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Aligning NJ Grade 7 Mathematics Curricula to the Common Core State Standards

NEW OLD
Common Core State Standards (CCSS) How is it related to 2008 NJ Core Curriculum Content If not related, where
adopted June 16, 2010 the old content? Standards (NJ cccs) did old content go?
Ratios and Proportional Relationships 7.RP
Analyze proportional relationships and use them to
solve real-world and mathematical problems.
7.RP.1. Compute unit rates associated This CCSS moves Although possibly
with ratios of fractions, including ratios of “rates” from grade 8 new in many 7th
lengths, areas and other quantities (4.1.8.A.3) to grade 7. grade classes, the
measured in like or different units. For It also moves content may have
example, if a person walks 1/2 mile in each “compound NEW (to grade 7) been included in
1/4 hour, compute the unit rate as the measurement units” others as “a variety
from grade 8
complex fraction 1/2/1/4 miles per hour, of situations” under
(4.2.8.D.6) to grade 7.
equivalently 2 miles per hour. NJ cccs 4.1.7.A.3.
7.RP.2. Recognize and represent Related, but the 4.1.7.A.3. Understand and use ratios,
proportional relationships between new CCSS contain proportions, and percents (including
quantities. more specific percents greater than 100 and less than
1) in a variety of situations.
expectations
a. Decide whether two quantities are in a 4.2.7.C.1. Use coordinates in four
proportional relationship, e.g., by
regarding quadrants to represent geometric
testing for equivalent ratios in a table or proportional concepts.
graphing on a coordinate plane and relationships. 4.3.7 B.1. Graph functions, and The new CCSS
observing whether the graph is a understand and describe their general postpone
straight line through the origin. behavior. introducing the
 Equations involving two variables concept of a
4.3.7.C.1. Analyze functional function until
relationships to explain how a change in grade 8.
one quantity can result in a change in
another, using pictures, graphs, charts,
and equations.
b. Identify the constant of proportionality Related, but the 4.3.7.A.1. Recognize, describe, extend,
(unit rate) in tables, graphs, equations, new CCSS move and create patterns involving whole
diagrams, and verbal descriptions of “rates” from grade numbers, rational numbers, and integers.
proportional relationships.
8 to grade 7.  Descriptions using tables, verbal and
symbolic rules, graphs, simple
equations or expressions
 Finite and infinite sequences Without the formal
terminology, sequences
 Generating sequences by using are introduced in grades
calculators to repeatedly apply a 4 and 5 in the CCSS.
formula The formal study of
arithmetic and
geometric sequences is
postponed until HS.
c. Represent proportional relationships by Although the new 4.3.7.C.2. Use patterns, relations,
equations. For example, if total cost t CCSS postpone symbolic algebra, and linear functions to
is proportional to the number n of items functions until model situations.
purchased at a constant price p, the grade 8, the use of  Using manipulatives, tables, graphs,
relationship between the total cost and symbolic algebra verbal rules, algebraic expressions/
the number of items can be expressed (equations) to equations/inequalities
as t = pn. model (represent)  Growth situations, such as population Growth functions and
relationships is growth and compound interest, using the formal study of
recursive (e.g., NOW-NEXT) formulas arithmetic and
explicit in bullet 1 of geometric sequences
NJ cccs 4.3.7.C.2. (cf. science standards and social
are postponed until HS.
studies standards)
d. Explain what a point (x, y) on the graph The new CCSS
of a proportional relationship means in move “rates” from
terms of the situation, with special grade 8 to NEW (to grade 7)
attention to the points (0, 0) and (1, r)
grade 7.
where r is the unit rate.
7.RP.3. Use proportional relationships to Related, but the new [“Understand and use ratios, proportions,
solve multistep ratio and percent problems. CCSS contain more and percents (including percents greater
Examples: simple interest, tax, markups and specific expectations than 100 and less than 1) in a variety of
markdowns, gratuities and commissions, fees, regarding proportional situations” from 4.1.7.A.3 above.]
percent increase and decrease, percent error. relationships.

Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later
grades, or because it is not included at any grade in the new CCSS.

