# Math Gr7 DistCorr

Document Sample

```					    Mathematics Crosswalk
Common Core State Standards to
Connecticut State Standards to
District Curriculum

Grade 7 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS
Analyze proportional relationships and use them to solve real-world and mathematical problems.
CCSS                          CT Standard Match             District Correlation                  CT Assessment
CC.7.RP.1 Compute unit         CT.6.2.2.11 Solve practical problems                                CMT 7.12 Ratios and Proportions
rates associated with ratios   involving rates, ratios, percentages and                            B. Solve 1-step problems involving
of fractions, including ratios proportionality.                                                    proportions in context.
of lengths, areas and other
quantities measured in like    CT.7.2.2.10 Write ratios and proportions                            CMT 8.12 Ratios and Proportions
or different units. For        to solve problems in context involving                              B. Solve problems involving
example, If a person walks     rates, scale factors and percentages.                               proportions in context.
1/2 mile in each 1/4 hour,
compute the unit rate as the CT.8.2.2.9 Use proportional reasoning to                              CMT 8.12 Ratios and Proportions
complex fraction (1/2)/(1/4) write and solve problems in context.                                  C. Solve multistep problems involving
miles per hour, equivalently                                                                       ratio or proportion, and explain how the
2 miles per hour.                                                                                  solution was determined.

1
Connecticut State Department of Education                                                                                   September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS
Analyze proportional relationships and use them to solve real-world and mathematical problems.
CC.7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent
proportional relationships between quantities.
CCSS                       CT Standard Match                District Correlation                   CT Assessment
CC.7.RP.2a Decide              CT.6.1.2.3 Examine tables, graphs                                   Deciding whether two quantities are in a
whether two quantities are     and equations to determine patterns of                              proportional relationship is not assessed
in a proportional              change in linear relationships.                                     on the CMT.
relationship, e.g., by testing
for equivalent ratios in a     CT.7.1.2.6 Examine situations with
table or graphing on a         constant or varying rates of change
coordinate plane and           and know that a constant rate of
observing whether the graph change describes a linear relationship.
is a straight line through the
origin.                        CT.8.1.1.3 Write and solve problems
involving proportional relationships
(direct variation) using linear
equations (y = mx).

CT.8.1.2.5 Represent linear and
nonlinear mathematical relationships
with verbal descriptions, tables,
graphs and equations (when possible).
CC.7.RP.2b Identify the          CT.7.2.2.10 Write ratios and                                       Constant of proportionality is not
constant of proportionality      proportions to solve problems in                                   assessed on the CMT.
(unit rate) in tables, graphs,   context involving rates, scale factors
equations, diagrams, and         and percentages.
verbal descriptions of
proportional relationships.

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Connecticut State Department of Education                                                                                      September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS
Analyze proportional relationships and use them to solve real-world and mathematical problems.
CC.7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent
proportional relationships between quantities.
CCSS                       CT Standard Match                District Correlation                   CT Assessment
CC.7.RP.2c Represent            CT.7.1.2.4 Write expressions,                                      Representing proportional relationships
proportional relationships      formulas, equations or inequalities                                by equations is not assessed on the CMT.
by equations. For example,      using variables to represent
if total cost t is proportional mathematical relationships and solve
to the number n of items        problems.
purchased at a constant
price p, the relationship
between the total cost and
the number of items can be
expressed as t = pn.
CC.7.RP.2d Explain what a CT.8.1.2.6 Determine the constant                                        Graphs of proportional relationships are
point (x, y) on the graph of a rate of change in a linear relationship                             not assessed on the CMT.
proportional relationship       and recognize this as the slope of a
means in terms of the           line.
situation, with special
attention to the points (0, 0)
and (1, r) where r is the unit
rate.

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Connecticut State Department of Education                                                                                    September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS
Analyze proportional relationships and use them to solve real-world and mathematical problems.
CCSS                     CT Standard Match               District Correlation                 CT Assessment
CC.7.RP.3 Use proportional CT.7.2.2.10 Write ratios and                                       CMT 7.13 Computation with Percents
relationships to solve       proportions to solve problems in                                 B. Solve 1-step problems involving
multistep ratio and percent  context involving rates, scale factors                           percents in context.
problems. Examples: simple and percentages.
interest, tax, markups and                                                                    CMT 8.12 Ratios and Proportions
markdowns, gratuities and    CT.7.2.2.11 Find and/or estimate a                               B. Solve problems involving proportions
commissions, fees, percent   percentage of a number, including                                in context.
increase and decrease,       percentages that are more than 100
percent error.               percent and less than 1 percent using a                          C. Solve multistep problems involving
variety of strategies, including:                                ratio or proportion, and explain how the
-- Number patterns - e.g., find 20                              solution was determined.
percent of 50.
-- Distributive Property - e.g., find                           CMT 8.13 Computation with Percents
150 percent of 20.                                               B. Solve problems involving percents in
-- Proportions - e.g., 75 percent of                            context.
