5th Grade Math Common Core Standards

If your state participates in the Common Core initiative you may be wondering: What are the 5th-grade math Common Core standards, and how can you make sure your child is on track? In the article, we outline the 5th grade common core math standards.

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Author
Amber Watkins

Published
November 3, 2023

4th Grade Math Problems

This comprehensive review of math problems for 4th graders is just the boost your child needs to succeed in math this year.

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Author
Amber Watkins

Published
Oct 19, 2023

4th Grade Math Problems

This comprehensive review of math problems for 4th graders is just the boost your child needs to succeed in math this year.

headshot of amber watkins #2

Author
Amber Watkins

Published
Oct 19, 2023

Key takeaways

  • 5th-grade math Common Core standards aim to help your child become skilled in using multi-digit numbers, decimals, fractions, and measurement conversions to solve real-world problems.
  • There are many online tools available to help your child master these 5th-grade Common Core math standards including online math worksheets, math games, and interactive math apps.

The Common Core State Standards Initiative, also known as Common Core, was created to ensure students in varying states are receiving a standard math education. Although 5th-grade math standards vary by state and school, the majority of the country has adopted Common Core. 

As a parent, you may be wondering: “What are the 5th-grade math Common Core standards and what tools are available to help my child master these objectives?” In this article, we outline the 5th grade math standards for Common Core with examples of each objective so you feel confident about where your child stands.

The 5th Grade Common Core Math Standards consist of five overarching standards with various math skills your 5th-grader is expected to master under each. The five Common Core math standards for 5th grade are as follows:

  • Operations and Algebraic Thinking
  • Numbers and Operations in Base 10
  • Numbers and Operations- Fractions
  • Measurement & Data
  • Geometry


Let’s dive into these standards to better understand what they mean and what skills they entail.

5th Grade Math Common Core Standards

Operations and Algebraic Thinking

This 5th-grade Common Core math standard ensures sure your child:

  1. Can write numerical expressions and interpret them.

    Numerical expressions are math sentences that include numbers and operations. For example 4 + 7 x 2 is a numerical expression. 

  2. Analyze and create mathematical patterns and relationships.

    This includes being able to create a pattern starting at a certain number and increasing by a
    certain rate and comparing that pattern to others.

Example Problems for Operations and Algebraic Thinking

Write and Interpret Numerical Expressions

Write Simple Expressions without Interpreting them

  • Write an expression to show six plus two minus five.
    • Answer: 6 + 2 – 5
  • Write an expression to show eight divided by four.
    • Answer: 8 – 3 + 9


Use Brackets, Parenthesis, and Braces in a Numerical Expression

  • Write an expression with brackets to represent three plus two times six. 
    • Answer: (3 + 2) 6
  • Write an expression with parentheses to represent seven minus four times ten. 
    • Answer: (7 – 4) 10


Evaluate Expressions with Brackets, Parenthesis, and Braces

  • What is the expression (10 – 3) 12 equal to?
    • Answer: 84
  • Solve the expression 4 (2 + 5).
    • Answer: 28


Prime Factorization (Representing Composite Numbers by multiplying Prime Numbers)

  • What is the prime factorization of 24? 
    • Answer: 3 x 2 x 2 x 2 
  • What is the prime factorization of 35? 
    • Answer: 5 x 7

Analyze mathematical patterns

Analyze mathematical patterns with numbers

  • Starting with the number 0, create a number pattern that increases by 3. 
    • Answer: 0, 3, 6, 9, 12
  • Starting with the number 0, create a number pattern that increases by 4. 
    • Answer: 0, 4, 8, 12, 16 

Compare mathematical patterns with numbers

  • Start with the number 0 and add 4 to create a number pattern, then start with the number 0 and add 8 to create a number pattern. Does the pattern double or triple? 
    • Answer: The pattern doubles. 
  • Start with the number 0 and add 3 to create a number pattern, then start with the number 0 and add 9 to create a number pattern. Does the pattern double or triple? 
    • Answer: The pattern triples.

