# Math Pacing Guide 6th Grade by Cy1lRA3S

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```									                                                                                6th Grade Math Pacing Guide
CCGPS
Operations with decimal fractions                                  positive rational numbers, factors, multiples,
decompose, prime numbers, prime
Addition and subtraction of common                                 factorization, Fundamental Theorem of
fractions and mixed numbers with                                   Arithmetic, GCF, LCM, evaluate, surface
unlike denominators such as                                        area, metric system of measurement,
2,3,4,5,6,8,10, and 12                                             customary system of
measurement,proportional relationships,
Taught Continuously

right rectangular prism, cylinder, pyramid,
Skills to Maintain

Terms/Symbols
cone, geometric solid, net, geometric
figures, line symmetry, rotational symmetry,
Modeling multiplication of common
fractions                                                          similar plane figures, scale factor, scale
drawings, relations, varying quantities, ratio,
Modeling percent                                                   direct proportion, proportions, proportional
reasoning, frequency distributions,
Graphing data                                                      pictographs, histograms, bar graphs, line
Multiples and factors                                              graphs, circle graphs, line plot, frequency
Perimeter, capacity, and area of                                   table, experimental probability, theoretical
geometric figures                                                  probability, sampling, event, random
sample, population, non-routine word
Evaluating algebraic expressions                                   problems.

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6th Grade Math Pacing Guide
CCGPS
1st 8 Weeks
CCGPS                                Related GPS standards                            Resources                 Schedule
MCC6.NS.2: Fluently divide multi-digit M6N1: Students will understand the meaning of                                       3 Weeks- 1 week
numbers using the standard             the four arithmetic operations as related to positve                                comp. fluency? 1
algorithm.                             rational numbers and will use these concepts to                                     week decimals? 1
solve problems.                                                                    week factor/multiples
MCC6.NS.3 Fluently add, subtract,      M6N1g. Solve problems involving fractions,             McDougal Littell: Chapter      and fractions?
multiply, and divide multi-digit       decimals, and percents.                                2 resources
decimals using the standard algorithm
for each operation.
Compute fluently with multi-digit      M6N1a. Apply factors and multiples                     McDougal Littell: Chapter
numbers and find common factors                                                               4 lesson 2, 4 resources
and multiples.
MCC6.NS.4: Find the greatest           M6N1c. Determine the greatest common factor            McDougal Littell: Chapter
common factor of two whole numbers (GCF) and the least common multiple (LCM) for a            4 lesson 2, 4 resources
less than or equal to 100 and the      set of numbers
1st 8 Weeks
Unit 1: Number System Fluency

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, (See standards for
exampes)

TRANSITION STANDARD- TAUGHT M6N1e. Multiply and divide fractions and mixed                    McDougal Littell: Chapter
IN 5th and 6th FOR 2012-2013:         numbers.                                                4 lesson 6, Chapter 5
MCC5.NF.6: Solve real world                                                                   lesson 3, Consult with
problems involving multiplication of                                                          5th grade resources for
fractions and mixed numbers, e.g., by                                                         modeling materials.
using visual fraction models or
equations to represent the problem.

Apply and extend previous              M6N1e. Multiply and divide fractions and mixed         McDougal Littell: Chapter
understandings of multiplication       numbers.                                               5, lesson 4
and division to divide fractions by
fractions

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6th Grade Math Pacing Guide
CCGPS
MCC6.NS.1: Interpret and compute       M6N1e. Multiply and divide fractions and mixed   McDougal Littell: Chapter
quotients of fractions, and solve word numbers.                                         5, lesson 4
problems involving division of
fractions by fractions, e.g., by using
visual fraction models and equations
to represent the problem. (See
standards for examples)

