Maryland State Department of Education 1
Grade 6
Maryland College and Career Ready Standards for Mathematics
6.RP Ratios and Proportional Relationships
6.RP.A UNDERSTANDING RATIO CONCEPTS AND USE RATIO REASONING TO SOLVE
PROBLEMS.
6.RP.A.1 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."
6.RP.A.2 Understand the concept of a unit rate
associated with a ratio : with 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
cup of flour for each cup
of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
(Expectations for unit rates in this grade are limited to non-complex fractions.)
6.RP.A.3 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.
a. 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.
b. 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?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means
times the quantity); solve problems involving finding the whole, given a
part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform
units appropriately when multiplying or dividing quantities.
Grade 6 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 2
6.NS The Number System
6.NS.A APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF MULTIPLICATION AND DIVISION
TO DIVIDE FRACTIONS BY FRACTIONS.
6.NS.A.1 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
÷
and use a
visual fraction model to show the quotient; use the relationship between
multiplication and division to explain that
÷
=
because
of
is
. In general,
÷
=
. How much chocolate will each person get if 3 people share
lb of
chocolate equally? How many
-cup servings are in
of a cup of yogurt? How wide is
a rectangular strip of land with length
mi and area
square mi?
6.NS.B COMPUTE FLUENTLY WITH MULTI-DIGIT NUMBERS AND FIND COMMON FACTORS
AND MULTIPLES.
6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
6.NS.B.4 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
)
.
6.NS.C APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF NUMBERS TO THE SYSTEM OF
RATIONAL NUMBERS.
6.NS.C.5 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.
Grade 6 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 3
6.NS.C.6 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.
a. 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
)
, and that 0 is its own opposite.
b. 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.
c. 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.
6.NS.C.7 Understand ordering and absolute value of rational numbers.
a. 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.
b. Write, interpret, and explain statements of order for rational numbers in real-
world contexts. For example, write > to express the fact that
is warmer than .
c. 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.
d. 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.
6.NS.C.8 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 second
coordinate.
Grade 6 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 4
6.EE Expressions and Equations
6.EE.A APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF ARITHMETIC TO ALGEBRAIC
EXPRESSIONS.
6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.
6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters
standing for numbers. For example, express the calculation "Subtract y
from 5" as 5 .
b. 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.
c. 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 =
and = 6
to
find the volume and surface area of a cube with sides of length =
.
6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example,
apply the distributive property to the expression 3
(
2 +
)
to produce the
equivalent expression 6 + 3; apply the distributive property to the expression
24 + 18 to produce the equivalent expression 6
(
4 + 3
)
; apply properties of
operations to + + to produce the equivalent expression 3.
6.EE.A.4 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 + + and 3 are equivalent because they name the same
number regardless of which number y stands for.
6.EE.B REASON ABOUT AND SOLVE ONE-VARIABLE EQUATIONS AND INEQUALITIES.
6.EE.B.5 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.
Grade 6 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 5
6.EE.B.6 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.
6
.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the
form + = and = for cases in which p, q and x are all nonnegative
rational numbers.
6
.EE.B.8 Write an inequality of the form > or < to represent a constraint or
condition in a real-world or mathematical problem. Recognize that inequalities of
the form > or < have infinitely many solutions; represent solutions of such
inequalities on number line diagrams.
6.EE.C REPRESENT AND ANALYZE QUANTITATIVE RELATIONSHIPS BETWEEN DEPENDENT AND
INDEPENDENT VARIABLES.
6.EE.C.9 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 = 65 to represent the
relationship between distance and time.
6.G Geometry
6.G.A SOLVE REAL-WORLD AND MATHEMATICAL PROBLEMS INVOLVING AREA, SURFACE
AREA, AND VOLUME.
6.G.A.1 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 mathematical problems.
6.G.A.2 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 = and = to find volumes of right rectangular prisms
with fractional edge lengths in the context of solving real-world and mathematical
problems.
Grade 6 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 6
6.G.A.3 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.
6.G.A.4 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.
6.SP Statistics and Probability
6.SP.A DEVELOP UNDERSTANDING OF STATISTICAL VARIABILITY.
6.SP.A.1 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 students' ages.
6.SP.A.2 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.
6.SP.A.3 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.
6.SP.B SUMMARIZE AND DESCRIBE DISTRIBUTIONS.
6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms,
and box plots.
6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it
was measured and its units of measurement.
c. 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.
d. 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.