48
-- Multiplication of decimal
equivalent - e.g., 0.7 percent of 48.
-- Estimation - e.g., 22 percent of
\$49.95.

CT.7.2.2.12 Solve percent problems
in context including what percentage
one number is of another, percentage
increase and percentage decrease
using a variety of strategies, e.g.,
proportions or equations.

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Connecticut State Department of Education                                                                                September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

RATIOS AND PROPORTIONAL RELATIONSHIPS
Analyze proportional relationships and use them to solve real-world and mathematical problems.
CCSS                         CT Standard Match               District Correlation          CT Assessment
CC.7.RP.3 (Cont.)            CT.8.2.2.9 Use proportional reasoning
to write and solve problems in context.

CT.8.2.2.10 Solve a variety of
problems in context involving percents,
including the following:
-- Percentage of a number, e.g., If 65
percent of the 250 applicants will be
accepted to the Arts Magnet School,
how many students will be accepted?
-- The percentage one number is of
another number, e.g., Find the percent
of students who play soccer if 39
students play soccer out of a total of
387 students.
-- The percentage of a missing
amount, e.g., 5 percent of the money
from a fundraiser will be donated to a
charity. If \$25 is donated to the charity,
how much money was made from the
fundraiser?
-- Percentage increase/decrease, e.g.,
increased from 1,345 per minute to
1,567 per minute. What is the
percentage increase?

5
Connecticut State Department of Education                                                                       September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers:
CC.7.NS.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:
CCSS                          CT Standard Match                 District Correlation                 CT Assessment
CC.7.NS.1a Describe            CT.7.2.2.16 Develop and describe in                                  Combining opposite quantities to make 0
situations in which            writing strategies for addition,                                     is not assessed on the CMT.
opposite quantities            subtraction, multiplication and division
combine to make 0. For         and solve problems with positive and
example, a hydrogen atom negative integers using models, number
has 0 charge because its       lines, coordinate grids and computational
two constituents are           strategies.
oppositely charged.
CC.7.NS.1b Understand p CT.7.2.2.9 Apply a variety of strategies                                    Interpreting sums of rational numbers by
+ q as the number located a to write and solve problems involving                                   describing real-world contexts is not
distance |q| from p, in the    addition, subtraction, multiplication and                            assessed on the CMT.
positive or negative           division of positive rational numbers, i.e.,
direction depending on         whole numbers, fractions and decimals.                               Absolute value and computation with
whether q is positive or                                                                            negative rational numbers is not assessed
negative. Show that a          CT.7.2.2.16 Develop and describe in                                  on the CMT.
number and its opposite        writing strategies for addition,
have a sum of 0 (are           subtraction, multiplication and division
additive inverses). Interpret and solve problems with positive and
sums of rational numbers       negative integers using models, number
by describing real-world       lines, coordinate grids and computational
contexts.                      strategies.
CT.7.2.2.17 Develop an understanding of
absolute value using a number line while
solving problems involving distance.
subtraction, multiplication and division)
and solve problems with positive and
negative rational numbers.

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Connecticut State Department of Education                                                                                      September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers:
CC.7.NS.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:
CCSS                        CT Standard Match             District Correlation                       CT Assessment
CC.7.NS.1c Understand           CT.7.2.2.9 Apply a variety of                                       Computation with negative rational
subtraction of rational         strategies to write and solve                                       numbers, subtraction with integers and
numbers as adding the           problems involving addition,                                        absolute value are not assessed on the
additive inverse, p - q = p + subtraction, multiplication and
CMT.
(-q). Show that the distance division of positive rational
between two rational            numbers, i.e., whole numbers,
numbers on the number line fractions and decimals.
is the absolute value of their
difference, and apply this      CT.7.2.2.16 Develop and describe
principle in real-world         in writing strategies for addition,
contexts.                       subtraction, multiplication and
division and solve problems with
positive and negative integers using
models, number lines, coordinate
grids and computational strategies.

CT.7.2.2.17 Develop an
understanding of absolute value
using a number line while solving
problems involving distance.

CT.8.2.2.5 Compute (using
and division) and solve problems
with positive and negative rational
numbers.

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Connecticut State Department of Education                                                                                      September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers:
CC.7.NS.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:
CCSS                        CT Standard Match                 District Correlation                   CT Assessment
CC.7.NS.1d Apply              CT.7.2.2.8 Apply the order of                                         CMT 7.8 Computation with Fractions
properties of operations as operations and algebraic properties;                                    and Integers
strategies to add and         i.e., commutative, associative,                                       A. Add and subtract fractions and mixed
subtract rational numbers. distributive, inverse operations, and                                    numbers with reasonable and appropriate
identities; to write, simplify, e.g., 4 (3
1/2) = 4 (3) + 4 (1/2) = 12 + 2 = 14,                                 CMT 8.8 Computation with Fractions
and solve problems, including those                                   and Integers
with parentheses and exponents.                                       A. Add and subtract fractions and mixed
numbers with reasonable and appropriate
CT.7.2.2.9 Apply a variety of                                         denominators.
strategies to write and solve problems
multiplication and division of
positive rational numbers, i.e., whole
numbers, fractions and decimals.