Number and Operations in Base 10

This 5th-grade common core math standard ensures your child: 

  1. Understands the value of each digit with the Base 10 math concept.


Base 10
for fifth grade describes each digit in a number as being worth 1/10 the number to the left and ten times the number to its right. This helps your child understand place values.

  1. Can read, compare, and write decimals to the thousands place using the greater than, less than, or equal to symbols: > , < , or = .
  2. Can round decimals to any place: tenths, hundredths, and thousandths.
  3. Can perform basic operations with multi-digit whole numbers and decimals (up to the hundreds place). 

Example Problems for Numbers and Operations in Base 10

Understand Place values 

Place Value Chart

  • Place the number 362.46 in a place value chart [Insert image of 362.46 in a place value chart].
  • Which digit in 23.465 is in the hundredths place? 


Read, Compare, and Write Decimals


Compare Decimals

  • Use > , < , or = in the expression .465 ____ .460. Write Decimals using Base 10 Numerals and Expanded Form
  • Write the number 245.32 using Base 10 Numerals and Expanded Form: 
    • Answer: 2 x 100 + 4 x 10 + 5 x 1 + 3 x 1/10 + 2 x 1/100 
  • Write the number 622.45 using Base 10 Numberals and Expanded Form: 
    • Answer: 6 x 100 + 2 x 10 + 2 x 1 + 4 x 1/10 + 5 x 1/100 


Round Decimals Using Place Value


Round Decimals to the Place Value

  • Round 6.538 to the nearest hundredths place. 
    • Answer: 6.54
  • Round 7.544 to the nearest hundredths place
    • Answer: 7.54


Perform Basic Operations with Whole Numbers and Decimals


Add and Subtract Whole Numbers and Decimals

  • Find the sum of 225.62 + 119.3 = 
    • Answer: 344.92
  • Find the difference between 64.2 – 13.9 = 
    • Answer: 50.3


Multiply and Divide Whole Numbers and Decimals

  • Find the product of 365 x 429 = 
    • Answer: 156,585
  • Find the Quotient of 12.9 / 3=
    • Answer: 4.3

Numbers and Operations-Fractions

This 5th-grade common core math standard ensures your child can:

 

  1. Understand fraction equivalence to add and subtract fractions with different denominators.

For example, ½ and ¼ can’t be added as they are because they have different denominators. If you use the fraction equivalent to 1/2, which is 2/4 then you can add 2/4 + ¼.

  1. Apply basic operations to multiply fractions and whole numbers.
  2. Solve real-world word problems with mixed numbers or fractions as answers.

Example Problems for Numbers and Operations-Fractions:

Using Understanding of Fraction Equivalence

Use Equivalent Fractions to Add Fractions with Different Denominators

  • Add ⅕ + 2/10
    • Answer: 4/10 (Explanation: ⅕ is equal to 2/10. So, 2/10 + 2/10 = 4/10.)

  • Add ¼ + 2/25
    • Answer: 33/100 (Explanation: ¼ is equal to 25/100 and 2/25 is equal to 8/100. So, 25/100 + 8/100 = 33/100.)

Use Fraction Equivalence to Solve Real-world Word Problems

  • If Tiffany ate ⅓ of the pizza pie and Frank ate 2/6 of the pie. How much pizza is left over? 
    • Answer: 2/6 (Explanation: ⅓ is equal to 2/6. 2/6 + 2/6 = 4/6. 6/6 – 4/6 = 2/6 of the pie is left over.)

  • Jan, Max, and Ethan run a mile relay race. If Jan runs ¼ of the mile. Max runs ½ of the mile. How much of the mile does have to run to finish the race?
    • Answer: Ethan has to run ¼ of a mile to finish the race. Explanation: ½ is equal to 2/4. 2/4 + ¼ is ¾. 4/4 – ¾ = ¼ of the mile left.


