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Common Core State Standards Grade 6Connected Mathematics 2,
Grade 6 Units
Connected Mathematics (CMP) is a field-tested and
research-validated program that focuses on a few big ideas at each
grade level. Students explore these ideas in depth, thereby
developing deep understanding of key ideas that they carry from one
grade to the next. The sequencing of topics from grade to grade,
the result of lengthy field-testing and validation, helps to ensure
the development of students’ deep mathematical understanding and
strong problem-solving skills. By the end of grade 8, CMP students
will have studied all of the content and skills in the Common Core
State Standards (CCSS) for middle grades (Grades 6-8).
The sequence of content and skills in CMP2 varies in some
instances from that in the CCSS, so in collaboration with the CMP2
authors, Pearson has created a set of investigations for each grade
level to further support and fully develop students’ understanding
of the CCSS.
The authors are confident that the CMP2 curriculum supplemented
with the additional investigations at each grade level will address
all of the content and skills of the CCSS, but even more, will
contribute significantly to advancing students’ mathematical
proficiency as described in the Mathematical Practices of the CCSS.
Through the in-depth exploration of concepts, students become
confident in solving a variety of problems with flexibility, skill,
and insightfulness, and are able to communicate their reasoning and
understanding in a variety of ways.
The following alignment of the Common Core State Standards for
Mathematics ( June 2, 2010 release) to Pearson’s Connected
Mathematics 2 (CMP2) ©2009 program includes the supplemental
investigations that complete the CMP2 program. These supplemental
investigations will be available this fall from your Pearson
Prentice Hall Account Representative.
CCSS Mathematical Practices and CMP2
The Common Core State Standards (CCSS) articulate a set of
Mathematical Practices that have been central to the development of
the Connected Mathematics Project (CMP) materials from their
inception. CMP focuses on developing mathematical situations that
give students opportunities to incorporate the mathematical
practices into their ways of thinking and reasoning.
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ImplementIng the Common Core StAte StAndArdS
Standards for Mathematical Practices 1. Make sense of problems
and persevere in solving them.
This goal is fundamental to the CMP approach. CMP is a
problem-centered curriculum. To be effective, problems must embody
critical concepts and skills and have the potential to engage
students in making sense of mathematics. Students build
understanding by reflecting, connecting, and communicating.
The problems themselves are developed to be engaging to students
and to support these practices. The contexts of the problems
support the development of students’ mathematical reasoning
abilities and understanding. The demands of the problems lead
students into thinking and reasoning about problem contexts and the
mathematics needed to solve the problems embedded in the
contexts.
The questions in the problems provide the scaffolding needed for
students to engage with the context and to make progress on solving
the problem. The CMP teacher materials give suggestions to help
teachers develop classroom cultures in which students learn to
engage in mathematics discourse and articulate their reasoning and
solution strategies around problems.
Practice in the Applications, Connections, and Extensions
problems assures that all students are given opportunities to
develop successful practices for engaging with a new problem
situation.
Throughout program; for examples see: Bits and Pieces I (Inv.
3); Bits and Pieces II (Inv. 3); Bits and Pieces III (Inv. 4);
Prime Time (Inv. 2); Data About Us (Inv. 1); How Likely Is It?
(Inv. 4); Covering and Surrounding (Inv. 2); Shapes and Designs
(Inv. 1)
2. Reason abstractly and quantitatively.
CMP provides help to teachers in creating classroom environments
where students have opportunities to “talk” mathematics, to engage
in mathematical arguments, and to grow in their ability to
persevere in solving problems. These environments promote the
acquisition of mathematical language and mathematical ways of
reasoning that are the underpinning of both abstract and
quantitative mathematical reasoning.
A key to establishing such classrooms at this level is the
teacher’s commitment to developing a classroom culture in which
explanation of one’s thinking and reasoning is an expectation at
all times. In order to support the building of such classroom
norms, the problems students engage with need to capture students’
interest and systematically push students to higher levels of
thinking. This has always been at the forefront of the authors’
problem development. A growing body of evidence from the cognitive
sciences shows that students make sense of mathematics if concepts
and skills are embedded within a context or problem. This research
is a cornerstone for developing the problem situations in CMP.