CT.7.2.2.16 Develop and describe in
subtraction, multiplication and
division and solve problems with
positive and negative integers using
models, number lines, coordinate
grids and computational strategies.

subtraction, multiplication and
division) and solve problems with
positive and negative rational
numbers.
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Connecticut State Department of Education                                                                                    September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers:
CC.7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers:
CCSS                     CT Standard Match                District Correlation                       CT Assessment
CC.7.NS.2a Understand         CT.7.2.2.8 Apply the order of                                          CMT 8.8 Computation with Fractions
that multiplication is        operations and algebraic                                               and Integers
extended from fractions to    properties; i.e., commutative,                                         C. Add or multiply positive and negative
rational numbers by           associative, distributive, inverse                                     integers.
requiring that operations     operations, and the additive and
continue to satisfy the       multiplicative identities; to write,
properties of operations,     simplify, e.g., 4 (3 1/2) = 4 (3) + 4
particularly the distributive (1/2) = 12 + 2 = 14, and solve
property, leading to          problems, including those with
products such as (-1)(-1) = 1 parentheses and exponents.
and the rules for multiplying
signed numbers. Interpret     CT.7.2.2.16 Develop and
products of rational numbers describe in writing strategies for
contexts.                     multiplication and division and
solve problems with positive and
negative integers using models,
number lines, coordinate grids
and computational strategies.

CT.8.2.2.5 Compute (using
multiplication and division) and
solve problems with positive and
negative rational numbers.

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Connecticut State Department of Education                                                                                     September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers:
CC.7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers:
CCSS                      CT Standard Match                District Correlation                        CT Assessment
CC.7.NS.2b Understand         CT.7.2.2.16 Develop and describe                                       Division of integers and computation
that integers can be divided, in writing strategies for addition,                                    with negative rational numbers is not
provided that the divisor is  subtraction, multiplication and                                        assessed on the CMT.
not zero, and every quotient division and solve problems with
of integers (with non-zero    positive and negative integers using
divisor) is a rational        models, number lines, coordinate
number. If p and q are        grids and computational strategies.
integers then –(p/q) = (–p)/q
= p/(–q). Interpret quotients CT.8.2.2.5 Compute (using
of rational numbers by        addition, subtraction, multiplication
describing real-world         and division) and solve problems
contexts.                     with positive and negative rational
numbers.
CC.7.NS.2c Apply              CT.7.2.2.9 Apply a variety of                                          CMT 7.8 Computation with Fractions
properties of operations as   strategies to write and solve                                          and Integers
strategies to multiply and    problems involving addition,                                           B. Multiply whole numbers and fractions
divide rational numbers.      subtraction, multiplication and                                        by fractions and mixed numbers.
division of positive rational
numbers, i.e., whole numbers,                                          CMT 8.8 Computation with Fractions
fractions and decimals.                                                and Integers
B. Multiply whole numbers and fractions
CT.8.2.2.5 Compute (using                                              by fractions and mixed numbers.
and division) and solve problems                                       integers.
with positive and negative rational
numbers.                                                               Division of integers and division of
fractions are not assessed on the CMT.
Computation with negative rational
numbers is not assessed on the CMT.

10
Connecticut State Department of Education                                                                                      September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers:
CC.7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers:
CCSS                    CT Standard Match                 District Correlation                       CT Assessment
CC.7.NS.2d Convert a         CT.6.2.1.6 Determine equivalent                                         CMT 6.3 Equivalent Fractions,
rational number to a decimal fraction, decimal and percentage                                        Decimals and Percents
using long division; know    representations and choose among                                        B. Rename improper fractions and mixed
that the decimal form of a   these forms to solve problems.                                          numbers as equivalent decimals and vice
rational number terminates                                                                           versa.
in 0s or eventually repeats. CT.7.2.1.2 Represent rational
numbers in equivalent fraction,                                         CMT 7.3 Equivalent Fractions,
decimal and percentage forms.                                           Decimals and Percents
A. Rename fractions and mixed numbers
CT.7.2.1.3 Represent fractions as                                       as equivalent decimals and vice versa.
terminating, e.g., 1/2 = 0.5, or
repeating, e.g., 1/3 = 0.333...                                         CMT 8.3 Equivalent Fractions,
decimals and determine when it is                                       Decimals and Percents
appropriate to round the decimal                                        A. Rename fractions and mixed numbers
form in context.                                                        as equivalent decimals and vice versa.

CT.8.2.1.4 Represent fractions,                                     Repeating decimals are not assessed on
mixed numbers, decimals and                                         the CMT.
percentages in equivalent forms.

