# Mathematics Pacing Guide

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```					                                                                 Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                 Supporting Grade Level Content Expectations   Vocabulary

Integrated and                                 Technology
Ongoing
6-16 Use, Transfer, and Apply Appropriate
Technology
 Use Calculators
- Operation keys
 memory/recall
 square root
- Order of operations

   Solve Problems Using Calculators
- Applying order of operations to operation
keys
- Using given information to calculate
solutions
 reverse operations
 changes in the unknown information

   Use Appropriate Computer Skills

   Solve Problems Using the Computer
- Tutorial programs/resources

Employability/Career Skills

6-17 Careers
 Understand the Connection Between
Mathematics and Career Clusters
- Arts and Communication
- Business Management, Marketing,
Technology
- Engineering and Manufacturing
Sixth Grade Mathematics Pacing Guide – May 2008 Revision                     1
Timing                        Content & Processes (MCF)                     Supporting Grade Level Content Expectations   Vocabulary

-    Industrial Technology
-    Health Sciences
-    Natural Resources and Agri-sciences

6-18 Personal Management
 Develop Skills for Maintaining           Personal
Finances
- Budgeting and spending
- Checkbook
- Savings
- Credit

6-19 Teamwork
 Develop Skills for Interacting with Others
- Negotiation
- Cooperative learning
- Respect for others
- Conflict resolution

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                    Supporting Grade Level Content Expectations               Vocabulary

Patterns in Algebra                 Number Sense and Numeration
multiplication
Integrated and             6-11 Number Relationships                                                                                    symbols
Ongoing                     Explain Meaning of Powers and Roots                 B Understand and use integer exponents,                operation
(IV.3.MS.4)                                          excluding powers of negative numbers;                integers
- Use calculators to computer powers and            express numbers in scientific notation.              power
square roots                                    N.ME.06.16                                           quantities
rational numbers
simplest
Numerical and Algebraic Operations                                                                         form/simplify
and Analytic Thinking                                                                                 algebraic
expressions
6-13 Algebraic and Analytic Thinking                  B Use letters, with units, to represent quantities     algebraic equation
 Read, Write, and Create Algebraic Expressions         in a variety of contexts, e.g., y lbs., k minutes,   coefficients
(V.2.MS.1)                                           x cookies. A.FO.06.03                                discount
- Simplify                                        B Distinguish between an algebraic expression          distance
- Translate                                         and an equation. A.FO.06.04                          formula
- Solve                                           B Use standard conventions for writing                 function
 linear equations                               algebraic expressions, e.g., 2x+1 means “two         f(x)=
 inequalities                                   times x, plus 1” and 2(x + 1) means “two times       graphs
the quantity (x + 1). A.FO.06.05                     inverse operations
B Represent information given in words using           like terms
algebraic expressions and equations.                 linear
A.FO.06.06                                           linear functions
- Simplify expressions of the first degree by          parenthesis
combining like terms, and evaluate using             scientific notation
specific values. A.FO.06.07                          solutions
- Represent simple relationships between               speed (mph)
quantities, using verbal descriptions, formulas      Tables
or equations, tables, and graphs, e.g.               variable
perimeter-side relationship for a square,            brackets
distance-time graphs, and conversions such as        constant
feet to inches. A.RP.06.10                           distributive property
B Relate simple linear equations with integer          evaluate

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Timing                        Content & Processes (MCF)       Supporting Grade Level Content Expectations              Vocabulary

coefficients to particular contexts, e.g., 3x = 8   inequality
or x + 5 = 10, and solve. A.FO.06.11                labels
linear equations
negative integer
non-linear
positive integer
standard notation
term
values
variable equations
word problems
Square numbers
Consecutive integer
Inverse operations
operation
Algorithms

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                  Supporting Grade Level Content Expectations       Vocabulary

Unit 1A                             Number Sense and Numeration
Decimal
Topic: Basic Skills       6-10 Representation and Uses of Numbers                                                              dividend
 Apply Geometric Representations (IV.2.MS.1)        B Order rational numbers and place them on      divisibility
Timing: 2 weeks               - Fractions                                        the number line. N.ME.06.05                   division
- Prime and composite                                                                            division symbol
- Triangular and square numbers                                                                  divisor
- Number line                                                                                    multiple
- Rational numbers                                                                               multiplication
- Integers                                                                                       place value
unit
6-11 Number Relationships                                                                            Manipulatives
 Classification (IV.3.MS.3)                                                                         Powers of ten
- Prime and composite numbers                                                                    Square roots
- Factors and multiples
- Relatively prime
- Divisibility
- Least common multiple
- Greatest common factor

   Explain Meaning of Powers and Roots              B Understand and use integer exponents,
(IV.3.MS.4)                                        excluding powers of negative numbers;
- Use calculators to computer powers and          express numbers in scientific notation.
square roots                                  N.ME.06.16

   Solve Problems (IV.3.MS.5)
- Apply understanding of number
relationship in solving problems

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Mathematics Pacing Guide

Timing                      Content & Processes (MCF)                   Supporting Grade Level Content Expectations       Vocabulary