Throughout program; for examples see: Prime Time (Inv. 2 p. 25);
Bits and Pieces I (Inv. 3 pp. 40–41); Bits and Pieces II (Inv. 3
pp. 36–38); Bits and Pieces III (Inv. 3 p. 46); Data About Us (Inv.
3 pp. 54–55); How Likely Is It? (Inv. 2 pp. 22–23); Covering and
Surrounding (Inv. 5 p. 88); Shapes and Designs (Inv. 3 p. 69)
The chart that follows highlights the opportunities these
materials create to make the Mathematical Practices a reality for
students. It explains how CMP supports the development of the
Mathematical Practices and provides some examples of how each
standard for Mathematical Practices is embedded in the CMP
materials.
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Standards for Mathematical Practices
3. Construct viable arguments and critique the reasoning of
others.
A classroom environment in which students expect to explain the
reasoning that led to the solution they put forth changes
mathematics from the dreaded subject it is for many students to a
subject that makes sense and provides challenges that students are
willing to undertake. Every module in CMP provides problems that
help create such an environment. The teacher guides provide
questions for teachers to use as they work to create a classroom
culture that focuses on argument and critique as a part of making
sense of and solving mathematical problems.
Reasoning and justification are central to all three grade
levels—6, 7, and 8. However, the sophistication of the problem
situations and mathematical discussions around the problem
solutions grows over the grades. The teacher materials provide help
for teachers in creating classroom norms that establish
expectations around classroom mathematical discourse.
The lens the authors used in creating and critiquing problems in
the curriculum is the following: A problem must have important,
useful mathematics embedded in it; investigation of the problem
should contribute to students’ conceptual development of important
mathematical ideas; work on the problem should promote skillful use
of mathematics; and problems should create opportunities for
teachers to assess what students are learning. Problems at all
grade levels are developed to promote opportunities to construct
mathematical arguments and to critique other students’ solutions
and strategies.
Throughout program; for examples see: Bits and Pieces I (Inv. 1
pp. 7–8, 10, Inv. 2 pp. 24–25, Inv. 4 pp. 56–58, 60); Bits and
Pieces II (Inv. 4 p. 54); Bits and Pieces III (Inv. 3 p. 39); Prime
Time (Inv. 1 p. 10); Data About Us (Inv. 2 p. 33); How Likely Is
It? (Inv. 3); Covering and Surrounding (Inv. 1 pp. 6–8);
Shapes and Designs (Inv. 2 pp. 36–37)
4. Model with mathematics.
In grades 6, 7, and 8, CMP engages students in learning to
construct, make inferences from, and interpret concrete symbolic,
graphic verbal, and algorithmic models of mathematical
relationships in problem situations as well as translating
information from one model to another. Building a standard set of
mathematical modeling tools begins in grade 6 and continues to grow
in sophistication throughout grades 7 and 8.
The basic set of modeling tools in CMP are number strips, number
lines, squares, diagrams, graphs, tables, equations, functions, and
technological supports such as calculators and computers.
Partitioning squares, strips, and lines support students’ insight
into rational numbers and rational number computation. Diagrams
help students model a problem situation and determine whether a
solution is correct. Graphs are fundamental to understanding
equations and functions. Students explore the relationships among
members of a set of functions such as linear, quadratic, and
exponential through graph models and algebraic models. These models
give students insight into the overall behavior of a particular
kind of function and allow students to make comparisons between
functions.
In data analysis, additional models are introduced that give
opportunities for students to experience a different kind of
reasoning—one based on seeing and reporting trends, anomalies,
outliers, and other aspects of the data as it is displayed in
various representations. Statistical thinking and reasoning is
extremely important to everyone in our society. Making decisions,
understanding survey data, reading newspaper reports, and being a
savvy consumer are all enhanced by developing tools for analyzing
and interpreting statistical claims that are ubiquitous in our
society. CMP provides a substantive data analysis module at each
grade level.
Throughout program; for examples see: Bits and Pieces I (Inv. 3
pp. 36–38, 40–41); Bits and Pieces II (Inv. 3 pp. 34–35); Bits and
Pieces III (Inv. 4 p. 58) Prime Time (Inv. 2 p. 25); Data About Us
(Inv. 1 pp. 18–20) How Likely Is It? (Inv. 4 pp. 57–58); Covering
and Surrounding (Inv. 2 p. 30); Shapes and Designs (Inv. 1 pp.