Apply Basic Operations to Multiply Fractions and Whole Numbers


Interpret Fractions as being Equal to the Numerator Divided by Denominator

  • What is 20/10 equal to?
    • Answer: 2
  • What is 28/4 equal to? 
    • Answer: 7 


Multiply Whole Numbers by Fractions

  • What is 10 x ½? 
    • Answer: 5
  • What is 25 x ⅕ ?
    • Answer: 5

Mixed Numbers and Fractions

Solve Word Problems with answers as Mixed Numbers and Fractions
 

  • Corey is baking three cakes for the school’s bake sale. If each cake recipe requires ½ cup of sugar. How much sugar will Corey use in all? Answer: 1 ½ cups of sugar
  • Jenny is running ⅓ of a mile every day this week to train for a marathon. After 7 days, how many total miles will she have run? Answer: 2 ⅓ miles 

Measurement and Data

This 5th-grade common core math standard ensures your child can:

  1. Convert different units of measurement. 
  2. Solve real-world math problems involving measurement and conversions.
  3. Interpret and represent data on graphs and line plots using fractions. 

Example Problems for Measurement and Data

Convert Standard Units of Measurement

Understand and Convert Units of Measurement

  • Convert 6.4 cm to ____ mm.  

 

Use the four operations (Adding, Subtracting, Multiplying, Dividing) to solve word problems measurement

  • Alex drinks 2 liters of water each day. How many total ounces will he have had after one week?

 

Represent Data

Solve measurement problems involving Line Plots

  • Use the line plot to answer the following question. Four students used ⅜ oz of glue to make slime. How many total ounces of glue did those four students use? Answer: 1 ½ ounces of glue: ⅜ + ⅜ + ⅜ + ⅜ = 12/8 or 1 ½

  • Use the line plot to answer the following question. Three students used 5/8 oz of glue to make slime. How many total ounces of glue did those four students use?  Answer: 1 ⅞ ounces of glue: ⅝ + ⅝ + ⅝ = 15/8 = 1 ⅞

Geometry

This 5th-grade common core math standard ensures your child can:

  1. Understand how to find the volume of an object and how it relates to addition and multiplication.
  2. Graph points on a coordinate plane. 
  3. Categorize shapes based on their characteristics.

Example Problems for Measurement and Data

Finding Volume Using Multiplication

  • Find the volume of a cube that has 4cm height, 4cm width, and 4cm length. 
    • Answer: 4 x 4 x 4 = 64 cubic cm

  • Find the volume of a cube that has 6 cm height, 6 cm width, and 6 cm length. 
    • Answer: 6 x 6 x 6 = 216 cubic cm


Graphing points on a Graph

Identify Points on a Coordinate Plane

Categorizing Shapes Based on Characteristics

How do 5th Grade Math Standards Vary by State?

Currently, 42 states follow 5th-grade math common core standards. However, there are eight states that don’t use Common Core standards at all. Those states include Texas, Virginia, Nebraska, Alaska, South Carolina, Arizona, Oklahoma, and Indiana which follow their own 5th-grade math standards. 

What Should Kids Know in Math by the End of 5th Grade?

By the end of 5th grade, students should know how to write expressions, solve problems that use decimals and fractions, convert units of measurement, and find the volume of different objects – 5th grade Common Core Math Standards cover each of these topics.

Where Can You Practice 5th-Grade Math Concepts?

Excellent ways to practice math include taking practice 5th-grade math tests, downloading free 5th-grade math worksheets, and playing online math games. Students can alway make practicing 5th-grade math fun by using a math app like DoodleMath.

FAQs About 5th Grade Math

A 5th grader should know how to write numerical expressions, used mixed numbers and fractions in real-world problems, and convert units of measurement. 

Common core 5th-grade math focuses on understanding place values of decimals, fraction equivalence, converting units of measurement, and geometry. 

Group 208

Lesson credits

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Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

headshot of amber watkins #2

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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