Academic standards list

Sixth 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.

Ratios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, the ratio of wings to beaks
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0. Use rate language in the context of a ratio relationship.
Use ratio and rate reasoning to solve real-world and mathematical problems.
     There are 4 components within this standard.

The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Interpret and compute quotients of fractions, and solve contextual problems involving division of fractions by fractions (e.g., using visual fraction models
Compute fluently with multi-digit numbers and find common factors and multiples.
Fluently divide multi-digit numbers using a standard algorithm.  
Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.  
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.  
Apply and extend previous understandings of numbers to the system of rational numbers.
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent
     There are 3 components within this standard.
Understand ordering and absolute value of rational numbers.
     There are 3 components within this standard.
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value

Expressions and Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.
Write and evaluate numerical expressions involving whole-number exponents.
Write, read, and evaluate expressions in which variables stand for numbers.
     There are 3 components within this standard.
Apply the properties of operations (including, but not limited to, commutative, associative, and distributive properties) to generate equivalent
Identify when expressions are equivalent (i.e., when the expressions name the same number regardless of which value is substituted into them)
Reason about and solve one-variable equations and inequalities.
Understand solving an equation or inequality is carried out by determining if any of the values from a given set make the equation or inequality true. Use
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an
Solve real-world and mathematical problems by writing and solving onestep equations of the form x + p = q and px = q for cases in which p, q, and x are all
Interpret and write an inequality of the form x > c or x < c which represents a condition or constraint in a real-world or mathematical problem. Recognize
Represent and analyze quantitative relationships between dependent and independent variables.
Use variables to represent two quantities in a real-world problem that change in relationship to one another.
     There are 2 components within this standard.


Solve real-world and mathematical problems involving area, surface area, and volume.
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other  
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and  
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or  
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these  

Statistics and Probability

Develop understanding of statistical variability.
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example,  
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean, median, mode),  
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how  
Summarize and describe distributions.
Display a single set of numerical data using dot plots (line plots), box plots, pie charts and stem plots.  
Summarize numerical data sets in relation to their context.  
     There are 4 components within this standard.
♦  Academic Standards marked with a diamond are "Supporting Content" within the grade level or course.
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