11
Connecticut State Department of Education                                                                                     September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

THE NUMBER SYSTEM
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers:
CCSS                   CT Standard Match                District Correlation                      CT Assessment
CC.7.NS.3 Solve real-world CT.7.2.2.9 Apply a variety of                                        CMT 6.9 Solve Word Problems
and mathematical problems strategies to write and solve                                         B. Solve two-step story problems
involving the four         problems involving addition,                                         involving whole numbers, decimals,
operations with rational   subtraction, multiplication and                                      fractions and money amounts without
numbers. (Computations     division of positive rational                                        extraneous information.
with rational numbers      numbers, i.e., whole numbers,
extend the rules for       fractions and decimals.                                              CMT 7.9 Solve Word Problems
manipulating fractions to                                                                       A. Solve one-step story problems
complex fractions.)        CT.8.2.2.5 Compute (using                                            involving whole numbers, fractions,
addition, subtraction,                                               decimals and money amounts with or
multiplication and division) and                                     without extraneous information.
solve problems with positive and
negative rational numbers.                                           CMT 7.9 Solve Word Problems
B. Solve multistep problems involving
fractions and mixed numbers with or
without extraneous information.

CMT 8.9 Solve Word Problems
A. Solve multistep problems involving
fractions, mixed numbers, decimals and
money amounts with or without
extraneous information.
B. Solve multistep problems involving
whole numbers, mixed numbers, money
amounts and decimals.
C. Solve multistep problems involving
whole numbers, fractions, mixed
numbers, decimals or money amounts,
and explain how the solution was
determined.

12
Connecticut State Department of Education                                                                                 September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS
Use properties of operations to generate equivalent expressions.
CCSS                      CT Standard Match               District Correlation                     CT Assessment
CC.7.EE.1 Apply properties CT.7.1.3.7 Evaluate and simplify                                      Adding, subtracting, factoring, and
of operations as strategies to algebraic expressions, equations                                  expanding linear expressions with
add, subtract, factor, and     and formulas using algebraic                                      rational coefficients is not assessed on
expand linear expressions      properties (i.e., commutative,                                    the CMT.
with rational coefficients.    associative, distributive, inverse
multiplicative identities) and the
order of operations.

CT.8.1.3.10 Evaluate and
simplify algebraic expressions,
equations and formulas, including
those with powers, using
algebraic properties and the order
of operations.

CC.7.EE.2 Understand that       CT.7.1.2.4 Write expressions,                                    CMT 7.23 Algebraic Concepts
rewriting an expression in      formulas, equations or                                           D. Represent situations with algebraic
different forms in a problem    inequalities using variables to                                  expressions.
context can shed light on the   represent mathematical                                           E. Write an expression to represent a
problem and how the             relationships and solve problems.                                situation.
quantities in it are related.
For example, a + 0.05a =                                                                         CMT 8.23 Algebraic Concepts
1.05a means that “increase                                                                       D. Represent situations with algebraic
by 5%” is the same as                                                                            expressions or equations.
“multiply by 1.05.”                                                                              E. Write an expression or equation to
represent a situation.

13
Connecticut State Department of Education                                                                                    September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
CCSS                       CT Standard Match              District Correlation                CT Assessment
CC.7.EE.3 Solve multi-step      CT.7.2.2.7 Estimate solutions to                              CMT 7.9 Solve Word Problems
real-life and mathematical      problems in context or computations                           A. Solve one-step story problems
problems posed with positive with rational numbers and justify the                            involving whole numbers, fractions,
and negative rational numbers reasonableness of the estimate in                               decimals and money amounts with or
in any form (whole numbers,     writing.                                                      without extraneous information.
fractions, and decimals), using                                                               B. Solve multistep problems involving
tools strategically. Apply      CT.7.2.2.10 Write ratios and                                  fractions and mixed numbers with or
properties of operations as     proportions to solve problems in                              without extraneous information.
strategies to calculate with    context involving rates, scale factors                        C. Solve multistep problems involving
numbers in any form; convert    and percentages.                                              whole numbers, decimals, money
between forms as appropriate; CT.7.2.2.12 Solve percent problems                              amounts and mixed numbers, including
and assess the reasonableness in context including what percentage                            means.
of answers using mental         one number is of another, percentage                          D. Solve multistep problems involving
computation and estimation      increase and percentage decrease                              whole numbers, decimals or money
strategies. For example: If a   using a variety of strategies, e.g.,                          amounts, and explain how the solution
woman making \$25 an hour        proportions or equations.                                     was determined.
gets a 10% raise, she will
make an additional 1/10 of her CT.7.2.2.16 Develop and describe in                            CMT 8.9 Solve Word Problems
salary an hour, or \$2.50, for a writing strategies for addition,                              A. Solve multistep problems involving
new salary of \$27.50. If you    subtraction, multiplication and                               fractions, mixed numbers, decimals and
want to place a towel bar 9     division and solve problems with                              money amounts with or without
3/4 inches long in the center   positive and negative integers using                          extraneous information
of a door that is 27 1/2 inches models, number lines, coordinate                              B. Solve multistep problems involving
wide, you will need to place    grids and computational strategies.                           whole numbers, mixed numbers, money
the bar about 9 inches from                                                                   amounts and decimals.
each edge; this estimate can    CT.7.1.3.8 Solve real world
be used as a check on the       problems using a variety of
exact computation.              algebraic methods including tables,
graphs, equations and inequalities.