Understand ratio concepts and use M6A1: Students will understand the concept of                                     5 Weeks. 2 weeks
ratio reasoning to solve problems. ratio and use it to represent quantitative                                       Ratio/Rates? 1 week
relationships.                                                                Percents? 2 weeks
MCC6.RP.1: Understand the concept M6A1: Students will understand the concept of
of a ratio and use ratio language to  ratio and use it to represent quantitative
describe a ratio relationship between relationships.
two quantities. (see standards for
examples)
MCC6.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. (see standards for
examples)
MCC6.RP.3: Use ratio and rate         M6A2b. Use manipulatives or draw pictures to
reasoning to solve real-world and     solve problems involving proportional
mathematical problems, e.g., by       relationships.
reasoning about tables of equivalent
ratios, tape diagrams, double number
line diagrams, or equations.
Using Equivalent Fractions

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6th Grade Math Pacing Guide
CCGPS
MCC6.RP.3a: Make tables of             M6A2e. Graph proportional relationships in the
equivalent ratios relating quantities  form y = kx and describe characteristics of the
with whole-number measurements,        graphs.
find missing values in the tables, and
Rate, Ratio and Proportional Reasoning, Using Equivalent Fractions

plot the pairs of values on the
coordinate plane. Use tables to
compare ratios. Analyze and describe
patterns arising from mathematical
rules, tables, and graphs.

MCC6.RP.3b: Solve unit rate
problems including those involving
unit pricing and constant speed. (see
standards for examples)
MCC6.RP.3c. Find a percent of a        M6A2c. Use proportions (a/b=c/d) to describe
quanitity as a rate per 100 (e.g. 30% relationships and solve problems, including
of a quantity means 30/100 times the percent problems.
quantity); solve problems involving
finding the whole given a part and the
percent. Explore and model percents
using multiple representations.

MCC6.RP.3d: Use ratio reasoning to     M6M1: Students will convert from one unit to
convert measurement unitsl             another within one system of measurement
manipulate and transform units         (customary or metric) by using proportional
appropriately when multiplying or      relationships.
dividing quantities. Students will
convert from one unit to another
within one system of measurement
Unit 2:

(customary or metric) by using
proportional relationships.

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6th Grade Math Pacing Guide
CCGPS
2nd 8-Weeks
CCGPS                                  Related GPS standards                   Resources   Schedule
Apply and Extend previous                 M6A3: Students will evaluate algebraic
understandings of arithmetic to           expressions, including those with exponents, and
algebraic expressions.                    solve simple one-step equations using each of the
four basic operations.
MCC6.EE.1: Write and evaluate             M6A3: Students will evaluate algebraic
numerical expressions involving           expressions, including those with exponents, and
whole-number exponents.                   solve simple one-step equations using each of the
four basic operations.
MCC6.EE.2 Write, read, and evaluate       M6A3: Students will evaluate algebraic
expressions in which letters stand for    expressions, including those with exponents, and
numbers.                                  solve simple one-step equations using each of the
four basic operations.
MCC6.EE.2b. Identify parts of an          M6A3: Students will evaluate algebraic
expression using mathematical terms       expressions, including those with exponents, and
(sum, term, product, factor, quotient,    solve simple one-step equations using each of the
coefficient); view one or more parts of   four basic operations.
Unit 3 Expressions
2nd 8-Weeks

an expression as a single entity.

MCC6.EE.2c. Evaluate expressions          M6A3: Students will evaluate algebraic
at specific values for their variables.   expressions, including those with exponents, and                3 Weeks.
Include expressions that arise from       solve simple one-step equations using each of the
formulas in real-world problems.          four basic operations.
Perform arithmetic operations,
including those involving those
involving whole-number exponents, in
the conventional order when there are
no parentheses to specify a particular
order (Order of Operations).

MCC6.EE.3 Apply the properties of         M6A3: Students will evaluate algebraic
operations to generate equivalent         expressions, including those with exponents, and
expressions.                              solve simple one-step equations using each of the
four basic operations.

