Academic standards list

Fifth 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 and Algebraic Thinking

Write and interpret numerical expressions.
Use parentheses and/or brackets in numerical expressions and evaluate expressions having these symbols using the conventional order (Order of Operations).  
Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them.  
Analyze patterns and relationships.
Generate two numerical patterns using two given rules.  
     There are 2 components within this standard.

Number and 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 what it
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 decimal
Read and write decimals to thousandths using standard form, word form, and expanded form (e.g., the expanded form of 347.392 is written as 3 x 100 + 4 x 10
Round decimals to the nearest hundredth, tenth, or whole number using understanding of place value.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Fluently multiply multi-digit whole numbers (up to three-digit by four-digit factors) using appropriate strategies and algorithms.
Find whole-number quotients and remainders of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value,
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. (See Table 1 - Addition and Subtraction Situations for whole number situations that can...
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to
Solve contextual problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark
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). For example, 3/4 = 3 ÷ 4 so when 3 wholes are shared equally
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction by a fraction.
     There are 2 components within this standard.
Interpret multiplication as scaling (resizing).
     There are 2 components within this standard.
Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
     There are 3 components within this standard.

Measurement and Data

Convert like measurement units within a given measurement system from a larger unit to a smaller unit.
Convert customary and metric measurement units within a single system by expressing measurements of a larger unit in terms of a smaller unit. 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 problems  
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 volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units.
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms.
     There are 3 components within this standard.


Graph points on the coordinate plane to solve real-world and mathematical problems.
Graph ordered pairs and label points using the first quadrant of the coordinate plane. Understand in the ordered pair that the first number indicates the  
Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in  
Classify twodimensional figures into categories based on their properties.
Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also  
♦  Academic Standards marked with a diamond are "Supporting Content" within the grade level or course.
Disclaimer: This website provides a reference tool for browsing academic standards and locating associated resources. We are not the originator of these academic standards. Although we strive to maintain accuracy, there may be revisions, updates, or errors within the text and structure of the information displayed. In case of any discrepancy, please respect the originator's published version ( as the definitive record.