/ CTYOnline / Courses / Mathematics

**Prerequisites:** Qualifying math score and completion of previous grade level math or equivalent

**Course Format:** Individually Paced

**Course Length:** Typically 3-6 months

**Course Codes:** GR1, GR2, GR3, GR4

Description

The sequence covers concepts typically found in an accelerated mathematics curriculum and is aligned with the Common Core Standards. CTY's Accelerated Math Courses are designed for the student to work independently; students begin at the appropriate grade level with a review before moving to new material. Each course is strand-based, and students are tracked in each individual strand: Integers, Fractions, Logic and Reasoning, Measurement, Geometry, Data/Statistics/Probability. Topics covered in each strand include addition, subtraction, multiplication, division, fractions, decimals, number concepts, equations, word problems, geometry, measurement, probability, statistics, graphs, functions, logic, and set theory.

New concepts are introduced through brief audio lectures. Exercises that follow lectures reinforce concepts, and students receive immediate feedback. As students master concepts, they are moved more rapidly through the material. Students needing more practice in a certain concept are given additional exercises in those particular skills. Math Races, an optional game within the sequence, provides drills on arithmetic operations. Students submit a comprehensive, written final exam after completing each grade level in the sequence. Each course is equivalent to a full year of mathematics.

**Please note:** The Grade 1 - 4 Accelerated Mathematics Series offered through CTY*Online* draws on software developed by Stanford PreCollegiate Studies. CTY*Online* provides its own instructors for the Stanford PreCollegiate Studies Math Series.

There are no required materials for this course.

Grade 1

- Matching Numbers to Objects
- Ordering Integers
- Concept of Zero
- Counting, 1 - 50
- Counting, 51 - 100
- Counting by Twos
- Counting by Tens
- Counting in Sequence
- Counting Backwards
- Addition
- Addition, Using Concrete and Pictorial Models
- Addition, Facts
- Addition, Horizontal
- Addition, Equations
- Addition, Vertical Format
- Place Value: tens and ones
- Place Value: Addition
- Place Value: Subtraction
- Subtraction
- Subtraction, Using Concrete/Pictorial Models
- Subtraction, Facts
- Subtraction Equations
- Subtraction, Vertical Format
- Addition and Subtraction Equations
- Number Words
- Estimation

- Exploring Equal Parts
- Halves
- Fractional Notation

- Inside and Outside
- Left and Right
- Above and Below
- Smaller and Larger
- Near and Far
- Over and Under
- Higher and Lower
- Before and After
- Between and Next To
- Into and Out Of
- Same Shape and Size
- Same Shape, Different Size
- Constructing and Recognizing Figures
- Equilateral Triangles
- Constructing & Recognizing Patterns
- Perimeter

- Reasoning about Daily Events, Predicting Events
- Using Information Given to Predict Outcomes:
- If/Than Statements

- Identifying the Correct Clock
- Identifying the Correct Time
- Ordinal Number Words
- Cent Sign
- Equivalent Value of Coins:
- Penny, Nickel, and Dime
- Counting, Matching, and Choosing Money
- Solving Word Problems Using Penny, Nickel, and
- Dime to Buy Given Objects
- Measurement in Inches and Feet
- Pints and Quarts
- Dozens
- Using a Ruler
- Feet and Inches
- Length and Perimeter

- Picture Graphs
- Interpreting Picture Graphs
- Tally Graph
- Interpreting Tally Graphs
- Patterns

Grade 2

- Addition
- Addition, Fact Families to 19
- Addition - One, Two and, Three Digit Numbers
- Addition, Carrying
- Regrouping using Models
- Addition, Word Problems
- Addition Equations
- Subtraction
- Subtraction, Facts
- Subtraction; One, Two, and Three Digit Numbers
- Subtraction, Regrouping
- Subtraction, Word Problems
- Subtraction Equations
- Addition, Horizontal and Column
- Subtraction, Horizontal and Column
- Counting by 2, 3, 4, 5, 10
- Counting Forward and Backward
- Place Value, Ones/Tens/Hundreds
- Place Value, Pictorial Models
- Ordinal Numbers
- Months of the Year
- Days of the Week
- Greater Than, Less Than, and Equal to using >, < and +
- Inequalities Involving the < and > Symbol
- Multiplication
- Multiplication, Using Sets as Models
- Multiplication, Facts
- Multiplication, Tables
- Multiplication, Word Problems
- Choosing the Operator: Addition, Subtraction, Multiplication
- Multiplication Equations
- Addition Equations with One and Two Variables
- Sums and Differences
- Writing Equations from Word Problems
- Communicative Law
- Communicative Law, Addition Problems
- Associative Law
- Associative Law, Addition Problems

