Maryland State Department of Education 1
Grade 7
Maryland College and Career Ready Standards for Mathematics
7.RP Ratios and Proportional Relationships
7.RP.A ANALYZE PROPORTIONAL RELATIONSHIPS AND USE THEM TO SOLVE REAL-WORLD
AND MATHEMATICAL PROBLEMS.
7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths,
areas and other quantities measured in like or different units. For example, if a
person walks
mile in each
hour, compute the unit rate as the complex fraction
miles per hour, equivalently 2 miles per hour.
7.RP.A.2 Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., by
testing for equivalent ratios in a table or graphing on a coordinate plane and
observing whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t
is proportional to the number n of items purchased at a constant price p, the
relationship between the total cost and the number of items can be
expressed as .
d. Explain what a point
on the graph of a proportional relationship means
in terms of the situation, with special attention to the points
and
where r is the unit rate.
7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.
Examples: simple interest, tax, markups and markdowns, gratuities and
commissions, fees, percent increase and decrease, percent error.
Grade 7 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 2
7.NS The Number System
7.NS.A APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF OPERATIONS WITH
FRACTIONS.
7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and
subtract rational numbers; represent addition and subtraction on a horizontal or
vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For
example, a hydrogen atom has 0 charge because its two constituents are
oppositely charged.
b. Understand as the number located a distance
from p, in the positive
or negative direction depending on whether q is positive or negative. Show
that a number and its opposite have a sum of 0 (are additive inverses).
Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse,
. Show that the distance between two rational numbers
on the number line is the absolute value of their difference, and apply this
principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.A.2 Apply and extend previous understandings of multiplication and division and of
fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational
numbers by requiring that operations continue to satisfy the properties of
operations, particularly the distributive property, leading to products such as
and the rules for multiplying signed numbers. Interpret
products of rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero,
and every quotient of integers (with non-zero divisor) is a rational number. If
p and q are integers, then
. Interpret quotients of rational
numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the
decimal form of a rational number terminates in 0s or eventually repeats.
7.NS.A.3 Solve real-world and mathematical problems involving the four operations with
rational numbers.(Computations with rational numbers extend the rules for
manipulating fractions to complex fractions.)
Grade 7 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 3
7.EE Expressions and Equations
7.EE.A USE PROPERTIES OF OPERATIONS TO GENERATE EQUIVALENT EXPRESSIONS.
7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand
linear expressions with rational coefficients.
7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can
shed light on the problem and how the quantities in it are related. For example,
means that "increase by 5%" is the same as "multiply by 1.05."
7.EE.B SOLVE REAL-LIFE AND MATHEMATICAL PROBLEMS USING NUMERICAL AND
ALGEBRAIC EXPRESSIONS AND EQUATIONS.
7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and
negative rational numbers in any form (whole numbers, fractions, and decimals),
using tools strategically. Apply properties of operations to calculate with numbers in
any form; convert between forms as appropriate; and assess the reasonableness of
answers using mental computation and estimation strategies. For example: If a
woman making $25 an hour gets a 10% raise, she will make an additional
of her
salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar
inches long in the center of a door that is
inches wide, you will need to place
the bar about 9 inches from each edge; this estimate can be used as a check on the
exact computation.
7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and
construct simple equations and inequalities to solve problems by reasoning about
the quantities.
a. Solve word problems leading to equations of the form and
, where p, q, and r are specific rational numbers. Solve
equations of these forms fluently. Compare an algebraic solution to an
arithmetic solution, identifying the sequence of the operations used in each
approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6
cm. What is its width?
b. Solve word problems leading to inequalities of the form or
, where p, q, and r are specific rational numbers. Graph the
solution set of the inequality and interpret it in the context of the problem.
For example: As a salesperson, you are paid $50 per week plus $3 per sale.
This week you want your pay to be at least $100. Write an inequality for the
number of sales you need to make, and describe the solutions.
Grade 7 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 4
7.G Geometry
7.G.A DRAW CONSTRUCT, AND DESCRIBE GEOMETRICAL FIGURES AND DESCRIBE THE
RELATIONSHIPS BETWEEN THEM.
