Skip Navigation

We are unable to take calls at this time, though your questions are important to us. Please send them to for the quickest response. Thank you.

Honors Grade 5 Mathematics

Arrow image that is used as button to enroll in courses. Enroll in this Course

Eligibility: CTY-level or Advanced CTY-level math score required

Prerequisites: Successful completion of Grade 4 Mathematics or equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: One academic year

Course Code: HG5

Course Description


The sequence covers concepts typically offered in a full-year in an honors mathematics curriculum and is aligned with the Common Core Standards. This course, drawing on software provided by Thinkwell, covers a full-year honors curriculum and prepares students for success in Honors Grade 6 Mathematics. This course begins with a review of grade 4 concepts. The course is equivalent to a full year of mathematics.

Online course materials, such as videos, notes, interactive web pages, and practice problems with solutions, are provided for the student. Students progress through the course at their own pace and are expected to watch videos and review notes regularly. Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructors via email with any questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include homework, chapter exams, and a cumulative midterm and final.

Instructors use virtual classroom software allowing video, voice, text, screen sharing, and whiteboard interaction. Students are strongly encouraged to work on the course at least 1 hour a day, 5 days a week (for a 6-month enrollment), and email their instructors at least once per week.

Topics include:

  • whole numbers and patterns
  • introduction to algebraic variables and expressions
  • decimals
  • number theory
  • fractions
  • operations with fractions
  • data displays
  • proportional relationships
  • geometric relationships
  • measurement
  • area and volume
  • integers and the coordinate plane
  • probability

For a detailed list of topics, click the "List of Topics" tab.

Materials Needed

There are no required materials for this course.

List of Topics

Whole Numbers and Patterns

  • Comparing and Ordering Whole Numbers
  • Estimating with Whole Numbers
  • Exponents
  • Order of Operations
  • Properties and Reasoning Methods
  • Patterns and Sequences

Introduction to Algebra

  • Variables and Expressions
  • Translate Between Words and Math
  • Translating between Tables and Expressions
  • Equations and their Solutions
  • Addition Equations
  • Subtraction Equations
  • Multiplication Equations
  • Division Equations


  • Representing, Comparing, and Ordering Decimals
  • Rounding and Estimating Decimals
  • Adding and Subtracting Decimals
  • Multiplying Decimals
  • Applying Exponents: Scientific Notation
  • Dividing Decimals by Whole Numbers
  • Dividing by Decimals
  • Solving Decimal Equations

Number Theory and Fractions

  • Divisibility
  • Factors and Prime Factorization
  • Greatest Common Factor
  • Decimals and Fractions
  • Equivalent Fractions
  • Mixed Numbers and Improper Fractions
  • Comparing and Ordering Fractions
  • Adding and Subtracting with Like Denominators
  • Estimating Fraction Sums and Differences

Operations with Fractions

  • Least common Multiple
  • Adding and Subtracting with Unlike Denominators
  • Adding and Subtracting Mixed Numbers
  • Regrouping to subtract Mixed Numbers
  • Solving Fraction Equations: Addition and Subtraction
  • Multiplying Fractions by Whole Numbers
  • Multiplying Fractions
  • Multiplying Mixed Numbers
  • Dividing Fractions and Mixed Numbers
  • Solving Fraction Equations: Multiplication and Division

Data Displays

  • Measures of Central Tendency
  • Frequency Tables, Stem-and –Leaf Plots, and Line Plots
  • Bar Graphs and Histograms
  • Line Graphs
  • Misleading Graphs
  • Choosing an Appropriate Display

Proportional Relationships

  • Ratios and Rates
  • Applying Rates and Ratios
  • Proportions
  • Similar Figures
  • Indirect Measurement
  • Scale drawings and Maps
  • Percents
  • Percents, Decimals, Fractions
  • Percent Problems
  • Using Percents

Geometric Relationships

  • Points, Lines, and Planes
  • Measuring and Classifying Angles
  • Angle Relationships
  • Classifying Lines
  • Triangles
  • Quadrilaterals
  • Polygons
  • Geometric Patterns
  • Congruent Polygons
  • Transformations
  • Line Symmetry


  • Understanding Customary Units of Measure
  • Understanding Metric Units of Measure
  • Converting Customary Units
  • Converting Metric Units
  • Time and Temperature
  • Finding Angle Measures in Polygons
  • Perimeter
  • Circles and Circumference

Area and Volume

  • Area of Rectangles and Parallelograms
  • Area of Triangles and Trapezoids
  • Area of Composite Figures
  • Changing Dimensions
  • Area of Circles
  • Three-Dimensional Figures
  • Volume of Prisms
  • Volume of Cylinders
  • Surface Area

Integers and the Coordinate Plane

  • Integers in Real-World Situations
  • Comparing and Ordering Integers
  • The Coordinate Plane
  • Adding Integers
  • Subtracting Integers
  • Multiplying Integers
  • Dividing Integers
  • Solving Integer Equations


  • Introduction to Probability
  • Experimental Probability
  • Counting Methods and Sample Spaces
  • Theoretical Probability
  • Compound Events
  • Making Predictions

Back to top

Elementary Math Help Room Grades 5 and 6

Help Room

Each week, all students are invited to an open Elementary Math Help Room for Grades 5 and 6 run by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week.

Grades 5 and 6 meet each Thursday from 7–8 p.m. E.T. 

Sample Video

Sample Video

Honors Grade 5 sample video


Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

Zoom online virtual classroom
This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students who are unable to attend live sessions will need a computer with the Zoom desktop client installed to watch recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.

This course uses Respondus LockDown Browser proctoring software for designated assessments. LockDown Browser is a client application that is installed to a local computer. Visit the Respondus website for system requirements.

While Chromebook can be used to progress through the course, all exams must be completed on a PC or Mac.