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Note: The specification of each standard is followed by links to lessons on AAAMath.com/AAAKnow.com that may be relevant to that standard.
Grade 6 Common Core State Standards
Grade 6 » Ratios & 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
in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak."
"For every vote candidate A received, candidate C received nearly three votes."
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. For example, "This
recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of
flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of
$5 per hamburger."
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g.,
by reasoning about tables of equivalent ratios, tape diagrams, double number line
diagrams, or equations.
Make tables of equivalent ratios relating quantities with whole-number
measurements, find missing values in the tables, and plot the pairs of values
on the coordinate plane. Use tables to compare ratios.
Solve unit rate problems including those involving unit pricing and constant
speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how
many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means
30/100 times the quantity); solve problems involving finding the whole, given a
part and the percent.
Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities.
Grade 6 » 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 word problems involving
division of fractions by fractions, e.g., by using visual fraction models and
equations to represent the problem. For example, create a story context for
(2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the
relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9
because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate
will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup
servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?.
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 equal to 12. Use
the distributive property to express a sum of two whole numbers 1-100 with a
common factor as a multiple of a sum of two whole numbers with no common factor.
For example, express 36 + 8 as 4 (9 + 2)..
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
zero, elevation above/below sea level, credits/debits, positive/negative electric
charge); use positive and negative numbers to represent quantities in real-world
contexts, explaining the meaning of 0 in each situation.
Understand a rational number as a point on the number line. Extend number line
diagrams and coordinate axes familiar from previous grades to represent points
on the line and in the plane with negative number coordinates.
Recognize opposite signs of numbers as indicating locations on opposite sides of
0 on the number line; recognize that the opposite of the opposite of a number
is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
Understand signs of numbers in ordered pairs as indicating locations in quadrants
of the coordinate plane; recognize that when two ordered pairs differ only by
signs, the locations of the points are related by reflections across one or both axes.
Find and position integers and other rational numbers on a horizontal or vertical
number line diagram; find and position pairs of integers and other rational numbers
on a coordinate plane.
Understand ordering and absolute value of rational numbers.
Interpret statements of inequality as statements about the relative position of
two numbers on a number line diagram. For example, interpret -3 > -7 as a
statement that -3 is located to the right of -7 on a number line oriented from
left to right.
Write, interpret, and explain statements of order for rational numbers in
real-world contexts. For example, write -3oC > -7oC to express the fact that
-3oC is warmer than -7oC.
Understand the absolute value of a rational number as its distance from 0 on the
number line; interpret absolute value as magnitude for a positive or negative
quantity in a real-world situation. For example, for an account balance of -30
dollars, write |-30| = 30 to describe the size of the debt in dollars.
Distinguish comparisons of absolute value from statements about order.
For example, recognize that an account balance less than -30 dollars represents
a debt greater than 30 dollars.
Solve real-world and mathematical problems by graphing points in all four
quadrants of the coordinate plane. Include use of coordinates and absolute value
to find distances between points with the same first coordinate or the same
Grade 6 » Expressions & 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 letters stand for numbers.
Write expressions that record operations with numbers and with letters standing
for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
Identify parts of an expression using mathematical terms (sum, term, product,
factor, quotient, coefficient); view one or more parts of an expression as a
single entity. For example, describe the expression 2 (8 + 7) as a product of
two factors; view (8 + 7) as both a single entity and a sum of two terms.
Evaluate expressions at specific values of their variables. Include expressions
that arise from formulas used in real-world problems. Perform arithmetic
operations, including those involving whole-number exponents, in the conventional
order when there are no parentheses to specify a particular order (Order of
Operations). For example, use the formulas V = s3 and A = 6 s2 to find the
volume and surface area of a cube with sides of length s = 1/2.
Apply the properties of operations to generate equivalent expressions.
For example, apply the distributive property to the expression 3 (2 + x) to
produce the equivalent expression 6 + 3x; apply the distributive property to the
expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply
properties of operations to y + y + y to produce the equivalent expression 3y.
Identify when two expressions are equivalent (i.e., when the two expressions name
the same number regardless of which value is substituted into them). For example,
the expressions y + y + y and 3y are equivalent because they name the same number
regardless of which number y stands for..
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 inequality true?
Use substitution to determine whether a given number in a specified set makes an
equation or inequality true.
Use variables to represent numbers and write expressions when solving a real-world
or mathematical problem; understand that a variable can represent an unknown number,
or, depending on the purpose at hand, any number in a specified set.
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 nonnegative
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 inequalities
of the form x > c or x < c have infinitely many solutions; represent solutions
of such inequalities on number line diagrams.
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 quantity, thought
of as the dependent variable, in terms of the other quantity, thought of as the
independent variable. Analyze the relationship between the dependent and independent
variables using graphs and tables, and relate these to the equation. For example,
in a problem involving motion at constant speed, list and graph ordered pairs of
distances and times, and write the equation d = 65t to represent the relationship
between distance and time
Grade 6 » Geometry
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
shapes; apply these techniques in the context of solving real-world and
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
show that the volume is the same as would be found by multiplying the edge
lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes
of right rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.
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 first
coordinate or the same second coordinate. Apply these techniques in the context
of solving real-world and mathematical problems.
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 techniques in the context of solving real-world and mathematical problems.
Grade 6 » Statistics & 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,
"How old am I?" is not a statistical question, but "How old are the students in
my school?" is a statistical question because one anticipates variability in
Understand that a set of data collected to answer a statistical question has a
distribution which can be described by its center, spread, and overall shape.
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 its
values vary with a single number.
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:
Reporting the number of observations.
Describing the nature of the attribute under investigation, including how it was
measured and its units of measurement.
Giving quantitative measures of center (median and/or mean) and variability
(interquartile range and/or mean absolute deviation), as well as describing any
overall pattern and any striking deviations from the overall pattern with
reference to the context in which the data were gathered.
Relating the choice of measures of center and variability to the shape of the
data distribution and the context in which the data were gathered.
Portions © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Portions © John Banfill 2014