5th Grade Math

Is your fifth grader on track with math? Discover fifth grade math topics, browse curriculum, learn about state tests, identify grade-level vocabulary, and see the best ways to teach fifth grade math right here with this comprehensive guide to all things 5th grade math. 

Fifth Grade Math Curriculum

Find complete fifth grade math curriculum with these five trusted options. Each option below has everything that you need for an entire school year math for 5th graders, including  instruction and practice. 

While these programs are based on standard 5th grade expectations, every child learns at a unique pace, so be sure to use the math placement tests to determine the best fit for each particular program.

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    Math-U-See Epsilon

Horizons 5 Program

In the fifth grade level of Horizons, students 

  • write simple ratios
  • add and subtract fractions with uncommon denominators
  • use a compass and protractor
  • calculate probability with one variable
  • understand percentages
  • recognize place value to a hundred billion

Horizons uses colorful illustrations and systematic review to make sure your student has a complete understanding of the concepts listed above. 

Horizons uses a spiral approach—concepts are introduced, practiced that day, and then the rest of the day is a review of previously covered concepts. Math topics periodically surface in the daily work so that the student has the opportunity to practice them over and over. 

Singapore 5A/5B Program

The main feature of Singapore 5th grade math series is the use of the three part approach:

Concrete Pictorial Abstract
Concrete → Pictorial → AbstractConcrete → Pictorial → Abstract

Instruction moves from concrete objects to pictures of objects and finally to abstractions (numerals). This systematic approach makes math meaningful and encourages active thinking.  process, communication of mathematical ideas and problem solving. This helps develop the foundation students will need for more advanced mathematics.

Singapore fifth grade math is a mastery-based curriculum. Unlike a spiral approach with lots of review, with a mastery approach, review is limited. Each lesson builds on the past lessons with the expectation that the student has mastered previous concepts. 

Singapore fifth grade curriculum includes suggestions for enrichment and mental math exercises. The workbook exercises are brief but have a heavy focus on solving word problems that make math relatable to the everyday world.

Saxon 6/5 Program

Combined with the teaching and resources of the included DIVE CD, Saxon 6/5 is a great math program for reluctant math learners as well as those who pick up on concepts easily. The spiral approach ensures that struggling students keep pace with the core concepts. Thus, Saxon is a strong choice for students with learning disabilities.

In each Saxon 6/5 lesson, students are introduced to a new topic, do practice problems using the new skill, then spend the remainder of the day practicing skills from previous lessons. 

Math U See Epsilon

Math U See is an innovative approach to not only learning how to do math but understanding how math works. Using hands-on and visual methods, the Epsilon level for fifth grade walks your student through the world of fractions. Each lesson takes approximately a week to complete and contains

  • a short teaching video, watched by both parent and student
  • worksheets to practice the concept
  • a short test to demonstrate mastery
  • a worksheet of review from previous lessons

Right Start Math Level F

Right Start Math is a unique program that heavily uses an abacus and games to deepen the student’s understanding of math. Because of this one-of-a-kind approach, a parent will rely heavily on the teacher’s manual for direction. At Level F for fifth grade, the program has a heavy emphasis on mental math and student-led discovery. Students complete worksheets after each lesson has been taught. 

5th Grade Math Topics, Materials, Supplements & Manipulatives

If you’re not looking for a complete math program, instead supplement your child's education with 5th grade math worksheets, 5th grade math books, math games, individual workbooks, and more extras to strengthen your child's skills.

Intermediate Series Life of Fred Books

Life of Fred uses a fun, lighthearted story approach to mathematics. A student ready for 5th grade math should start with Life of Fred: Kidneys followed by Liver, and finally Mineshaft. These hardcover books will help students master fractions, unit conversions, volume, perimeter, exponents, and more. 

As a perk, Life of Fred at this level offers instruction for practical daily life skills including check writing, grammar rules, and figuring sale prices—all with no boring drill-and-kill worksheets. Each book contains problems for the student to complete on a separate piece of paper and should take about 4 to 6 weeks to complete.

MathTacular 3

If your student needs reinforcement in multiplication, division, factors, money, or fractions,MathTacular DVDs (and digital access!) are a unique way to review. Join Professor Justin as he makes math more understandable through short and quirky lessons. Each video includes word problems with solutions. The included workbook provides opportunities to use the math concepts covered in the videos to solve similar problems. 

  • MathTacular 3 contains over four hours of real-world math.
  • MathTacular 4 gives your student the tools to crack the code of word problems. 

Math Adventures Grade 5 Spy School

Math Adventures is a consumable workbook series that helps your child discover math in everyday life. In Grade 5 Spy School you’ll practice math fact fluency, fractions, and logic skills by solving mysteries. Students won’t even know they are learning as they take this adventure.

