Academic standards list

5th Grade — Mathematics


Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

Operations & Algebraic Thinking

Write and interpret numerical expressions.
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express
Analyze patterns and relationships.
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting

Number & Operations in Base Ten

Understand the place value system.
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the
Read, write, and compare decimals to thousandths.
     There are 2 components within this standard.
Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Fluently multiply multi-digit whole numbers using the standard algorithm.
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of

Number & Operations - Fractions

Use equivalent fractions as a strategy to add and subtract fractions.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
     There are 2 components within this standard.
Interpret multiplication as scaling (resizing), by:
     There are 2 components within this standard.
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
     There are 3 components within this standard.

Measurement & Data

Convert like measurement units within a given measurement system.
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these
Represent and interpret data.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
     There are 2 components within this standard.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
     There are 3 components within this standard.


Graph points on the coordinate plane to solve real-world and mathematical problems.
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of
Classify two-dimensional figures into categories based on their properties.
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all
Classify two-dimensional figures in a hierarchy based on properties.
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