14–15)
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ImplementIng the Common Core StAte StAndArdS
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Standards for Mathematical Practices
5. Use appropriate tools strategically.
CMP chose a small set of tools as the primary vehicles for
exploring problem situations. Students use these tools to gain
insight into situations, to compute, and to represent relationships
in tables, graphs, and spreadsheets. Students use calculators in
many ways: to compute, to check their thinking, to explore
possibilities, to see whether an approach makes sense, and to use
the graphing capability to examine functions to see how they behave
– what is common and what is different in the behavior of classes
of functions.
In addition, students use tools such as polystrips, plastic
two-dimensional shapes, and three-dimensional shapes to explore
mathematics. The polystrips allow students to explore the rigidity
of triangle forms and the lack of rigidity of square forms. The
two-dimensional shapes support many kinds of mathematical
explorations. For example, students explore the question of what
shape has the greatest area when built from a given number of
squares. Graphing tools have become essential in classrooms to give
students support in engaging with mathematics both in exploratory
ways to “see into a problem situation” and to find solutions to
problems.
Through out grades 6, 7, and 8, students are encouraged to
determine the reasonableness of answers by using “benchmarks” to
estimate measures and other strategies to approximate a calculation
and to compare estimates.
Throughout program; for examples see: Shapes and Designs (Inv.
2, 4); Bits and Pieces I (Inv. 1); Bits and Pieces II (Inv. 3);
Prime Time (Inv. 1, 2); How Likely Is It? (Inv. 1, 2, 3, 4)
6. Attend to precision.
As students transition from elementary programs into CMP, a key
goal is learning to “talk” mathematics using precise terms and
definitions. The clarity of a student’s thinking is dependent on
the student’s precise understanding of mathematical language. CMP
is judicious in supporting the use of mathematical language. The
key mathematical goals determine which important mathematical
terms, definitions, and ways of thinking and reasoning are
highlighted. Student books include mathematical definitions that
are student-friendly. For example, the definition of congruent
figures is: Two figures are congruent if one is the image of the
other under a translation, a reflection, a rotation, or some
combination of these transformations. The goal is to develop
students’ facility in talking mathematics at an appropriate level
of mathematical maturity.
In addition to supporting the development of precise use of
mathematical language, CMP supports students in developing
precision in their presentation of arguments. The series of
questions in a problem pushes students to think more deeply and to
articulate more clearly their solutions and the processes by which
they reached these solutions.
A regular feature of the CMP student materials is the
Mathematical Reflections (MR) pages that occur at the end of each
investigation. The MR pages consist of a set of questions that help
students synthesize and organize their understandings of important
concepts and strategies. After thinking about the questions and
sketching their own ideas, students discuss the questions with
their teacher and classmates, and then write a summary of their
findings.
Throughout program; for examples see: Shapes and Designs (Inv.
2)
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Standards for Mathematical Practices
7. Look for and make use of structure.
The CMP materials were designed to build mathematics in ways
that illuminate and make use of mathematical structure. In grade 6,
for example, students examine data tables and look for patterns in
the data, and they analyze numbers to determine their prime
structure.
In grade 7, students examine proportional reasoning situations
of various kinds and develop tools for solving proportions. They
examine the structure of algebraic expressions, algebraic
operations, equations, and equation solving. In all grades,
students see structure in measurement. They examine formulas,
create algorithms for computation with rational numbers, and
compare algorithms for scope of use and efficiency.
In grade 8, students examine the structure of linear,
exponential, and quadratic relationships. They examine graphical
representations of functions and develop ways of solving equations
of each kind. Although it is unusual to examine quadratic and
exponential functions in middle school, the mathematical payoff for
examining these three kinds of relationships is very great.
Linearity is amazingly complex for students. The contrast with two
other kinds of functions helps students understand the structure of
a function and to see what is revealed about the function through
its structure.
Throughout program; for examples see: Bits and Pieces I (Inv. 1,
2, 3); Bits and Pieces II (Inv. 2, 3, 4); Bits and Pieces III (Inv.
1, 2, 5); Prime Time (Inv. 1, 2, 4); Covering and Surrounding (Inv.