- Review of Fractions
- Halves
- Quarters
- Thirds
- Fourths
- Parts of Regions
- Pictorial Models of Fractions
- Numerator and Denominator
- Fraction Word Problems
- Fractions and Division

- Area
- Line Segments
- Constructing Segments, Triangles and Quadrilaterals
- Classifying Geometric Shapes
- Concave and Convex
- Vertex and Vertices
- Inside and Outside
- Intersections
- Ways
- Measuring Distances along a Way
- Polygons

- Deducting an Outcome
- Drawing Conclusions
- Predicting Outcomes
- If/Than Statements
- Reasoning Word Problems

- Feet and Inches
- Dozens
- Coins
- Telling Time and Elapsed Time
- Pins and Quarts
- Lengths and Widths
- Area and Square Units
- Linear Measure, Using Units and Rulers
- Estimating Distances
- Counting Bills and Coins

- Tally Charts
- Bar Graphs
- Interpreting Bar Graphs
- Patterns

Grade 3

- Addition
- Addition Equations
- Multiplication
- Multiplication, English Sentences
- Multiplication, Word Problems
- Length and Width
- Multiplication, Area
- Multiplication, Zero
- Multiplication Tables
- Multiplication with Variables
- Solving Word Problems using Variables
- Review of Place Value
- Place Value, Notation
- Addition, Vertical
- Addition, Horizontal
- Addition with Carrying
- Addition, Regrouping Tens and Ones
- Addition, Two-digit Numbers
- Place value and Addition: Mixed Notation
- Addition: Hundreds/Three-digit Numbers/ 3 & 4 one-digit numbers/3 Two-Digit Numbers (carrying 2 times)
- Subtraction
- Subtraction Equations
- Subtraction, Borrowing
- Subtraction Word Problems with Borrowing
- Division
- Division, Word Problems
- Division, Checking with Multiplication
- Patterns of Multiples up to 100
- Equations, Variable in Various Positions
- Choose the Operator
- Multiplication and Division in Word Problems
- Place Value: Thousands, Hundreds, Tens, and Ones
- Number Words to Numerals
- Addition: 4 Single Numbers/4 Two-digit Numbers/4 Numbers, Hundreds/Three-digit Numbers with Carrying
- Word Problems using Maps and Tables
- Binary Operations
- Commutative Law
- Not-equal sign
- Subtraction with Parentheses
- Associative Operations
- Associative Law
- Associative Law, Word Problems
- Multiplication: Ones, Tens, Hundreds
- Distributive Law

- Fractional Parts 1/2, 1/3, 1/4, and 1/5
- Fractional Parts 2/4, 2/3, 3/4
- Fractions to 1/10
- Fractions as Parts of Sets
- Fractions and Division
- Writing Fractions
- Addition, Fractions
- Subtraction, Fractions
- Definition of Numerator and Denominator
- Addition and Subtraction using a Number Line

- Inside and Outside
- Concave and Convex Plane Figures
- Points of Intersection
- Introduction of Vertices
- Definition of Perimeter
- Same Shape, Size, and Position
- Closed and Open
- Lines of Symmetry
- Points
- Lines
- Segments
- Rays
- Angles and Vertices
- Length of Segments
- Doubling and Tripling Segments
- Bisecting Segments
- Comparing Segments and Triangles

- Sets
- Empty Sets
- Equal Sets
- Union of Sets
- N Notation
- Addition with N Notation
- Difference of Sets
- Intersection of Sets
- Subtraction with N Notation
- Subtraction Equations
- Even and Odd in Word Problems
- Magic Squares
- Subsets
- Less-than
- Greater-than
- Sets and the Communicative Law
- Describing Sets
- Mathematical Notation of Set Description
- Union and Intersection of Sets using Variables
- Sets and the Associative Law

- Carrying in Addition, Money
- Borrowing in Subtraction, Money
- Word Problems, Money
- Word Problems, Mathematical Sentence and Corresponding English Sentences
- Money Words to Money Numbers
- Averages
- Inches
- Feet
- Yards
- Rods
- Miles
- Linear Measure, Word Problems
- Seconds
- Minutes
- Hours
- Telling Time
- Calendar: Days, Weeks, Months, Years, Decades, Centuries, and Number of Days in the Month
- Time Measure, Word Problems

- Coin Toss
- Coin Toss Sequence
- Recording and Representing Data
- Predicting Events

