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Honors Grade 5 Mathematics

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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 honors mathematics curriculum and is aligned with the Common Core Standards. This course 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.

This course has synchronous virtual class meetings, but participation is optional. Students may also schedule one-on-one virtual meetings directly with the instructor to answer questions or concerns. View the Help Room schedule on this webpage for class meeting times. Meetings will be recorded for students who are unable to attend due to scheduling conflicts.

Terms and Conditions

Virtual classrooms, and student activities in the classroom, may be recorded and added to the course as an ongoing asset for all class students to review. Students may be invited to interact in CTY community spaces that include students and instructors and potentially specially invited guests that are not enrolled in their course. Student contributions (e.g., projects, forum posts, etc.) may remain in the course after the student completes the course. These artifacts may be preserved to showcase student work or to continue important conversations.

Topics include:

  • whole numbers and patterns
  • introduction to algebraic variables and expressions
  • decimals
  • fractions
  • operations with fractions
  • percents
  • data displays
  • geometric relationships
  • 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

Arithmetic Review

  • Estimating with Whole Numbers
  • Properties and Reasoning Methods
  • Multiplication and Division
  • Adding and Subtracting Decimals

Operations and Patterns

  • Exponents
  • Comparing Numbers
  • Order of Operations
  • Patterns and Sequences
  • Greatest Common Factor (GCF)
  • Least Common Multiple (LCM)

Introduction to Algebra

  • Variables and Expressions
  • Translate Between Words and Math
  • Translating Between Tables and Expressions
  • Equations and Their Solutions

Integers and the Coordinate Plane

  • Introduction to Integers
  • Integers in Real-World Situations
  • Comparing and Ordering Integers
  • The Coordinate Plane
  • Patterns in the Coordinate Plane

Fractions and Mixed Numbers

  • Adding and Subtracting Mixed Numbers
  • Regrouping to Subtract Mixed Numbers
  • Real World Fraction Operations: Addition and Subtraction
  • Multiplying Fractions and Whole Numbers
  • Multiplying Mixed Numbers
  • Dividing Fractions and Mixed Numbers
  • Real World Fractions Operations: Multiplication and Division


  • Rounding and Estimating Decimals
  • Multiplying Decimals
  • Dividing Decimals by Whole Numbers
  • Dividing Decimals
  • Converting Fractions and Decimals


  • Percents
  • Percents, Decimals, and Fractions
  • Estimating with Percents
  • Finding Percents

Data Display

  • Line Plots
  • Stem-and-Leaf Plots
  • Circle Graphs
  • Line Graphs
  • Choosing an Appropriate Display


  • Classifying Triangles
  • Classifying Quadrilaterals
  • Congruent Figures
  • Perimeter and Circumference
  • Three-Dimensional Figures
  • Volume
  • Volume of Prisms

Probability and Competitive Math

  • Introduction to Probability
  • Counting Methods and Sample Spaces
  • Theoretical Probability
  • Competitive Math Sample Problems

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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. 

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 which can be used for instructor-student communication if the student has any questions about the course or curriculum. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students will need a computer with the Zoom desktop client installed to watch any 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.