1, 2, 3, 4, 5); How Likely Is It? (Inv. 2, 4); Data About Us (Inv.
1, 2, 3); Shapes and Designs (Inv. 1, 2, 3, 4)
8. Look for and express regularity in repeated reasoning.
The CMP curriculum was developed expressly to engage students in
making sense of mathematics, in seeing regularity, in learning to
apply strategies and tools developed in one context to a very
different problem context, in seeking mathematical connections, and
in recognizing and using powerful mathematical ways of thinking and
reasoning. The materials provide repeated opportunities for
students to examine mathematical situations, presented in a context
or in mathematical form, and to look for connections to previous
problems and previous solution strategies.
Students are aided in seeing opportunities to use strategies
previously used to solve a problem in order to solve a new problem
that looks on the surface to be very different. This kind of
thinking and reasoning about solving problems promotes a view of
mathematics as connected in many different ways, rather than as an
endless set of problems to be solved and forgotten.
The CMP teacher materials tell how to create a learning
environment that promotes student-to-student discourse around
mathematics. The problems are written to be engaging to students in
the middle grades and to encourage the development of mathematical
thinking and reasoning. Even the titles of the materials express
the importance the authors place on making connections–all kinds of
mathematics connections. Noting such connections is fundamental in
seeing mathematics as a connected whole rather than an endless
string of algorithms or processes to be learned.
Throughout program; for examples see: Prime Time (Inv. 2, 3);
Bits and Pieces I (Inv. 3); Bits and Pieces II (Inv. 2, 3); Shapes
and Designs (Inv. 1, 3); Covering and Surrounding (Inv. 1, 2,
4)
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ImplementIng the Common Core StAte StAndArdS
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Common Core State Standards Grade 6Meeting the Common Core State
Standards
with Connected Mathematics 2 (CMP2)
Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve
problems.
6.RP.1 Understand the concept of a ratio and use ratio language
to describe a ratio relationship between two quantities. For
example, “The ratio of wings to beaks in the bird house at the zoo
was 2:1, because for every 2 wings there was 1 beak.” “For every
vote candidate A received, candidate C received nearly three
votes.”
Bits and Pieces I (Inv. 4)
6.RP.2 Understand the concept of a unit rate a/b associated with
a ratio a:b with b ≠ 0, and use rate language in the context of a
ratio relationship. For example, “This recipe has a ratio of 3 cups
of flour to 4 cups of sugar, so there is 3/4 cup of flour for each
cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of
$5 per hamburger.”
NOTE: Expectations for unit rates in this grade are limited to
non-complex fractions.
CCSS Investigation 1: Ratios and Rates
6.RP.3Use ratio and rate reasoning to solve real-world and
mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or
equations.
Bits and Pieces I (Inv. 3, 4)
Shapes and Designs (Inv. 2 ACE 29–35)
How Likely Is It? (Inv. 1, 2, 3, 4)
6.RP.3.aMake tables of equivalent ratios relating quantities
with whole number measurements, find missing values in the tables,
and plot the pairs of values on the coordinate plane. Use tables to
compare ratios.
Bits and Pieces I (Inv. 4)
CCSS Investigation 1: Ratios and Rates
6.RP.3.b Solve unit rate problems including those involving unit
pricing and constant speed. For example, if it took 7 hours to mow
4 lawns, then at that rate, how many lawns could be mowed in 35
hours? At what rate were lawns being mowed?
Bits and Pieces I (Inv. 4)
CCSS Investigation 1: Ratios and Rates
6.RP.3.c Find a percent of a quantity as a rate per 100 (e.g.,
30% of a quantity means 30/100 times the quantity); solve problems
involving finding the whole, given a part and the percent.
Bits and Pieces III (Inv. 4, 5)
6.RP.3.d Use ratio reasoning to convert measurement units;
manipulate and transform units appropriately when multiplying or
dividing quantities.
CCSS Investigation 1: Ratios and Rates
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Common Core State Standards Grade 6Meeting the Common Core State
Standards
with Connected Mathematics 2 (CMP2)
The Number System
Apply and extend previous understandings of multiplication and
division to divide fractions by fractions.