Grade 4

- Regrouping for Subtraction
- Subtracting Tens and Ones
- Subtracting Tens and Ones, with Borrowing, Column Form
- Addition and subtraction, column form, carry and borrow
- Subtraction word problem, borrow
- Regrouping Hundreds and Tens
- Introduction of Factors and Product
- Checking Multiplication with Division
- Finding Factors and Products
- Finding factors and products as variables
- Definition of Any Number divided by One Equals the Number
- Division, Horizontal Format
- Division and subtraction, horizontal format
- Solving Equations by Division
- Using Parentheses and Introduction to Parentheses
- Example of Distributive Law for Multiplication
- Example of distributive law for multiplication (second expression)
- Working with the two forms of the distributive law
- Finding Products by Use of the Distributive Law
- Multiplication, horizontal, find product
- Multiplication, Horizontal, Find Factor, First, Second
- Using the Distributive Law to Find Product of Multiplying by 11 and 12
- Multiplication Solve the Equation, Variable in Mixed Position
- Solving Multiplication with Use of Distributive Law and algorithms
- Multiplication of a 1 Digit and 2 Digit Number
- Multiplication of a 1 Digit and 2 Digit Number, Fill in Product
- Multiplication of a 1 Digit and a 3 Digit Number
- Multiplication of a 1 Digit and 3 Digit Number, Fill in Product
- Division, Horizontal Format, Find Quotient
- Division, solve the equation, find the variable, quotient, divisor
- Division, solve the equation, find the variable, divisor, dividend
- Equations with division and addition together
- Word problems, multiplication and division
- Distributive Law for Division
- Distributive Law for Division over Addition
- Concept of Ones, Tens, Hundreds, Thousands, Ten-Thousands find the sum
- Find the sum (3, 5 digit numbers), remainder (2, 5 digit numbers), column format
- Working with large numbers (ten-thousands), bar graph and sum/difference
- Addition and subtraction (ten-thousands)
- Concept of Hundred-Thousands
- Concept of Millions
- Reading Numerals, i.e. "One Million", "Ten Million", ...
- Division and Remainders
- Estimating in Division
- Number lines
- Division
- Recognizing greatest multiples
- Expressing Hundreds as Tens
- Dividing Tens
- Dividing Tens and Ones
- Dividing Tens and Ones Word Problems
- Number Line and Negative and Positive Numbers
- Negative Numbers
- Adding Negative Numbers
- Comparing Numbers
- Adding Positive and Negative Numbers
- Adding Positive and Negative Numbers on a Number Line
- Adding numbers positive-positive, negative-negative, positive-negative, negative-positive
- Dividing by Multiples of Ten
- Dividing by ones and multiples of ten (some with remainders)
- Dividing by Numbers that are Not Multiples of Ten
- Division Word Problems
- Set of multiples of a number
- Least Common Multiple of Two Numbers
- Binary Operations on Numbers
- Complete the operation, indicate sum, difference, product, or quotient
- Find the sum, difference, product, and quotient
- Find the find the addend, factor, divisor/dividend, subtrahend/minuend
- Solve the equation, find for the variable, sum, difference, product, quotient
- Solve the Equation, Find for the Variable, Addend, Subtrahend, Factor, and Divisor
- Solve the Equation, Find for the Variable, Addend, Minuend, Factor, and Dividend
- Equal or Not Equal? (Equations)
- Commutative Law for Addition
- Associative Law for Addition
- Column Addition
- Subtraction is Not Commutative
- Is Subtraction Associative?

- Equal Fractions as in 1/2 = 2/4 with Pictures
- Equal Fractions, Find the Numerator
- Fractions, Choose Equal or Not-Equal
- Adding and Subtracting of Like Fractions
- Whole Numbers and Fractions
- Finding Mixed Numbers and Whole Numbers
- Dividing One by a Number
- Using a Ruler and the Correlation of Fractions
- Intro to Numerator/Denominator
- Give the Numerator of the Fraction
- Give the Denominator of the Fraction
- Factional parts of whole objects
- Fractional Parts of a Set of Objects
- Proper/improper fractions
- Showing Whole Numbers and Fractions on a Number Line
- Mixed Numbers
- Proper Fractions
- Is the Fraction Equal to 1?
- Comparing Fractions
- Addition of Whole Numbers and Fractions
- Some Fractions Equal Whole Numbers
- Correlation between division and fractions
- Some Fractions Equal Mixed Numbers
- Correlation between Division of Fractions and Mixed numbers
- Addition of Fractions
- Adding and Subtracting Like Fractions
- Subtracting like fractions
- Like fractions, find the missing addend, subtrahend/minuend
- Addition of Mixed Numbers
- Fraction word problems
- Adding like fractions
- Subtracting like fractions
- Adding and subtracting like fractions
- Number Line for Fractions
- Adding Fractions with a Number Line
- Subtraction of Fractions
- Subtraction of Mixed Numbers
- Subtraction of Mixed Numbers, Column Form
- Addition & Subtraction of Mixed Numbers, Word Problems
- Multiplication of Fractions
- Multiplying Fractions
- Multiplication of whole number by a fraction as addition
- Addition of three or more fractions
- Multiplying a whole number by a fraction
- Division of Fractions
- Fraction Word Problems