1
The Number System 7.NS
Apply and extend previous understandings of
operations with fractions to add, subtract, multiply, and
divide rational numbers.
7.NS.1. Apply and extend previous Similar, but the 4.1.7.A.1. Extend understanding of the
understandings of addition and subtraction new CCSS contain number system by constructing
to add and subtract rational numbers; more specific meanings for the following:
represent addition and subtraction on a
expectations  Rational numbers Exponents get more
horizontal or vertical number line diagram.  Percents attention in grades 6
regarding
 Whole numbers with exponents and HS in the CCSS.
operations
a. Describe situations in which opposite 4.1.7.B.1. Use and explain procedures Also linked to
quantities combine to make 0. For involving negative for per-forming calculations with integers CCSS 7.NS.2
example, a hydrogen atom has 0 numbers. and all number types named above below for
charge because its two constituents are (Rational numbers, Percents, Whole
multiplication and
oppositely charged. numbers with exponents) with:
b. Understand p + q as the number  Pencil-and-paper
division
located a distance |q| from p, in the  Mental math
positive or negative direction depending  Calculator
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 4.3.7 D.1. Use graphing techniques on a In Transition:
numbers as adding the additive number line. Students coming to
inverse, p – q = p + (–q). Show that the  Absolute value seventh grade from
classes in which the
distance between two rational numbers  Arithmetic operations represented by 2008 standards were
on the number line is the absolute vectors (arrows) used may not yet have
value of their difference, and apply this (e.g., “-3 + 6” is “left 3, right 6”) been introduced to
principle in real-world contexts. absolute value. Until
the curriculum change
has been implemented
at grade 6, teachers will
need to continue
introducing this concept
at grade 7.
d. Apply properties of operations as 4.3.7.D.4. Understand and apply the
strategies to add and subtract rational properties of operations, numbers,
numbers. equations, and inequalities.
 Additive inverse
 Multiplicative inverse
7.NS.2. Apply and extend previous Related, but the 4.1.7.B.1. Use and explain procedures Also linked to
understandings of multiplication and new CCSS contain for performing calculations with integers CCSS 7.NS.1
division and of fractions to multiply and more specific and all number types named above above for addition
divide rational numbers. (Rational numbers, Percents, Whole
expectations and subtraction
a. Understand that multiplication is numbers with exponents) with:
extended from fractions to rational numbers
regarding  Pencil-and-paper
by requiring that operations continue to operations  Mental math
satisfy the properties of operations, involving negative  Calculator
particularly the distributive property, leading numbers.
to products such as (–1)(–1) = 1 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 –(p/q) = (–p)/q = p/(–q).
Interpret quotients of rational numbers by
describing real-world contexts.
c. Apply properties of operations as Related but much 4.3.7.D.4. Understand and apply the Also linked to the
strategies to multiply and divide rational more specific properties of operations, numbers, new CCSS 7.EE.1
numbers. expectation equations, and inequalities. above
 Additive inverse
 Multiplicative inverse

2
d. Convert a rational number to a decimal Similar 4.1.7.A.6. Understand that all fractions
using long division; know that the decimal can be represented as repeating or
form of a rational number terminates in 0s terminating decimals.
or eventually repeats.

From the introduction to 4.1.7.A.5. Use whole numbers, While not explicitly
Grade 7, critical area fractions, decimals, and percents to articulated in the
(2): “Students develop represent equivalent forms of the same CCSS for grade 7,
a unified understanding these expectations
of number, recognizing
number.
from the 2008 NJ cccs
fractions, decimals (that are part of the
have a finite or a
“understanding of
repeating decimal 4.1.7.A.2. Demonstrate a sense of the
representation), and
number” as explained
percents as different
relative magnitudes of numbers (as in the CCSS Grade 7
representations of applied to rational numbers and introduction.
rational numbers.” percents).
4.1.7.A.4. Compare and order numbers Compare & order are
of all named types not explicitly articulated
 Rational numbers in the grade 7 CCSS.
 Percents Exponents get more
 Whole numbers with exponents attention in grades 6
and HS in the CCSS.
7.NS.3. Solve real-world and mathematical Similar, except 4.5.7.A.2. Solve problems that arise in
problems involving the four operations with that manipulating mathematics and in other contexts.
rational numbers. [“Computations with complex fractions  Open-ended problems
rational numbers extend the rules for
is new at this  Non-routine problems
manipulating fractions to complex
grade level.  Problems with multiple solutions
fractions.” (Footnote to Common Core  Problems that can be solved in several
State Standards)] ways
[An application of CCSS 7.NS.1 and
7.NS.2 (NJ cccs 4.1.7.B.1) above]
Expressions and Equations 7.EE
4.3.7.D.3. Create, evaluate, and simplify In CCSS, this is
algebraic expressions involving variables. grade 6 content.
 Order of operations, including In Transition:
appropriate use of parentheses Students coming to
seventh grade from
 Substitution of a number for a classes in which the
variable 2008 standards were
used may not yet have
mastered this content.
Until the curriculum
change has been
implemented at grade 6,
teachers will need to
continue including this
material at grade 7.
Use properties of operations to generate equivalent
expressions.
7.EE.1. Apply properties of operations as Related but more 4.3.7.D.4. Understand and apply the Also linked to the
strategies to add, subtract, factor, and specific expectation properties of operations, numbers, new CCSS 7.NS.1d
expand linear expressions with rational that goes beyond the equations, and inequalities. and 7.NS.2c above
coefficients. 2008 NJ cccs for this  Additive inverse
grade level.  Multiplicative inverse
7.EE.2. Understand that rewriting an Instructional 4.5.7.E.2. Select, apply, and translate
expression in different forms in a problem guidance beyond the among mathematical representations to
context can shed light on the problem and level of specificity solve problems.
how the quantities in it are related. For provided in the
example, a + 0.05a = 1.05a means that NJ cccs
“increase by 5%” is the same as “multiply
by 1.05.”
4.1.7 B.2. Use exponentiation to find CCSS move this from
whole number powers of numbers. grade 7 to grade 6
(6.EE.1 & 2c).
In Transition:
Students coming to
seventh grade from
classes in which the
2008 standards were
used may not yet have
mastered this content.
Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later
grades, or because it is not included at any grade in the new CCSS.