14
Connecticut State Department of Education                                                                              September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
CCSS                      CT Standard Match              District Correlation                 CT Assessment
CC.7.EE.3 (Cont.)             CT.7.3.3.11 Write and solve                                     CMT 8.9 Solve Word Problems
problems in context involving                                   C. Solve multistep problems involving
conversions of customary or metric                              whole numbers, fractions, mixed
units and units of time.                                        numbers, decimals or money amounts,
and explain how the solution was
subtraction, multiplication and
division; solve problems with                                   Problem solving with negative rational
positive and negative rational                                  numbers is not assessed on the CMT.
numbers.

CT.8.2.2.8 Estimate reasonable
context involving rational and
common irrational numbers, ratios
and percentages, including
percentage of increase and decrease,
and justify solutions in writing.

15
Connecticut State Department of Education                                                                                September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
CC.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.
CCSS                       CT Standard Match                 District Correlation                    CT Assessment
CC.7.EE.4a Solve word           CT.7.1.1.1 Analyze a variety of                                      CMT 7.23 Algebraic Concepts
problems leading to equations patterns (physical phenomena,                                          A. Solve simple 1- or 2-step algebraic
of the form px + q = r and p(x numeric and geometric patterns,                                       equations.
+ q) = r, where p, q, and r are arithmetic sequences) and generalize
specific rational numbers.      with algebraic expressions, formulas                                 CMT 8.23 Algebraic Concepts
Solve equations of these        or equations.                                                        A. Solve simple equations, including 2-
forms fluently. Compare an                                                                           step equations.
algebraic solution to an        CT.7.1.2.4 Write expressions,                                        B. Solve multistep problems using
arithmetic solution,            formulas, equations or inequalities                                  algebraic concepts.
identifying the sequence of     using variables to represent                                         C. Evaluate expressions or solve
the operations used in each     mathematical relationships and solve                                 equations and use formulas.
approach. For example, The      problems.                                                            D. Represent situations with algebraic
perimeter of a rectangle is 54                                                                       expressions or equations.
cm. Its length is 6 cm. What is CT.7.1.2.9 Write, model and solve                                    E. Write an expression or equation to
its width?                      one- and two-step equations such as                                  represent a situation.
2x + 3 = 11 using a variety of
methods, including tables, concrete                                  Solving word problems leading to
models and the Properties of                                         equations of the form px + q = r and p(x
Equality, and justify the solution.                                  + q) = r, where p, q, and r are specific
rational numbers and comparing an
CT.8.1.3.12 Write and solve                                          algebraic solution to an arithmetic
multistep equations using various                                    solution are not assessed on the CMT.
algebraic methods including the
distributive property, e.g., 3 (x + 2)
=10), combining like terms, e.g., 3x
+ 2x = 15, and properties of equality
and justify the solutions.

16
Connecticut State Department of Education                                                                                       September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

EXPRESSIONS AND EQUATIONS
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
CCSS                      CT Standard Match            District Correlation                   CT Assessment
CC.7.EE.4b Solve word           CT.7.1.3.8 Solve real world                                   Solving word problems leading to
problems leading to             problems using a variety of                                   inequalities is not assessed on the CMT.
inequalities of the form px + q algebraic methods including tables,
> r or px + q < r, where p, q,  graphs, equations and inequalities.
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.

17
Connecticut State Department of Education                                                                                September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

GEOMETRY
Draw, construct, and describe geometrical figures and describe the relationships between them.
CCSS                      CT Standard Match                District Correlation                 CT Assessment
CC.7.G.1 Solve problems       CT.6.3.2.7 Use measurements to                                   Solving problems involving scale
involving scale drawings of   examine the ratios between                                       drawings of geometric figures is not
geometric figures, including  corresponding side lengths of scale                              assessed on the CMT.
computing actual lengths and models and similar figures.
areas from a scale drawing
and reproducing a scale       CT.7.2.2.10 Write ratios and
drawing at a different scale. proportions to solve problems in
context involving rates, scale factors
and percentages.

CT.7.3.1.5 Compare and describe in
writing the relationships, including
congruence, equality and scale,
between the angles, sides, perimeters
and areas of congruent and similar
geometric shapes.

CT.8.3.1.1 Determine the effect of
scale factors (resulting in similar
figures) on the perimeters and areas
of two-dimensional shapes and on
the surface areas and volumes of
three-dimensional solids.

18
Connecticut State Department of Education                                                                                 September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

GEOMETRY
Draw, construct, and describe geometrical figures and describe the relationships between them.