6.NS.1 Interpret and compute quotients of fractions, and solve
word problems involving division of fractions by fractions, e.g.,
by using visual fraction models and equations to represent the
problem. For example, create a story context for (2/3) ÷ (3/4)
and use a visual fraction model to show the quotient; use the
relationship between multiplication and division to explain that
(2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷
(c/d) = ad/bc.) How much chocolate will each person get if 3 people
share 1/2 lb of chocolate equally? How many 3/4-cup servings are in
2/3 of a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi?
Bits and Pieces II (Inv. 4)
Compute fluently with multi-digit numbers and find common
factors and multiplies.
6.NS.2 Fluently divide multi-digit numbers using the standard
algorithm.
Bits and Pieces I (Inv. 3)
Bits and Pieces III (Inv. 3)
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit
decimals using the standard algorithm for each operation.
Bits and Pieces III (Inv. 1, 2, 3)
6.NS.4 Find the greatest common factor of two whole numbers less
than or equal to 100 and the least common multiple of two whole
numbers less than or equal to 12. Use the distributive property to
express a sum of two whole numbers 1–100 with a common factor as a
multiple of a sum of two whole numbers with no common factor. For
example, express 36 + 8 as 4(9 + 2).
Prime Time (Inv. 2, 3)
CCSS Investigation 2: Number Properties and Algebraic
Equations
Apply and extend previous understandings of numbers to the
system of rational numbers.
6.NS.5 Understand that positive and negative numbers are used
together to describe quantities having opposite directions or
values (e.g., temperature above/below zero, elevation above/below
sea level, credits/debits, positive/negative electric charge); use
positive and negative numbers to represent quantities in real-world
contexts, explaining the meaning of 0 in each situation.
Bits and Pieces II (Inv. 2 ACE 51)
6.NS.6 Understand a rational number as a point on the number
line. Extend number line diagrams and coordinate axes familiar from
previous grades to represent points on the line and in the plane
with negative number coordinates.
Bits and Pieces I (Inv. 1, 2, 3, 4)
Bits and Pieces II (Inv. 1, 2, 3, 4)
Bits and Pieces III (Inv. 1, 2, 3, 4)
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ImplementIng the Common Core StAte StAndArdS
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Common Core State Standards Grade 6Meeting the Common Core State
Standards
with Connected Mathematics 2 (CMP2)
6.NS.6.a Recognize opposite signs of numbers as indicating
locations on opposite sides of 0 on the number line; recognize that
the opposite of the opposite of a number is the number itself,
e.g., –(–3) = 3, and that 0 is its own opposite.
Bits and Pieces II (Inv. 2 ACE 51)
CCSS Investigation 3: Integers and the Coordinate Plane
6.NS.6.b Understand signs of numbers in ordered pairs as
indicating locations in quadrants of the coordinate plane;
recognize that when two ordered pairs differ only by signs, the
locations of the points are related by reflections across one or
both axes.
CCSS Investigation 3: Integers and the Coordinate Plane
6.NS.6.c Find and position integers and other rational numbers
on a horizontal or vertical number line diagram; find and position
pairs of integers and other rational numbers on a coordinate
plane.
CCSS Investigation 3: Integers and the Coordinate Plane
6.NS.7 Understand ordering and absolute value of rational
numbers.
Bits and Pieces I (Inv. 1, 2, 3)
6.NS.7.a Interpret statements of inequality as statements about
the relative position of two numbers on a number line diagram. For
example, interpret –3 > –7 as a statement that –3 is located to
the right of –7 on a number line oriented from left to right.
Bits and Pieces I (Inv. 1, 2, 3, 4)
Bits and Pieces II (Inv. 2 ACE 51)
6.NS.7.b Write, interpret, and explain statements of order for
rational numbers in real-world contexts. For example, write –3 °C
> –7 °C to express the fact that –3 °C is warmer than –7 °C.
Bits and Pieces II (Inv. 2 ACE 51)
Bits and Pieces III (Inv. 1 ACE 58)
6.NS.7.c Understand the absolute value of a rational number as
its distance from 0 on the number line; interpret absolute value as
magnitude for a positive or negative quantity in a real-world
situation. For example, for an account balance of –30 dollars,
write |–30| = 30 to describe the size of the debt in
dollars.