3
Until the curriculum
change has been
implemented at grade 6,
teachers will need to
continue including this
material at grade 7.
4.1.7 B.3. Understand and apply the In CCSS, this is
standard algebraic order of operations, grade 6 content
including appropriate use of parentheses. (6.EE.1 & 6.EE.2c).
[Also including exponents, from NJ cccs In Transition:
4.1.7.A.1 and 4.1.7.B.2] Students coming to
seventh grade from
classes in which the
2008 standards were
used may not yet have
mastered this content.
Until the curriculum
change has been
implemented at grade 6,
teachers will need to
continue including this
material at grade 7.
Solve real-life and mathematical problems using
numerical and algebraic expressions and equations.
7.EE.3. Solve multi-step real-life and Similar but more 4.5.7.A.2. Solve problems that arise in
mathematical problems posed with positive specific mathematics and in other contexts.
and negative rational numbers in any form expectation  Open-ended problems
(whole numbers, fractions, and decimals),  Non-routine problems
using tools strategically. Apply properties of  Problems with multiple solutions
operations to calculate with numbers in any  Problems that can be solved in several
form; convert between forms as appropriate; ways
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 1/10 of her salary 4.1.7.C.1. Use equivalent
an hour, or $2.50, for a new salary of representations of numbers such as
$27.50. If you want to place a towel bar 9 fractions, decimals, and percents to
3/4 inches long in the center of a door that facilitate estimation.
is 27 1/2 inches wide, you will need to 4.5.7.D.4. Rely on reasoning, rather than
place the bar about 9 inches from each answer keys, teachers, or peers, to
edge; this estimate can be used as a check check the correctness of their problem
on the exact computation. solutions.
7.EE.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 Somewhat similar, 4.3.7.D.2. Solve simple linear equations
equations of the form px + q = r and p(x although CCSS informally and graphically.
+ q) = r, where p, q, and r are specific move fluent use of  Multi-step, integer coefficients only
rational numbers. Solve equations of algebraic methods (although answers may not be
these forms fluently. Compare an from grade 8 to integers)
algebraic solution to an arithmetic grade 7. Note also  Using paper-and-pencil, calculators,
solution, identifying the sequence of the that the new CCSS graphing calculators, spreadsheets,
operations used in each approach. For are more limiting in and other technology
example, the perimeter of a rectangle is terms of types of
54 cm. Its length is 6 cm. What is its equations to be
width? solved.
b. Solve word problems leading to Somewhat related 4.3.7.D.4. Understand and apply the Also linked to the
inequalities of the form px + q > r or px + but much more properties of operations, numbers, new CCSS 7.EE.1,
q < r, where p, q, and r are specific specific expectation. equations, and inequalities. 7.NS.1d, and
rational numbers. Graph the solution set CCSS move the  Additive inverse 7.NS.2c above
of the inequality and interpret it in the solving of linear  Multiplicative inverse
context of the problem. For example: As inequalities from
a salesperson, you are paid $50 per week grade 8 (4.3.8.D.3)
plus $3 per sale. This week you want your to grade 7.
pay to be at least $100. Write an inequality
for the number of sales you need to NEW (to grade 7)
make, and describe the solutions.

