Academic standards list

6th Grade — Mathematics

Introduction

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 & Proportional Relationships

CCSS.Math.Content.6.RP
 
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
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0, and use rate language in the context of a ratio relationship.
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,
     There are 4 components within this standard.

The Number System

CCSS.Math.Content.6.NS
 
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction
Compute fluently with multi-digit numbers and find common factors and multiples.
Fluently divide multi-digit numbers using the standard algorithm.
Fluently add, subtract, multiply, and divide multi-digit decimals using the 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
 
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
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to
     There are 3 components within this standard.
Understand ordering and absolute value of rational numbers.
     There are 4 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

Expressions & Equations

CCSS.Math.Content.6.EE
 
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 letters stand for numbers.
     There are 3 components within this standard.
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into
Reason about and solve one-variable equations and inequalities.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that
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; write an equation to express one

Geometry

CCSS.Math.Content.6.G
 
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
 
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge
 
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same
 
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.
 

Statistics & Probability

CCSS.Math.Content.6.SP
 
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
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and
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
 
Summarize and describe distributions.
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
 
Summarize numerical data sets in relation to their context, such as by:
     There are 4 components within this standard.
 
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