CCSS                      CT Standard Match               District Correlation                  CT Assessment
CC.7.G.2 Draw (freehand,       CT.7.3.1.1 Classify two- and three-                               CMT 5.17 Geometric Shapes and
with ruler and protractor, and dimensional geometric figures based                               Properties
with technology) geometric     on their properties including                                     B. Draw, describe and/or classify 2-
shapes with given conditions. relationships of sides and angles and                              dimensional geometric shapes and
Focus on constructing          symmetry (line and/or rotational)                                 figures.
triangles from three measures and apply this information to solve
of angles or sides, noticing   problems.                                                         CMT 6.17 Geometric Shapes and
when the conditions                                                                              Properties
determine a unique triangle,   CT.8.3.1.3 Construct and/or                                       B. Draw, describe and classify 2-
more than one triangle, or no  examine right triangles, make and                                 dimensional geometric shapes and
triangle.                      test conjectures about the                                        figures.
relationships of the angles and sides
and develop the Pythagorean                                       CMT 7.17 Geometric Shapes and
Theorem.                                                          Properties
B. Draw, describe and classify 2-
dimensional geometric shapes and
figures.

CMT 8.17 Geometric Shapes and
Properties
B. Draw, describe and classify 2- and 3-
dimensional geometric shapes and
figures.

Drawing geometric shapes with given
conditions is assessed on the Grades 5, 6,
7 and 8 CMT without the use of a
protractor and technology.

19
Connecticut State Department of Education                                                                                   September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

GEOMETRY
Draw, construct, and describe geometrical figures and describe the relationships between them.
CCSS                        CT Standard Match             District Correlation                  CT Assessment
CC.7.G.3 Describe the two-      CT.9-12.3.E.2a (1) Visualize three-                            Describing the two-dimensional figures
dimensional figures that result dimensional objects from different                             that result from slicing three-dimensional
from slicing three-             perspectives and analyze cross-                                figures is not assessed on the CMT.
dimensional figures, as in      sections, surface area and volume.
plane sections of right
rectangular prisms and right
rectangular pyramids.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
CCSS                        CT Standard Match             District Correlation                  CT Assessment
CC.7.G.4 Know the formulas CT.6.3.1.5 Recognize the                                            CMT 8.16 Customary and Metric
for the area and circumference relationships among radius,                                     Measures
of a circle and use them to     diameter, circumference and area of                            A. Measure and determine perimeters,
solve problems; give an         circles and develop formulas for                               areas and volumes. Explain or show how
informal derivation of the      finding circumference and area                                 the solution was determined.
relationship between the        based on these relationships.                                  B. Determine perimeters, areas and
circumference and area of a                                                                    volumes.
circle.                         CT.7.3.3.8 Use formulas to solve
problems involving perimeters and
areas of polygons and circles.
CC.7.G.5 Use facts about        No match                                                       Supplementary, complementary, vertical,
supplementary,                                                                                 and adjacent angles are not assessed on
complementary, vertical, and                                                                   the CMT.
problem to write and solve
simple equations for an
unknown angle in a figure.

20
Connecticut State Department of Education                                                                                  September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

GEOMETRY
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
CCSS                      CT Standard Match                District Correlation                  CT Assessment
CC.7.G.6 Solve real-world CT.7.3.2.7 Use two-dimensional                                       CMT 6.16 Customary and Metric
and mathematical problems representations of rectangular prisms,                               Measures
involving area, volume and pyramids and cylinders to determine                                 A. Measure and determine perimeter,
surface area of two- and   surface area.                                                       area and volume. Explain or show how
three-dimensional objects                                                                      the solution was determined.
composed of triangles,     CT.7.3.3.9 Develop and use formulas to
quadrilaterals, polygons,  determine volumes of geometric solids                               CMT 7.16 Customary and Metric
cubes, and right prisms.   (rectangular prisms and cylinders).                                 Measures
CT.7.3.3.10 Use estimation and                                      A. Measure and determine perimeters,
measurement strategies to solve                                     areas and volumes. Explain or show how
problems involving area of irregular                                the solution was determined.
polygons and volumes of irregular                                   B. Determine perimeters, areas and
solids and justify solutions in writing.                            volumes.

CT.7.3.3.8 Use formulas to solve                                  CMT 8.16 Customary and Metric
problems involving perimeters and areas                           Measures
of polygons and circles.                                          A. Measure and determine perimeters,
areas and volumes. Explain or show how
CT.8.3.2.6 Develop and use formulas to                            the solution was determined.
determine the surface areas of
rectangular prisms, cylinders and                                 CMT 8.16 Customary and Metric
pyramids.                                                         Measures
CT.8.3.2.7 Develop formulas using                                 B. Determine perimeters, areas and
measurement strategies and concrete                               volumes.
models, and use formulas to determine
the volumes of pyramids, cones and                                Surface area is not assessed on the CMT.
spheres.
CT.8.3.3.9 Use estimation and
measurement strategies, including
formulas, to solve surface area and
volume problems in context.
21
Connecticut State Department of Education                                                                                 September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY
Use random sampling to draw inferences about a population.