4
Geometry 7.G
Draw, construct, and describe geometrical figures and
describe the relationships between them.
7.G.1. Solve problems involving scale Similar although 4.2.7 A.2. Understand and apply the 3-D objects are
drawings of geometric figures, including slightly more concept of similarity. not explicitly
computing actual lengths and areas from a specific  Using proportions to find missing measures included at this
scale drawing and reproducing a scale
expectation  Scale drawings grade level.
drawing at a different scale.  Models of 3D objects
7.G.2. Draw (freehand, with ruler and Instructional 4.2.7.A.3. Use logic and reasoning to
protractor, and with technology) geometric guidance beyond make and support conjectures about
shapes with given conditions. Focus on the level of geometric objects. [Related to
constructing triangles from three measures specificity provided Mathematical Process No. 3 description,
of angles or sides, noticing when the that students “make conjectures and build a
in the NJ cccs
conditions determine a unique triangle, logical progression of statements to explore
more than one triangle, or no triangle. the truth of their conjectures.”]
7.G.3. Describe the two-dimensional The new CCSS
figures that result from slicing three- move this from grade
dimensional figures, as in plane sections of 8 (NJ cccs 4.2.8.A.1) NEW (to grade 7)
right rectangular prisms and right to grade 7.
rectangular pyramids.
4.2.7.A.1. Understand and apply In the CCSS,
properties of polygons. Identification and
classification of two-
 Quadrilaterals, including squares,
dimensional figures,
rectangles, parallelograms, including quadrilaterals,
trapezoids, rhombi are in grade 5 (5.G.3
 Regular polygons and 4). Applying those
properties is not
explicitly articulated in
CCSS at any grade.
4.2.7 B.2. Understand and apply CCSS move this
transformations. from grade 7 to
 Finding the image, given the pre-image, grade 8.
and vice-versa
 Sequence of transformations needed to
map one figure onto another
 Reflections, rotations, and translations
result in images congruent to the pre-image
 Dilations (stretching/shrinking) result in
images similar to the pre-image
4.2.7.C.2. Use a coordinate grid to CCSS move this from
model and quantify transformations (e.g., grade 7 to grade 8.
translate right 4 units).
4.2.7.D.1. Solve problems requiring Not explicitly
calculations that involve different units of articulated in CCSS
measurement within a measurement system at any grade
(e.g., 4’3” plus 7’10” equals 12’1”).
Solve real-life and mathematical problems involving
angle measure, area, surface area, and volume.
4.2.7.D.3. Recognize that all Although not explicitly
measurements of continuous quantities articulated in the
are approximations. CCSS, these are
4.2.7.D.2. Select and use appropriate critical understandings
units and tools to measure quantities to for students to solve
real-life problems at
the degree of precision needed in a
this grade
particular problem-solving situation.
7.G.4. Know the formulas for the area and CCSS move area In Transition:
circumference of a circle and use them to and circumference Students coming to
solve problems; give an informal derivation seventh grade from
of a circle from
of the relationship between the classes in which the
grade 6 (NJ cccs 2008 standards were
circumference and area of a circle. 4.2.6.E.2) to used may already know
grade 7. NEW (to grade 7) this content. Once the
curriculum change has
been implemented at
grade 6, teachers can
no longer assume
previous familiarity with
circumference and area
of a circle.