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6th Grade Math Pacing Guide
CCGPS
MCC6EE.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).
Unit 4: One-Step Equations and Inequalities

M6A3: Students will evaluate algebraic
2nd 8-Weeks

expressions, including those with exponents, and
Reason about and solve one-         solve simple one-step equations using each of the
variable equations and inequalities four basic operations.

MCC6.EE.5 Understand solving and
equation or inequality as a process of   M6A3: Students will evaluate algebraic
answering a question: which values       expressions, including those with exponents, and
from a specified set, if any, make the   solve simple one-step equations using each of the
equation or inequality true.             four basic operations.
MCC6.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         M6A3: Students will evaluate algebraic
unknown number, or, depending on         expressions, including those with exponents, and
the purpose at hand, any number in a     solve simple one-step equations using each of the
specified set.                           four basic operations.
MCC6.EE7 Solve real-world and
mathematical problems by writing and
solving equations of the form x + p =    M6A3: Students will evaluate algebraic
q and px = q for cases in which p, q,    expressions, including those with exponents, and
and x are all nonnegative rational       solve simple one-step equations using each of the
numbers.                                 four basic operations.
MCC6.EE.8 Write an inequality of the                                                         5 weeks
form x > c or x < c have infinitely      M6A3: Students will evaluate algebraic
many solutions; represent solutions of   expressions, including those with exponents, and
such inequalities on number line         solve simple one-step equations using each of the
diagrams.                                four basic operations.

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5 weeks

6th Grade Math Pacing Guide
CCGPS
M6A3: Students will evaluate algebraic
Represent and analyze quantitative expressions, including those with exponents, and
relationships between dependant solve simple one-step equations using each of the
and independent variables.         four basic operations.

MCC6.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 dependant variable,
in terms of the other quantity, thought
of as the independant variable.
Analyze the relationship between the      M6A3: Students will evaluate algebraic
dependant and independant variables       expressions, including those with exponents, and
using graphs and tables, and relate       solve simple one-step equations using each of the
these to the equation.                    four basic operations.

Understand ratio concepts and use
ratio reasoning to solve problems.
MCC6.RP3a.b.c.d- State pacing                                                                 Investigate state intent
guide revisits standards from Unit 3 in                                                       in revisiting these
the context of equations and                                                                  standards- Frameworks?
inequalities.                                                                                 Portal?

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6th Grade Math Pacing Guide
CCGPS
3rd 8-weeks
Solve real-world and mathematical M6M2 Students wil use appropriate units of
problems involving area, surface  measure for finding length, perimeter, area, and
area, and volume.                 volume and will express each quantity using the
appropriate unit. M6M3d: Solve application
problems involving the volume of fundamental
solid figures. M6M4d: Solve application problems
involving surface are of right rectangular prisms.

MCC6.G.1 Find area of right triangles,
other triangles, special quadrilaterals,
and polygons by composing into
rectangles or decomposing into
triangles and other shapesl apply
these techniques in the context of
solving real-world and mathematical
Area and Volume

problems.
3rd 8-weeks

MCC6.G.2 Find the volume of a right M6M3 a.b.c.d (note- no longer finding volume of
rectanglar prism with fractional edge cylinders or cones)
2 Weeks
lengths by packing it with unit cubes
of the appropriate unit fraction edge
lengths, and show tha 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.

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6th Grade Math Pacing Guide
CCGPS
MCC6.G.4 Represent three-               M6M4 a,b,c,d (note- no longer finding surface
dimensional figures using nets made     area of cylinders or using nets beyond rectangular
up of rectangles and triangles, and     prisms)
use the nets to find the surface area
of these figures. Apply these
techniques in the context of solving
real-world and mathematical
problems.

Develop understanding of
statistical variability
MCC6.SP.1 Recognize a statistical      M6D1e. Relate the data analysis to the context of
question as one that anticipates       the questions posed.
variability in the data related to the
question and accounts for it in the
MCC6.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.

MCC6.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.