CCSS                        CT Standard Match          District Correlation                CT Assessment
CC.7.SP.1 Understand that        CT.8.4.2.8 Explain the effects of                             Random sampling is not assessed on the
statistics can be used to gain   sample size and sampling techniques                           CMT.
information about a population (convenience sampling, voluntary
by examining a sample of the     response sampling, systematic
population; generalizations      sampling and random sampling) on
about a population from a        statistical claims.
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.
CC.7.SP.2 Use data from a        CT.9-12.C.4.2.a (2) Use data from                             CAPT.4.2.a (2) Use data from samples
random sample to draw            samples to make inferences about a                            to make inferences about a population
inferences about a population    population and determine whether                              and determine whether claims are
with an unknown characteristic claims are reasonable or false.                                 reasonable or false.
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.

22
Connecticut State Department of Education                                                                               September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY
Draw informal comparative inferences about two populations.
CCSS                       CT Standard Match            District Correlation                  CT Assessment
CC.7.SP.3 Informally assess       CT.7.4.2.5 Compare two sets of                               Informally assessing the degree of visual
the degree of visual overlap of   data based on their spread and                               overlap of two numerical data
two numerical data distributions measures of central tendency.                                 distributions with similar variabilities is
with similar variabilities,                                                                    not assessed on the CMT.
measuring the difference          CT.8.4.1.3 Identify where
between the centers by            measures of central tendency and
expressing it as a multiple of a  spread are found in graphical
measure of variability. For       displays, including box-and-
example, the mean height of       whisker plots, stem-and-leaf
players on the basketball team is plots, scatter plots and histograms
10 cm greater than the mean
height of players on the soccer
(mean absolute deviation) on
either team; on a dot plot, the
separation between the two
distributions of heights is
noticeable.
CC.7.SP.4 Use measures of         CT.7.4.2.5 Compare two sets of                               CAPT.4.2.a (3) Determine and use
center and measures of            data based on their spread and                               measures of spread and central tendency
variability for numerical data    measures of central tendency.                                to describe and compare sets of data.
from random samples to draw
informal comparative inferences CT.9-12.4.2.a (3) Determine and
example, decide whether the       central tendency to describe and
words in a chapter of a seventh- compare sets of data.
generally longer than the words
in a chapter of a fourth-grade
science book.

23
Connecticut State Department of Education                                                                                  September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY
Investigate chance processes and develop, use, and evaluate probability models.
CCSS                    CT Standard Match                District Correlation                     CT Assessment
CC.7.SP.5 Understand that CT.2.4.3.5 Describe and explain                                        CMT.3.21 Probability
the probability of a chance  the likelihood of the occurrence                                    A. Identify correct solutions to problems
event is a number between 0 of various events. State                                             involving elementary notions of
and 1 that expresses the     possibilities, make predictions                                     probability.
likelihood of the event      and test the predictions in
occurring. Larger numbers    practical situations.                                               CMT.4.21 Probability
indicate greater likelihood.                                                                     A. Identify correct solutions to problems
A probability near 0         CT.3.4.3.6 Describe the                                             involving elementary notions of
indicates an unlikely event, probability of an outcome as ___                                    probability.
a probability around 1/2     out of ___ such as three out of
five.                                                               CMT.5-6.21 Probability
indicates an event that is                                                                       A. Identify correct solutions to problems
neither unlikely nor likely, CT.4.4.3.5 Conduct probability                                      involving elementary notions of
and a probability near 1     experiments and express the                                         probability and fairness.
indicates a likely event.    probability based on possible                                       B. Solve problems involving elementary
outcomes. For example: Eight out                                  notions of probability and fairness,
of ten tiles chosen were red.                                     including justifying solutions.
CT.5.4.3.6 Determine and                                          CMT.7-8.21 Probability
describe possible outcomes, and                                   A. Identify correct solutions to problems
express the likelihood of events as                               involving elementary notions of
a fraction.                                                       probability and fairness expressed as
fractions, decimals or percents.
CT.6.4.3.7 Express probabilities                                  B. Solve problems involving elementary
as fractions, ratios, decimals and                                notions of probability and fairness
percentages.                                                      expressed as fractions, decimals or
CT.7.4.3.9 Solve probability                                      percents and justify solutions.
problems in familiar contexts,
including simple events such as
flipping a coin and compound
events such as flipping a coin and
rolling a number cube.

24
Connecticut State Department of Education                                                                                   September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY
Investigate chance processes and develop, use, and evaluate probability models.
CCSS                      CT Standard Match              District Correlation                    CT Assessment
CC.7.SP.6 Approximate the CT.4.4.3.5 Conduct probability                                         CMT.7.21 Probability
probability of a chance        experiments and express the                                       C. Solve problems involving expected
event by collecting data on    probability based on possible                                     outcomes or predictions and justify
the chance process that        outcomes. For example: Eight out                                  solutions.
produces it and observing its of ten tiles chosen were red.
long-run relative frequency,                                                                     CMT.8.21 Probability
and predict the approximate CT.5.4.3.5 Design and conduct                                        C. Solve problems involving expected
relative frequency given the probability experiments and                                         outcomes or predictions and justify
probability. For example,      simple games of chance to test                                    solutions.
when rolling a number cube predictions about outcomes and
600 times, predict that a 3 or fairness.                                                         Collecting data requires a performance
6 would be rolled roughly                                                                        task and is not assessed on the CMT.