CCSS Investigation 3: Integers and the Coordinate Plane
6.NS.7.d Distinguish comparisons of absolute value from
statements about order. For example, recognize that an account
balance less than –30 dollars represents a debt greater than 30
dollars.
CCSS Investigation 3: Integers and the Coordinate Plane
6.NS.8 Solve real-world and mathematical problems by graphing
points in all four quadrants of the coordinate plane. Include use
of coordinates and absolute value to find distances between points
with the same first coordinate or the same second coordinate.
Covering and Surrounding (Inv. 2)
Data About Us (Inv. 2)
CCSS Investigation 3: Integers and the Coordinate Plane
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Common Core State Standards Grade 6Meeting the Common Core State
Standards
with Connected Mathematics 2 (CMP2)
Expressions and Equations
Apply and extend previous understandings of arithmetic to
algebraic expressions.
6.EE.1 Write and evaluate numerical expressions involving
whole-number exponents.
Prime Time (Inv. 4)
6.EE.2 Write, read, and evaluate expressions in which letters
stand for numbers.
Bits and Pieces II (Inv. 2, 3, 4)
Bits and Pieces III (Inv. 1, 2, 3)
CCSS Investigation 2: Number Properties and Algebraic
Equations
6.EE.2.a Write expressions that record operations with numbers
and with letters standing for numbers. For example, express the
calculation “Subtract y from 5” as 5 – y.
CCSS Investigation 2: Number Properties and Algebraic
Equations
6.EE.2.b Identify parts of an expression using mathematical
terms (sum, term, product, factor, quotient, coefficient); view one
or more parts of an expression as a single entity. For example,
describe the expression 2(8 + 7) as a product of two factors; view
(8 + 7) as both a single entity and a sum of two terms.
Prime Time (Inv. 1, 3, 4, 5)
Bits and Pieces II (Inv. 2, 3, 4)
Bits and Pieces III (Inv. 1, 2, 3)
CCSS Investigation 2: Number Properties and Algebraic
Equations
6.EE.2.c Evaluate expressions at specific values of their
variables. Include expressions that arise from formulas used in
real-world problems.Perform arithmetic operations, including those
involving whole number exponents, in the conventional order when
there are no parentheses to specify a particular order (Order of
Operations). For example, use the formulas V = s3 and A = 6s2 to
find the volume and surface area of a cube with sides of length s =
1/2.
Covering and Surrounding (Inv. 1, 2, 3, 4, 5)
CCSS Investigation 2: Number Properties and Algebraic
Equations
6.EE.3 Apply the properties of operations to generate equivalent
expressions.For example, apply the distributive property to the
expression 3(2 + x) to produce the equivalent expression 6 + 3x;
apply the distributive property to the expression 24x + 18y to
produce the equivalent expression 6(4x + 3y); apply properties of
operations to y + y + y to produce the equivalent expression
3y.
CCSS Investigation 2: Number Properties and Algebraic
Equations
6.EE.4 Identify when two expressions are equivalent (i.e., when
the two expressions name the same number regardless of which value
is substituted into them). For example, the expressions y + y + y
and 3y are equivalent because they name the same number regardless
of which number y stands for.
CCSS Investigation 2: Number Properties and Algebraic
Equations
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ImplementIng the Common Core StAte StAndArdS
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Common Core State Standards Grade 6Meeting the Common Core State
Standards
with Connected Mathematics 2 (CMP2)
Reason about and solve one-variable equations and
inequalities.
6.EE.5 Understand solving an equation or inequality as a process
of answering a question: which values from a specified set, if any,
make the equation or inequality true? Use substitution to determine
whether a given number in a specified set makes an equation or
inequality true.
Bits and Pieces II (Inv. 2, 3, 4)
Bits and Pieces III (Inv. 1, 2, 3)
6.EE.6 Use variables to represent numbers and write expressions
when solving a real-world or mathematical problem; understand that
a variable can represent an unknown number, or, depending on the
purpose at hand, any number in a specified set.
CCSS Investigation 2: Number Properties and Algebraic
Equations
6.EE.7 Solve real-world and mathematical problems by writing and
solving equations of the form x + p = q and px = q for cases in
which p, q and x are all nonnegative rational numbers.