Unit 2                               Data Analysis and Statistics
Order of operations
Topic: Integers           6-7 Description and Interpretation                                                                   Base
 Read Data From Tables, Charts, and Graphs                                                          Exponent
Timing: 4 weeks               (III.2.MS.1)                                                                                     Operations
- Identify source                                                                                Inverse operation
Absolute value
   Data Distribution (III.2.MS.2)                                                                   Powers of ten
- Shape                                                                                          Scientific notation
- Mean                                                                                           Linear
- Median
- Mode
- Range
- Quartile
- Outlier

   Draw, Explain, and Justify Conclusions
(III.2.MS.3)
- Biased sources
- Data interpretation
- Inferences
- Sources of bias

   Analysis of Data (III.2.MS.4)
- Data sources
- Collection techniques

   Formulate Real-Life Problems and Apply Prior
Knowledge (III.2.MS.5)

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Timing                       Content & Processes (MCF)          Supporting Grade Level Content Expectations          Vocabulary

Number Sense and Numeration         - Represent rational numbers as fractions or
terminating decimals when possible, and
6-9 Concepts and Properties of Numbers         translate between these representations.
 Apply Concepts (IV1.MS.1)                    N.ME.06.06
- Integers                               - Understand that a fraction or a negative
- Rational numbers
fraction is a quotient of two integers, e.g.,
- Fractions
- Decimals                                 is 8 divided by 3. N.ME.06.07
- Powers                                 - Locate negative rational numbers (including
integers) on the number line; know that
numbers and their negatives add to 0, and are
on opposite sides and at equal distance from 0
on a number line. N.ME.06.17
- Understand that rational numbers are
quotients of integers (nonzero denominators),
e.g., a rational number is either a fraction or a
negative fraction. N.ME.06.18

   Utilize Numeration (IV.1.MS.2)           - Understand and use integer exponents,
- Decimal                                  excluding powers of negative numbers;
- Scientific notation                      express numbers in scientific notation.
- Nondecimal                               N.ME.06.16

   Apply Properties (IV.1.MS.3)             - Understand integer subtraction as the inverse
- Order                                    of integer addition; add and subtract integers,
- Density                                  using integers from 10 to -10. N.MR.06.08
- Zero                                   - Locate negative rational numbers (including
- One                                      integers) on the number line; know that
- Pi                                       numbers and their negatives add to 0, and are
- Additive inverse                         on opposite sides and at equal distance from 0
- Multiplicative inverse                   on a number line. N.ME.06.17
- Understand that 0 is an integer that is neither
negative nor positive. N.ME.06.19
- Know that the absolute value of a number is
the value of the number, ignoring the sign; or
is the distance of the number from 0.
N.ME.06.20

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Timing                       Content & Processes (MCF)                   Supporting Grade Level Content Expectations     Vocabulary

   Solve Problems (IV.1.MS.4)                        - Understand that multiplying or dividing both
- Model and solve mathematical and applied          sides of an equation by the same non-zero
problems                                        number creates a new equation that has the
- Order of operations                               same solutions. A.FO.06.13

Patterns, Relationships, and Functions

6-1 Patterns
 Describe, Analyze, and Generalize Patterns
(I.1.MS.1)
- Explore numeric, algebraic, and geometric
examples of patterns
- Extend patterns
- Generalize a rule to describe a pattern

   Represent and Record Patterns (I.1.MS.2)          - Understand that graphs and tables can
- Tables                                            suggest relationships between quantities.
- Charts                                            A.RP.06.08
- Graphs

   Use Patterns to Make Inferences (I.1.MS.3)
- Analyzing and predicting
- Testing and evaluation
- Problem solving

   Explore and Describe Visual and Numeric
Patterns (I.1.MS.4)
- Linear/near linear
- Squares, cubes
- Exponents, powers, roots

   Use Patterns and Generalizations to Solve
Problems and Explore New Content (I.1.MS.5)
- Tables
- Charts
- Graphs
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Timing                       Content & Processes (MCF)                Supporting Grade Level Content Expectations        Vocabulary

-   Equations

6-2 Variability and Change
 Represent Variability or Change (I.2.MS.4)       - Represent simple relationships between
- Ordered pairs                                  quantities, using verbal descriptions, formulas
- Tables                                         or equations, tables, and graphs, e.g.
- Graphs                                         perimeter-side relationship for a square,
- Equations                                      distance time graphs, and conversions such as
feet to inches. A.RP.06.10

Number Sense and Numeration

6-9 Concepts and Properties of Numbers
 Apply Concepts (IV1.MS.1)                        - Order rational numbers and place them on
- Integers                                       the number line. N.ME.06.05
- Rational numbers
- Fractions
- Decimals
- Powers

6-11 Number Relationships
 Compare and Order (IV.3.MS.1)                    - Order rational numbers and place them on
- Integers                                       the number line. N.ME.06.05
- Rational numbers                             - Locate negative rational numbers (including
- Equality                                       integers) on the number line; know that
- Inequality                                     numbers and their negatives add to 0, and are
on opposite sides and at equal distance from 0
on a number line. N.ME.06.17

