivativeTutorial
Uses of the First DerivativeExercises
The Second Derivative Tutorial
The Second Derivative Exercises
Finding Maxima and Minima of
Functions - Tutorial
Finding Maxima and Minima of
Functions - Exercises
Derivatives of
Trigonometric
Functions
Concavity and the Second
Derivative Test - Tutorial
Concavity and the Second
Derivative Test - Exercises
Graphing Rational FunctionsTutorial
Graphing Rational FunctionsExercises
Narrative Max-Min ProblemsTutorial
Narrative Max-Min Problems-Exercises
The Pinching Theorem Tutorial
The Pinching Theorem Exercises
Differentiation of
Trigonometric
Functions - Tutorial
Differentiation of
Trigonometric
Functions . Exercises
Chain Rule and Related
Rates
Derivatives of Composite
Functions - Tutorial
Derivatives of Composite
Functions - Exercises
More on the Chain Rule
- Tutorial
More on the Chain Rule
- Exercises
Implicit Differentiation Tutorial
Implicit Differentiation Exercises
Related Rates - Tutorial
Related Rates - Exercises
Tangent Line
Approximations and
Differentials
Tangent Line
ApproximationTutorial
Tangent Line
ApproximationExercises
Differentials at a Point Tutorial
Differentials at a Point –
Exercises
Applications of the
First
Derivative
The Behavior of a Function
as
Related to the Sign of the
Derivative - Tutorial
The Behavior of a Function
as
Related to the Sign of the
Derivative - Exercises
-8-
Applications of the
Second Derivative
General Properties of
Continuous and
Differentiable Functions
Basic Theorems - Tutorial
Basic Theorems . Exercises
The Indefinite Integral
The Indefinite Integral: Physical and
Geometrical Interpretation of the
Antiderivative - Tutorial
The Indefinite Integral: Physical and
Geometrical Interpretation of the
Antiderivative - Exercises
Integration by Substitution- Tutorial
Integration by SubstitutionExercises
Definite Integral
Introduction to the Definite
Integral: Approximations and
Areas - Tutorial
Introduction to the Definite
Integral: Approximations and
Areas - Exercises
Introduction to the Definite
Integral: Definition and
Applications - Tutorial
Introduction to the Definite
Integral: Definition and
Applications . Exercises
The Fundamental
Theorem
The Fundamental Theorem of
Calculus - Tutorial
The Fundamental Theorem of
Calculus – Exercises
Derivatives of Integrals with
Functions as Limits - Tutorial
Derivatives of Integrals with
Functions as Limits – Exercise
Geometrical Applications
of the Definite Integral
Other Logarithm and
Exponential Functions
Area Between Curves - Tutorial
Area Between Curves - Exercises
Volumes of Solids of Revolution by
the Method of Disks - Tutorial
Volumes of Solids of Revolution by
the Method of Disks - Exercises
Volumes of Solids of Revolution by
the Method of Shells - Tutorial
Volumes of Solids of Revolution by
the Method of Shells - Exercises
Properties and Graphs of
the
General Exponential and
Logarithm Functions
Applications of the Common
Logarithm
Physical Applications of the
Definite Integral
Work Done by Moving an Object
Horizontally or by Stretching or
Compressing Spring - Tutorial
Work Done by Moving an Object
Horizontally or by Stretching or
Compressing Spring - Exercises
Work Done by Lifting an Object or
Pumping a Liquid - Tutorial
Work Done by Lifting an Object or
Pumping a Liquid - Exercises
Force Due to Hydrostatic PressureTutorial
Force Due to Hydrostatic PressureExercises
Center of Mass - Tutorial
Center of Mass - Exercises
Calculus 2
35 Hours
77 Objectives
Skill Level: Advanced
Target Audience: H, PS
This curriculum is intended as the second
semester of a course in the fundamentals
of differential and integral calculus.
Introduction to Inverse
Functions
Properties of Inverse Functions
Derivatives of Inverse Functions
Inverse Trigonometric
Functions
The Arcsine Function
The Arctangent Function
The Natural Logarithm
Properties of the Natural Logarithm
The Natural Exponential
Function
The Natural Exponential Function
Exponential Growth and Decay
Hyperbolic Functions
L.Hopital.s Rule
L.Hopital.s Rule
Further Indeterminate
Forms
Integration by
Substitution and by
Parts
Integration by Substitution
Integration by Parts
Techniques of
Integration
Involving Trigonometric
Functions
Trigonometric Integrals
Integration by Trigonometric
Substitution
Partial Fractions
Partial Fractions
Integration by Partial
Fractions
Numerical Integration
Riemann Sums and the
Trapezoidal Rule
Simpson.s Rule
Improper Integrals
Improper Integrals
Lengths of Curves
Lengths of Graphs of
Functions
Introduction to
Sequences
Polynomial Approximation
and Taylor.s Theorem
Sequences
Further Properties of
Convergent Sequences
Introduction to Series
Introduction to Series
Preliminary Results on
Infinite
Series
-9-
Tests of Convergence on
Non-negative Series
The Integral Test and the
Comparison Tests
The Ratio Test and the Root Test
Additional Topics on
Convergence and
Divergence of Series
The Alternating Series Tests
Absolute and Conditional
Convergence
Power Series
The Radius and Interval of
Convergence of Power Series
Differentiation and Integration of
Power Series
Taylor Series
The Binomial Series