Grade 5 Common Core Standards for
Mathematics
The Common Core State Standards provide
a consistent, clear understanding of what students are expected
to learn, so teachers and parents know what they need to do to
help them. The standards are designed to be robust and relevant
to the real world, reflecting the knowledge and skills that our
young people need for success in college and careers. With
American students fully prepared for the future, our communities
will be best positioned to compete successfully in the global
economy. 
In Grade 5, instructional time should focus on three critical areas: (1)
developing fluency with addition and subtraction of fractions, and
developing understanding of the multiplication of fractions and of
division of fractions in limited cases (unit fractions divided by whole
numbers and whole numbers divided by unit fractions); (2) extending
division to 2digit divisors, integrating decimal fractions into the
place value system and developing understanding of operations with
decimals to hundredths, and developing fluency with whole number and
decimal operations; and (3) developing understanding of volume.

1. Students apply their understanding of fractions and fraction
models to represent the addition and subtraction of fractions with
unlike denominators as equivalent calculations with like
denominators. They develop fluency in calculating sums and
differences of fractions, and make reasonable estimates of them.
Students also use the meaning of fractions, of multiplication and
division, and the relationship between multiplication and division
to understand and explain why the procedures for multiplying and
dividing fractions make sense. (Note: this is limited to the case of
dividing unit fractions by whole numbers and whole numbers by unit
fractions.)

2. Students develop understanding of why division procedures work
based on the meaning of baseten numerals and properties of
operations. They finalize fluency with multidigit addition,
subtraction, multiplication, and division. They apply their
understandings of models for decimals, decimal notation, and
properties of operations to add and subtract decimals to hundredths.
They develop fluency in these computations, and make reasonable
estimates of their results. Students use the relationship between
decimals and fractions, as well as the relationship between finite
decimals and whole numbers (i.e., a finite decimal multiplied by an
appropriate power of 10 is a whole number), to understand and
explain why the procedures for multiplying and dividing finite
decimals make sense. They compute products and quotients of decimals
to hundredths efficiently and accurately.

3. Students recognize volume as an attribute of threedimensional
space. They understand that volume can be measured by finding the
total number of samesize units of volume required to fill the space
without gaps or overlaps. They understand that a 1unit by 1unit by
1unit cube is the standard unit for measuring volume. They select
appropriate units, strategies, and tools for solving problems that
involve estimating and measuring volume. They decompose
threedimensional shapes and find volumes of right rectangular
prisms by viewing them as decomposed into layers of arrays of cubes.
They measure necessary attributes of shapes in order to determine
volumes to solve real world and mathematical problems.
Grade 5 Overview

Operations and Algebraic Thinking

Write and interpret numerical expressions.

Analyze patterns and relationships.

Number and Operations in Base Ten

Understand the place value system.

Perform operations with multidigit whole numbers and with
decimals to hundredths.

Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract
fractions.

Apply and extend previous understandings of multiplication and
division to multiply and divide fractions.

Measurement and Data

Convert like measurement units within a given measurement
system.

Represent and interpret data.

Geometric measurement: understand concepts of volume and relate
volume to multiplication and to addition.

Geometry

Graph points on the coordinate plane to solve realworld and
mathematical problems.

Classify twodimensional figures into categories based on their
properties.

Mathematical Practices

1. Make sense of problems and
persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of
others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.