- Using the Drawing Interface - Deleting, Drawing Segments, Midpoints, Identifying
- Doubling Line Segments
- Lines of Symmetry in Triangles
- Other Lines of Symmetry
- Midpoints
- Definition of Plane and Space Figures
- Rectangular Prisms
- Triangular Prisms
- Pentagonal Prisms
- Hexagonal Prisms
- Right Angles
- Perpendicular Line Segments and Bisectors
- Laying Off Congruent Segments
- Perpendicular Bisectors
- Triangles
- Triangular Pyramids
- Rectangular Pyramids
- Pentagonal Pyramids
- Hexagonal Pyramids
- Parallel Lines
- Constructing Rectangles
- Constructing Squares, 1-2
- Space Figures: Spheres, Cylinders, and Cones
- Prisms and Pyramids
- Defining Volume
- Constructing Polygons
- Chords of a Circle
- Definition of Chord and Diameter

- Applications: Set Descriptions
- Union of Sets, 1-4
- Difference of Sets, 1-3
- Disjoint and Overlapping Sets, 1-3
- Intersection of Sets, 1-4
- Difference of Two Sets of Numbers
- Finite and Infinite Sets
- Sets and Members, 1-2
- Equal Sets
- Equivalent Sets
- Equal and Equivalent Sets and the Empty Set
- Element of a Set
- Subset of a Set, 1-2
- Elements and Subsets
- Set Operations, 1-6
- Inequalities and Subsets
- Set Descriptions, 1-7
- Sets of Points 1-2
- Set Operations and Set Members
- Set Descriptions and Set Operations
- Drawing Conclusions, 1-7
- Atomic and Molecular Sentences, 1-2
- Connectives, 1-2
- Conjunctions and Disjunctions, 1-2
- Antecedents and Consequents
- Conjunctions, Disjunctions, and Conditionals
- Conjunctions, Disjunctions, Conditionals, and Drawing conclusions

- Dry Measure
- Liquid Measure: Cup, Pint, Quart, Gallon
- Liquid Measure Conversion
- Weight Measure: Ounces, Pounds, Hundredweight, Tons
- Liquid Measure Word Problems
- Money: Penny, Cent, Nickel, Dime, Quarter, Half Dollar, dollar
- Money
- Money: Coin Values
- Money: More Coin Values
- Money Word Problems: Converting Colloquial Money To Decimals
- Time Zones
- Time Zones of the U.S.
- Convert 12 to 24 Hour Clock
- Comparing 12 and 24 Hour Time and Word Problems
- Rounding Measurements
- Area of a Rectangle
- Perimeters and Areas
- Perimeter and Area: Importance Of Units
- Perimeter and Area: Different Units
- Drawing to a Scale
- Temperature: Celsius Scale, Fahrenheit Scale
- Definition of Coordinate System, Coordinates, Horizontal Axis, Vertical Axis
- Ordered Pairs
- Plotting Points
- Fractions as Coordinates
- Identifying Horizontal and Vertical Lines
- Introduction and Definition of Bar Graphs
- Definition of Line Graphs

- Comparing Survey Questions 1-3
- Collecting and Representing Data 1-3
- Identifying Modes 1-3
- Identifying the Median
- Identifying Outliers
- Identifying Modes and Outliers
- Circle Graphs
- Bar Graphs
- Interpreting Line Graphs
- Probability Trees 1-4

This course requires a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Note that many tablets or handhelds (particularly the iPad) do not support Flash and cannot view the lessons.

Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course requires the Java Runtime Environment. In general, only standard desktop and laptop computers can run Java applets; most tablets, handhelds or consoles cannot. Some netbooks (such as the Chromebook) also do not support Java; please check before considering one for this course.

Your browser will need to allow javascript, login cookies, and popup windows from ctyjhu.org, stanford.edu, and any other course web sites.

This course does __not__ run on a Google Chromebook or iPad.