Summarize and describe
distributions.
Statistics

MCC6.SP.4 Display numerical data in M6D1 b, Using data, construct frequency
plots on a number line, including dot distributions, frequency tables, and graphs.           3 weeks
plots, histograms, and box plots.

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Statistics
6th Grade Math Pacing Guide                        3 weeks

CCGPS
MCC6.SP5 Summarize numberical           M6D1d. Use tables and graphs to examine
data sets in relation to their context, variation that occurs within a group and variation
such as by: a. Reporting the number that occurs between groups.
of observations; b. Describing the
nature of the attribute under
investigation, including how it was
measured and its units of
measurement. C. Giving quantitative
measure 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 was gathered. d. Relating the
choice of measures of center and
variability to the shape of the data
distribution and the context in which
the data was gathered.

Apply and extend previous
understandings of numbers to the
system of rational numbers.

10
s
6th Grade Math Pacing Guide
CCGPS
MCC6.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,
debits/credits, positive/negative
electric charge); use positive and
negative numbers to represent
quantities in real-world contexts,
explaining the meaning of 0 in each
situation.
3rd 8-weeks

ers and their Opposites

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6th Grade Math Pacing Guide
CCGPS
MCC6.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
3rd 8-weeks

on the line and in the plane with
negative number coordinates .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. 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. Given a point in the
Rational Explorations: Numbers and their Opposites

coordinate plane, determine the
coordinates resulting from a
reflection. c. Find and position
integers and other reational numbers
on a horizontal or vertical number line
diagram; find and position pairs of
integers and other rational numbrs on
a coordinate plane.

3 weeks

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Rational Explorations: Numbers and th
6th Grade Math Pacing Guide
CCGPS               3 weeks
MCC6.NS.7 Understand ordering and
absolute value of rational numbers.
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. 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 . 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. 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.

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6th Grade Math Pacing Guide
CCGPS
MCC6.NS.8 Solve real-world and
mathematival 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.
MCC6.G.3 Draw polygons in the
coordinate plane given coordinates
for the vertices; use coordinates to
find he 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.

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6th Grade Math Pacing Guide
CCGPS
Week by Week Pacing Guide
* Note- this suggested week by week guide does not have much room for delay if the units draw long; particularly with getting
all standards in prior to Benchmarks. There has been effort made to end neatly with breaks. This contains built- in CRCT
review, however, any pushing back of 3rd quarter standards into this "free time" will miss content assessed by 3rd quarter
benchmarks.
(3 wks)
Weeks 4-8 Weeks 1-3

Unit 1                      Number System Fluency
(5 wks)

Unit 2              Rate, Ratio, and Proportional Reasoning;   PLAN FOR THE
Using Equivalent Fractions          BENCHMARK
PREP/POST
TEST/PRE TEST
WINDOW TO CUT
OFF THE END OF
THIS 5 WEEK UNIT
1st Quarter BENCHMARK (November 1-7 Post/Pre window)
Weeks 9-11

(3 wks)

Unit 3                         Expressions

THANKSGIVING BREAK
(5 wks)
Weeks 12-16

Unit 4                 One-Step Equations and Inequalities      **5 week unit overlaps
and ends just after
Christmas Break.

CHRISTMAS BREAK **
Week 17-18

(2 wks)

Unit 5                          Area and Volume

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6th Grade Math Pacing Guide
CCGPS
Week 19- 21                  2nd Quarter BENCHMARK (January 14-17 Post/Pre window)

(3 wks)
Unit 6                           Statistics                  If timed carefully, this
chapter should end just
prior to Mid-Winter
Break

MID WINTER BREAK
(3 wks)
Weeks 22-24

Unit 7             Rational Explorations: Numbers and their
Opposites

3rd Quarter BENCHMARK (March 11-15 Post window)
(4 wks)
Weeks 25-28

CRCT REVIEW (Split in the
middle by SPRING BREAK)

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