7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale drawing at a
different scale.
7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes
with given conditions. Focus on constructing triangles from three measures of
angles or sides, noticing when the conditions determine a unique triangle, more
than one triangle, or no triangle.
7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional
figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
7.G.B SOLVE REAL-LIFE AND MATHEMATICAL PROBLEMS INVOLVING ANGLE MEASURE,
AREA, SURFACE AREA, AND VOLUME.
7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve
problems; give an informal derivation of the relationship between the circumference
and area of a circle.
7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a
multi-step problem to write and solve equations for an unknown angle in a figure.
7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface
area of two- and three-dimensional objects composed of triangles, quadrilaterals,
polygons, cubes, and right prisms.
7.SP Statistics and Probability
7.SP.A USE RANDOM SAMPLING TO DRAW INFERENCES ABOUT A POPULATION.
7.SP.A.1 Understand that statistics can be used to gain information about a population by
examining a sample of the population; generalizations about a population from a sample
are valid only if the sample is representative of that population. Understand random
sampling tends to produce representative samples and support valid inferences.
7.SP.A.2 Use data from a random sample to draw inferences about a population with an
unknown characteristic of interest. Generate multiple samples (or simulated
samples) of the same size to gauge the variation in estimates or predictions. For
example, estimate the mean word length in a book by randomly sampling words
from the book; predict the winner of a school election based on randomly sampled
survey data. Gauge how far off the estimate or prediction might be.
Grade 7 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 5
7.SP.B DRAW INFORMAL COMPARATIVE INFERENCES ABOUT TWO POPULATIONS.
7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions
with similar variabilities, measuring the difference between the centers by
expressing it as a multiple of a measure of variability. For example, the mean height
of players on the basketball team is 10 cm greater than the mean height of players
on the soccer team, about twice the variability (mean absolute deviation) on either
team; on a dot plot, the separation between the two distributions of heights is
noticeable.
7.SP.B.4 Use measures of center and measures of variability for numerical data from random
samples to draw informal comparative inferences about two populations. For
example, decide whether the words in a chapter of a seventh-grade science book
are generally longer than the words in a chapter of a fourth-grade science book.
7.SP.C INVESTIGATE CHANCE PROCESSES AND DEVELOP, USE, AND EVALUATE
PROBABILITY MODELS.
7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that
expresses the likelihood of the event occurring. Larger numbers indicate greater
likelihood. A probability near 0 indicates an unlikely event, a probability around
indicates an event that is neither unlikely nor likely, and a probability near 1
indicates a likely event.
7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance
process that produces it and observing its long-run relative frequency, and predict
the approximate relative frequency given the probability. For example, when rolling
a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times,
but probably not exactly 200 times.
7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare
probabilities from a model to observed frequencies; if the agreement is not good,
explain possible sources of the discrepancy.
a. Develop a uniform probability model by assigning equal probability to all
outcomes, and use the model to determine probabilities of events. For
example, if a student is selected at random from a class, find the probability
that Jane will be selected and the probability that a girl will be selected.
b. Develop a probability model (which may not be uniform) by observing
frequencies in data generated from a chance process. For example, find the
approximate probability that a spinning penny will land heads up or that a
tossed paper cup will land open-end down. Do the outcomes for the spinning
penny appear to be equally likely based on the observed frequencies?
Grade 7 August 2022
Maryland College and Career Ready Standards for Mathematics
Maryland State Department of Education 6
7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams,
and simulation.
a. Understand that, just as with simple events, the probability of a compound
event is the fraction of outcomes in the sample space for which the
compound event occurs.
b. Represent sample spaces for compound events using methods such as
organized lists, tables and tree diagrams. For an event described in everyday
language (e.g., "rolling double sixes"), identify the outcomes in the sample
space which compose the event.
c. Design and use a simulation to generate frequencies for compound events.
For example, use random digits as a simulation tool to approximate the
answer to the question: If 40% of donors have type A blood, what is the
probability that it will take at least 4 donors to find one with type A blood?