CCSS Investigation 2: Number Properties and Algebraic
Equations
6.EE.8 Write an inequality of the form x > c or x < c to
represent a constraint or condition in a real-world or mathematical
problem. Recognize that inequalities of the form x > c or x <
c have infinitely many solutions; represent solutions of such
inequalities on number line diagrams.
CCSS Investigation 3: Integers and the Coordinate Plane
Represent and analyze quantitative relationships between
dependent and independent variables.
6.EE.9 Use variables to represent two quantities in a real-world
problem that change in relationship to one another; write an
equation to express one quantity, thought of as the dependent
variable, in terms of the other quantity, thought of as the
independent variable. Analyze the relationship between the
dependent and independent variables using graphs and tables, and
relate these to the equation. For example, in a problem involving
motion at constant speed, list and graph ordered pairs of distances
and times, and write the equation d = 65t to represent the
relationship between distance and time.
CCSS Investigation 2: Number Properties and Algebraic
Equations
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Common Core State Standards Grade 6Meeting the Common Core State
Standards
with Connected Mathematics 2 (CMP2)
Geometry
Solve real-world and mathematical problems involving area,
surface area, and volume.
6.G.1 Find the area of right triangles, other triangles, special
quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these techniques
in the context of solving real-world and mathematical problems.
Covering and Surrounding (Inv. 1, 2, 3, 4, 5)
6.G.2 Find the volume of a right rectangular prism with
fractional edge lengths by packing it with unit cubes of the
appropriate unit fraction edge lengths, and show that the volume is
the same as would be found by multiplying the edge lengths of the
prism. Apply the formulas V = lwh and V = bh to find volumes of
right rectangular prisms with fractional edge lengths in the
context of solving real-world and mathematical problems.
CCSS Investigation 4: Measurement
6.G.3 Draw polygons in the coordinate plane given coordinates
for the vertices; use coordinates to find the length of a side
joining points with the same first coordinate or the same second
coordinate. Apply these techniques in the context of solving
real-world and mathematical problems.
CCSS Investigation 3: Integers and the Coordinate Plane
6.G.4 Represent three-dimensional figures using nets made up of
rectangles and triangles, and use the nets to find the surface area
of these figures. Apply these techniques in the context of solving
real-world and mathematical problems.
Covering and Surrounding (Inv. 3 ACE 39)
CCSS Investigation 4: Measurement
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ImplementIng the Common Core StAte StAndArdS
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Common Core State Standards Grade 6Meeting the Common Core State
Standards
with Connected Mathematics 2 (CMP2)
Statistics and Probability
Develop understanding of statistical variability.
6.SP.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts for it
in the answers. For example, “How old am I?” is not a statistical
question, but “How old are the students in my school?” is a
statistical question because one anticipates variability in
students’ ages.
Data About Us (Inv. 1, 2, 3, Unit Project p. 64)
6.SP.2 Understand that a set of data collected to answer a
statistical question has a distribution which can be described by
its center, spread, and overall shape.
Data About Us (Inv. 1, 2, 3)
6.SP.3 Recognize that a measure of center for a numerical data
set summarizes all of its values with a single number, while a
measure of variation describes how its values vary with a single
number.
Data About Us (Inv. 1, 2, 3)
Summarize and describe distributions.
6.SP.4 Display numerical data in plots on a number line,
including dot plots, histograms, and box plots.
Data About Us (Inv. 1, 3)
CCSS Investigation 4: Histograms and Box Plots
6.SP.5 Summarize numerical data sets in relation to their
context, such as by:
Data About Us (Inv. 1, 2, 3)
6.SP.5.a Reporting the number of observations.
How Likely Is It? (Inv. 1, 2, 3, 4)
6.SP.5.b Describing the nature of the attribute under
investigation, including how it was measured and its units of
measurement.
Data About Us (Inv. 1, 2)
6.SP.5.c Giving quantitative measures of center (median and/or
mean) and variability (interquartile range and/or mean absolute
deviation), as well as describing any overall pattern and any
striking deviations from the overall pattern with reference to the
context in which the data were gathered.
Data About Us (Inv. 3)
CCSS Investigation 4: Histograms and Box Plots
6.SP.5.d Relating the choice of measures of center and
variability to the shape of the data distribution and the context
in which the data were gathered.
Data About Us (Inv. 3)