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Honors Grade 5 Mathematics

Prerequisites: Qualifying math score and completion of Grade 4 mathematics or the equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Course Code: HG5

Course Description


The sequence covers concepts typically found 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 Pre-algebra. This course begins with a review of grade 4 concepts. The course is equivalent to a full year of mathematics.

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
  • Choose the Method of Computation
  • 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

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Elementary Math Help Room

Help Room

Each week, all students are invited to an open Elementary Math Help Room 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.

The Elementary Math Help Room meets each Tuesday from 7 – 8 p.m. ET. 

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.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.