200 times, but probably not CT.6.4.3.5 Investigate and
exactly 200 times.             describe the relationship between
the number of trials in an
experiment and the predicted
outcomes.

CT.6.4.3.6 Design and conduct
probability experiments to test
fairness.

CT.7.4.3.7 Perform experiments
to determine experimental
probabilities.

CT.7.4.3.8 Compare and contrast
experimental probability results to
theoretical probabilities in
writing.

25
Connecticut State Department of Education                                                                                  September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY
Investigate chance processes and develop, use, and evaluate probability models.
CC.7.SP.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.
CCSS                       CT Standard Match                   District Correlation                    CT Assessment
CC.7.SP.7a Develop a            CT.7.4.3.6 Identifying all possible                                   CMT.8.21 Probability
uniform probability model       outcomes using models, tree                                           C. Solve problems involving expected
by assigning equal              diagrams, tables and/or organized                                     outcomes or predictions and justify
probability to all outcomes, lists to determine theoretical                                           solutions.
and use the model to            probabilities.
determine probabilities of
events. For example, if a       CT.7.4.3.7 Perform experiments to
student is selected at          determine experimental
random from a class, find       probabilities.
the probability that Jane will
be selected and the             CT.7.4.3.8 Compare and contrast
probability that a girl will be experimental probability results to
selected.                       theoretical probabilities in writing.
CC.7.SP.7b Develop a            CT.5.4.3.5 Design and conduct                                         Developing a probability model by
probability model (which        probability experiments and simple                                    observing frequencies in data generated
may not be uniform) by          games of chance to test predictions                                   from a chance process requires a
observing frequencies in        about outcomes and fairness.
performance task and is not assessed on
data generated from a
chance process. For             CT.6.4.3.6 Design and conduct                                         the CMT.
example, find the              probability experiments to test
approximate probability that   predictions about outcomes and
a spinning penny will land     fairness.
heads up or that a tossed
paper cup will land open-      CT.7.4.3.7 Perform experiments to
end down. Do the outcomes      determine experimental
for the spinning penny         probabilities.
appear to be equally likely
based on the observed          CT.7.4.3.8 Compare and contrast
frequencies?                   experimental probability results to
theoretical probabilities in writing.
26
Connecticut State Department of Education                                                                                       September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY
Investigate chance processes and develop, use, and evaluate probability models.
CC.7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
CCSS                    CT Standard Match                   District Correlation                      CT Assessment
CC.7.SP.8a Understand         CT.7.4.3.9 Solve probability                                            CMT.7-8.21 Probability
that, just as with simple     problems in familiar contexts,                                          C. Solve problems involving expected
events, the probability of a  including simple events such as                                         outcomes or predictions and justify
compound event is the         flipping a coin and compound                                            solutions.
fraction of outcomes in the   events such as flipping a coin and
sample space for which the    rolling a number cube.
compound event occurs.
CC.7.SP.8b Represent          CT.7.4.3.6 Identifying all                                              CMT.7.24 Classification and Logical
sample spaces for             possible outcomes using models,                                         Reasoning
compound events using         tree diagrams, tables and/or                                            A. Solve problems involving the
methods such as organized     organized lists to determine                                            organization of data.
lists, tables and tree        theoretical probabilities.                                              B. Sort or classify objects, and draw
diagrams. For an event                                                                                logical conclusions from data including
described in everyday         CT.7.4.3.9 Solve probability                                            Venn diagrams, combinations,
language (e.g., “rolling      problems in familiar contexts,                                          permutations and transitive reasoning
double sixes”), identify the  including simple events such as                                         questions.
outcomes in the sample        flipping a coin and compound
space which compose the       events such as flipping a coin and                                      CMT.7.25 Mathematical Applications
event.                        rolling a number cube.                                                  A. Solve extended numerical, statistical
and spatial problems.

CMT.8.24 Classification and Logical
Reasoning
A. Solve problems involving the
organization of data.
B. Sort or classify objects, and draw
logical conclusions from data including
Venn diagrams, combinations,
permutations and transitive reasoning
questions.

27
Connecticut State Department of Education                                                                                       September 2010
Grade 7 Mathematics Crosswalk – CCSS to CT Standards

STATISTICS AND PROBABILITY
Investigate chance processes and develop, use, and evaluate probability models.
CCSS                       CT Standard Match             District Correlation                   CT Assessment
CC.7.SP.8c Design and use CT.7.4.3.7 Perform experiments                                       Designing and using a simulation to
a simulation to generate        to determine experimental                                      generate frequencies requires a
frequencies for compound        probabilities.                                                 performance task and is not assessed on
events. For example, use
the CMT.
random digits as a
simulation tool 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?

28
Connecticut State Department of Education                                                                                September 2010

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