Academic standards list

Fourth 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

Use the four operations with whole numbers to solve problems.
Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5).
Multiply or divide to solve contextual problems involving multiplicative comparison, and distinguish multiplicative comparison from additive comparison.
Solve multi-step contextual problems posed with whole numbers and having whole-number answers using the four operations, including problems in which
Gain familiarity with factors and multiples.
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given  
Generate and analyze patterns.
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For   

Number and Operations in Base Ten

Generalize place value understanding for multidigit whole numbers.
Recognize that in a multi-digit whole number (less than or equal to 1,000,000), a digit in one place represents 10 times as much as it represents in the
Read and write multi-digit whole numbers (less than or equal to 1,000,000) using standard form, word form, and expanded form (e.g. the expanded form of
Round multi-digit whole numbers to any place (up to and including the hundred-thousand place) using understanding of place value.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Fluently add and subtract within 1,000,000 using appropriate strategies and algorithms.
Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of

Numbers and Operations- Fractions

Extend understanding of fraction equivalence and comparison.
Explain why a fraction a/b is equivalent to a fraction (axn)/(bxn) or (a/n)/(b/n) by using visual fraction models, with attention to how the number and size
Compare two fractions with different numerators and different denominators by creating common denominators or common numerators or by comparing to a
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 4/5 = 1/5 + 1/5 + 1/5 + 1/5.
     There are 4 components within this standard.
Apply and extend previous understandings of multiplication as repeated addition to multiply a whole number by a fraction.
     There are 3 components within this standard.
Understand decimal notation for fractions and compare decimal fractions.
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective
Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line.
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole.

Measurement and Data

Estimate and solve problems involving measurement.
Measure and estimate to determine relative sizes of measurement units within a single system of measurement involving length, liquid volume, and mass/weight  
Solve one- or two-step real-world problems involving whole number measurements with all four operations within a single system of measurement including  
Know and apply the area and perimeter formulas for rectangles in realworld and mathematical problems.  
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 angle and measure angles.
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.  
     There are 2 components within this standard.
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.  
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures  


Draw and identify lines and angles and classify shapes by properties of their lines and angles.
Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in   
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified  
Recognize and draw lines of symmetry for two-dimensional figures.  
♦  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.