Fifth Grade Math Worksheets

Sample fifth grade math worksheets with these PDFs from Horizons 5:

Horizons 5 Surface Area WorksheetHorizons 5 Surface Area Worksheet

Worksheet 3

Surface Area

Horizons 5 Probability WorksheetHorizons 5 Probability Worksheet

Worksheet 4


Fifth Grade Math Lessons

Take a peek at fifth grade math lessons with these samples:

  1. Right Start Math Level F Fifth Grade Sample Lessons
  2. Saxon 6/5 Fifth Grade Sample Lessons: page 1 & page 2
  3. Singapore 5A/5B Fifth Grade Sample Lessons

Charts of Key Fifth Grade Math Formulas

Geometric Formulas

Perimeter of rectangle

2l + 2w = P

Perimeter of rectangle geometric formulaPerimeter of rectangle geometric formula
Perimeter of square

4s = P

Perimeter of square geometric formulaPerimeter of square geometric formula
Circumference of circle

2πr = C or πd = C

Circumference of circle geometric formulaCircumference of circle geometric formula
Area of rectangle

lw = A

Area of rectangle geometric formulaArea of rectangle geometric formula
Area of square

s2 = A

Area of square geometric formulaArea of square geometric formula
Area of triangle

½ bh = A

Area of triangle geometric formulaArea of triangle geometric formula
Area of circle

πr2 = A

Area of circle geometric formulaArea of circle geometric formula
Volume of rectangular prism

lwh = V

Volume of rectangular prism geometric formulaVolume of rectangular prism geometric formula

Fifth Grade Conversion Factors


12 inches = 1 foot

3 feet = 1 yard

5,280 feet = 1 mile

10 millimeters = 1 centimeter

100 centimeters = 1 meter

1,000 meters = 1 kilometer


8 fl oz = 1 cup

2 cups = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

10 milliliters = 1 centiliter  

100 centiliters = 1 liter

1,000 liters = 1 kiloliter


16 oz = 1 pound

2, 000 pounds = 1 ton

10 milligrams = 1 centigram

100 centigrams = 1 gram 

1,000 grams = 1 kilogram


60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

7 days = 1 week

52 weeks = 1 year = 365 days

5th Grade Geometric Formulas and Imperial Measurement Conversion Factors5th Grade Geometric Formulas and Imperial Measurement Conversion Factors

Fifth Grade Math: Problems & Equations

Fifth grade math problems include all of these varied topics:

  • Recognizing and Generating Equivalent Fractions
  • Adding and Subtracting Fractions, Mixed Numbers, and Decimals
  • Finding Common Factors
  • Order of Operations
  • Finding the Area of Circles and Triangles
  • Classifying 4-Sided Figures (Quadrilaterals)
  • Representing Fractions on Number Lines
  • Using Coordinates to Graph Ordered Relationships
  • Multiplying and Dividing by 10s, 100s, or 1000s
  • Ratios
  • Finding Unknown Angles
  • Percents and Rates
  • Tessellations
  • Volume of Solids
  • Statistics and Probability
  • Negative Numbers
  • Multiplying and Dividing Fractions and Decimals
  • Exponents
  • Factoring
  • Long Division
  • Negative Numbers

These concepts should not only be mastered in math for 5th graders, but also applied in 

  • Multi-Step Problem Solving
  • Interpreting and Solving Word Problems
  • Mental Math

Fifth Grade Math: Numbers & Operations

Establishing fluency with fractions and decimals is a huge portion of fifth grade numbers and operations. You can see great detail of the kinds of strategies and example problems for this grade level on the Common Core website

Fifth graders should be able to work problems with fractions as well as set up problems from real world situations and word problems. For example, see this test on simplifying improper fractions taken from Saxon Math 6/5.

Fifth Grade Math: Fractions & Decimals

Fifth graders need to master

  • decimal place value
  • adding and subtracting decimals
  • adding and subtracting fractions
  • multiplying and dividing decimals
  • multiplying and dividing fractions

These concepts are introduced as early as fourth grade and will be repeated again in sixth grade.

Along with these computational skills, it’s important for fifth graders to grasp the relationship between fractions and decimals—they are two ways to represent the same values. Plotting both fractions and decimals on a single number line is a valuable way to visually represent the values. 

Use a number line to help students see the relationship relationship between fractions and decimalsUse a number line to help students see the relationship relationship between fractions and decimals

Fifth Grade Math Standards

You can read the Common Core Standards for 5th grade here. For the 9 states that haven’t adopted state standards, check with their state boards of education websites for their particular 5th grade math standards.

If meeting Common Core standards is important to you, choose from:

Both of these programs do cover the standards, albeit in a slightly different order than outlined in Common Core. In other words, a certain topic may be assigned to 5th grade in Common Core but is covered in 3rd or 1st grade in one of the programs above. 

Fifth Grade Math State Tests

If your child is in public school, you can expect your fifth grader to take a standardized test in math. The 2015 Every Student Succeeds Act (ESSA) requires states to test students in math and language arts each year for grades 3-8. While each state can set their own standards and compose their own tests, the ESSA dictates that they be “challenging.” 

In some states, this testing requirement carries over to homeschoolers as well. 

If your child is using and seeing success with any solid fifth grade math curriculum (like those shown and described above) the fifth grade math state tests should pose no problem. If you do find gaps in understanding, you can meet those with supplements and extra practice.  

Find out what your particular state does in terms of fifth grade math testing by visiting your state’s department of education website. The U.S. Department of Education has all of those links mapped out for you.

Fifth Grade Math Vocabulary

Here’s a list of common vocabulary words covered in math for 5th graders:

  • Sequences
  • Numerator
  • Denominator
  • Whole Numbers
  • Improper Fractions
  • Mixed Numbers
  • Place value
  • Number lines
  • Tally marks
  • Quotient
  • Remainder
  • Least Common Multiple
  • Greatest Common Factor
  • Least Common Denominator
  • Volume
  • Quadrilaterals
  • Area
  • Perimeter
  • Composite Number
  • Prime Number
  • Line Plots
  • Coordinates
  • Coordinate Plane
  • Mean
  • Median
  • Mode
The G Family, Sonlighters from Flint, TXThe G Family, Sonlighters from Flint, TX
The G Family, Sonlighters from Flint, TX

Fifth Grade Math FAQ

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