# Also linked to CCSS 7 by 7K103y

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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
complex fraction 1/2/1/4 miles per hour,                                                                                    of situations” under
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
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)
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:
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
need to continue
introducing this concept
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.
 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
 Multiplicative inverse

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.

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
 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
teachers will need to
continue including this
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
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
(6.EE.1 & 2c).
In Transition:
Students coming to
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
teachers will need to
continue including this
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
classes in which the
2008 standards were
used may not yet have
mastered this content.
Until the curriculum
change has been
teachers will need to
continue including this
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
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.

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.

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-
dimensional figures,
trapezoids, rhombi                          are in grade 5 (5.G.3
 Regular polygons                              and 4). Applying those
properties is not
explicitly articulated in
4.2.7 B.2. Understand and apply                   CCSS move this
 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
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
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
curriculum change has
been implemented at
no longer assume
previous familiarity with
circumference and area
of a circle.

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.

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
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)
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
unknown characteristic of interest.             (4.4.8.A.4) to
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                                           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.

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.

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
 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
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.

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.

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
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
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