5
4.2.7 E.1. Develop and apply strategies Although this 2008
for finding perimeter and area. CPI is somewhat
 Geometric figures made by combining related to CCSS
triangles, rectangles and circles or parts 7.G.4 above, the
of circles emphasis is very
 Estimation of area using grids of various different.
sizes
7.G.5. Use facts about supplementary, CCSS move this
complementary, vertical, and adjacent from grade 8 to
angles in a multi-step problem to write and grade 7. NEW (to grade 7)
solve simple equations for an unknown
angle in a figure.
7.G.6. Solve real-world and mathematical CCSS move this
problems involving area, volume and from grade 8 to
surface area of two- and three-dimensional grade 7.
objects composed of triangles, NEW (to grade 7)
quadrilaterals, polygons, cubes, and right
prisms.
4.2.7 E.2. Recognize that the volume of CCSS move volume
a pyramid or cone is one-third of the of a cone from grade
volume of the prism or cylinder with the 7 to grade 8.
same base and height (e.g., use rice to Finding the volume
compare volumes of figures with same of a pyramid is
base and height). postponed until HS.
Statistics and Probability 7.SP
Use random sampling to draw inferences about a
population.
7.SP.1. Understand that statistics can be Related but much 4.4.7 A.2. Make inferences and
used to gain information about a population more specific formulate and evaluate arguments based
by examining a sample of the population; expectations on displays and analysis of data.
generalizations about a population from a
sample are valid only if the sample is
representative of that population.
Understand that random sampling tends to
produce representative samples and
support valid inferences.
7.SP.2. Use data from a random sample to CCSS move this
draw inferences about a population with an from grade 8
unknown characteristic of interest. (4.4.8.A.4) to
Generate multiple samples (or simulated
grade 7.
samples) of the same size to gauge the
variation in estimates or predictions. For
example, estimate the mean word length in NEW (to grade 7)
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.
Draw informal comparative inferences about two
populations.
7.SP.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 NEW
deviation) on either team; on a dot plot, the
separation between the two distributions of
heights is noticeable.

6
7.SP.4. Use measures of center and Related but much 4.4.7 A.1. Select and use appropriate Identification of
measures of variability for numerical data more specific and representations for sets of data, and appropriate data
from random samples to draw informal measures of central tendency (mean, displays is not explicitly
more demanding included in the CCSS
comparative inferences about two median, and mode).
expectation. at any grade, but is
populations. For example, decide whether  Type of display most appropriate for critical throughout.
the words in a chapter of a seventh-grade given data
science book are generally longer than the
 Box-and-whisker plot, upper quartile, In CCSS, box plots
words in a chapter of a fourth-grade lower quartile and interquartile range
science book. are in grade 6
 Scatter plot In CCSS, scatter plots
are in grade 8
 Calculators and computer used to Supportive of CCSS
record and process information Mathematical Practice #5
Investigate chance processes and develop, use, and
evaluate probability models.
7.SP.5. Understand that the probability of a CCSS move this
chance event is a number between 0 and 1 from grade 6
that expresses the likelihood of the event NEW (to grade 7)
(4.4.6.B.1) to
occurring. Larger numbers indicate greater
grade 7.
likelihood. A probability near 0 indicates an
4.4.7.B.1. Interpret probabilities as
unlikely event, a probability around 1/2
ratios, percents, and decimals.
indicates an event that is neither unlikely
nor likely, and a probability near 1 indicates
a likely event.
7.SP.6. Approximate the probability of a Similar, but slightly 4.4.7.B.2. Model situations involving
chance event by collecting data on the more specific probability with simulations (using
chance process that produces it and expectation. spinners, dice, calculators and
observing its long-run relative frequency, computers) and theoretical models.
and predict the approximate relative  Frequency, relative frequency
frequency given the probability. For
example, when rolling a number cube 600
times, predict that a 3 or 6 would be rolled 4.4.7.B.3. Estimate probabilities and
roughly 200 times, but probably not exactly make predictions based on experimental
200 times. and theoretical probabilities.
7.SP.7. Develop a probability model and Related to and an [“Estimate probabilities and make
use it to find probabilities of events. extension of predictions based on experimental and
Compare probabilities from a model to NJ cccs 4.4.7.B.3 theoretical probabilities” from 4.4.7.B.3
observed frequencies; if the agreement is above.]
above
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 4.4.7.B.4. Play and analyze probability- In CCSS, concepts
down. Do the outcomes for the spinning based games, and discuss the concepts of fairness and
penny appear to be equally likely based of fairness and expected value. expected value are
on the observed frequencies? postponed until HS.

7
7.SP.8. Find probabilities of compound CCSS move this “Explore
events using organized lists, tables, tree from grade 8 compound events”
diagrams, and simulation. (4.4.8.B.2) to was included in
a. Understand that, just as with simple grade 7. 2008 NJ cccs at
events, the probability of a compound
event is the fraction of outcomes in the
grade 6 (4.4.6.B.3)
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 NEW (to grade 7)
(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?
4.4.7.C. Discrete Mathematics- In CCSS, Systematic
Systematic Listing and Counting Listing and Counting
Is postponed until HS
4.4.7.D. Discrete Mathematics- Vertex-Edge Graphs
Vertex-Edge Graphs and Algorithms are not included in
the new CCSS at
any grade level