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Mathematics Pacing Guide

Timing                       Content & Processes (MCF)                   Supporting Grade Level Content Expectations             Vocabulary

Unit 3                           Numerical and Algebraic Operations
and Analytical Thinking
Topic: Applying                                                                                                                       Cross Multiplication
fractions (addition,      6-13 Algebraic and Analytical Thinking                                                                      Denominator
subtraction,                                                                                                                          Equivalent Fraction
multiplication, and          Read, Write, and Create Algebraic Expression        -   Understand division of fractions as the         Factor
division)                     (V.2.MS.1)                                                                                              Fractions
inverse of multiplication, e.g., if        ,
- Simplify                                                                                              LCD – Least
Timing: 2 weeks               - Translate                                             then        =   , so  =             .           Common
- Solve                                                                                                   Denominator
 linear equations                                  N.MR.06.01                                      Mixed Numbers
 inequalities                                  -   Given an applied situation involving dividing   Multiple
fractions, write a mathematical statement to    Multiplication
represent the situation. N.FL.06.02             Numerator
-   Solve for the unknown in equations such as:     Equivalent
=          =                     .    Common Factor
GCF- Greatest
N.MR.06.03                                        Common Factor
LCM Least
Common
Multiple
Factor Tree
Reciprocal
Reduce

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                Supporting Grade Level Content Expectations            Vocabulary

Unit 4                            Numerical and Algebraic Operations
and Analytical Thinking                                                                       Denominator
Topic: Fractions,                                                                                                                   Equivalent Fraction
Decimals, and Percents     6-12 Operations and the Properties                                                                       Factor
 Calculate (V.1.MS.2)                               -   Given an applied situation involving dividing   Fractions
Timing: 3 weeks                - Integers                                           fractions, write a mathematical statement to    LCD – Least
- Rational numbers                                   represent the situation. N.FL.06.02               Common
 fractions                                   -   Multiply and divide any two fractions,            Denominator
 decimals                                        including mixed numbers, fluently.              Mixed Numbers
 percents                                        N.FL.06.04                                      Multiple
- Simple Algebraic Expression                    -   Add, subtract, multiply, and divide integers    Numerator
- Methods                                            between -10 and 10; use number line and         Equivalent
 estimation                                      strip models for addition and subtraction.      Common Factor
 paper/pencil                                    N.FL.06.09                                      GCF- Greatest
 calculator                                  -   Add, subtract, multiply and divide positive       Common Factor
 mental math                                     rational numbers fluently. N.FL.06.10           LCM Least
-   Calculate part of a number given the              Common Multiple
percentage and the number. N.FL.06.12           Factor Tree
-   For applied situations, estimate the answers
to calculations involving operations with
rational numbers. N.FL.06.14
Number Sense and Numeration

6-9 Concepts and Properties of Numbers
 Apply Concepts (IV1.MS.1)                          -   Represent rational numbers as fractions or
- Integers                                           terminating decimals when possible, and         Decimal
- Rational numbers                                   translate between these representations.        Dividend
- Fractions                                          N.ME.06.06                                      Divisibility
- Decimals                                       -   Understand that a fraction or a negative        Division Symbols
- Powers                                             fraction is a quotient of two integers, e.g.,   Divisor
Number Line
is 8 divided by 3. N.ME.06.07
Percent
Percentage
Quotient

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Timing                        Content & Processes (MCF)                     Supporting Grade Level Content Expectations            Vocabulary

6-10 Representation and Uses of Numbers                   -   Represent rational numbers as fractions or      Terminating
 Equivalent Representations (IV.2.MS.2)                      terminating decimals when possible, and         Decimals
- Fractions                                               translate between these representations.        Repeating Decimals
- Decimals                                                N.ME.06.06
- Percent
- Ratios
- Proportions
- Scientific notation

   Number Use (IV.2.MS.3)
- Counting
- Ordering
- Measuring
- Naming

   Estimating (IV.2.MS.4)                                -   For applied situations, estimate the answers
- Strategies                                              to calculations involving operations with
- Appropriateness                                         rational numbers. N.FL.06.14
- Evaluate for reasonableness

   Solve Problems (IV.2.MS.5)
- Select representations to simplify and solve        -   Solve contextual problems involving
percentages in such contexts as sales taxes
and tips
and involving positive rational numbers
N.MR.06.13
-   For applied situations, estimate the answers
to calculations involving operations with
rational numbers
 use story problems with familiar
situations so that students can test for
reasonableness
 Tim walked 0.41 miles to his friend’s
house, then 0.53 miles to the store. From
there, he walked N.FL.06.14

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                 Supporting Grade Level Content Expectations       Vocabulary

Unit 5                                   Geometry and Measurement
Length
Topic: Geometry –           6-5 Measurement                                                                                    Area
Measurement                  Identify Systems of Measurement (II.3.MS.1)                                                      Conversion
- Metric                                                                                       Degree
Timing: 2 weeks                 - Customary                                                                                    Cup
Pint
   Determine the Appropriate Unit of                                                              quart
Measurement (II.3.MS.2)                                                                        gallon
- Length                                                                                       Inch
- Mass                                                                                         foot
- Weight                                                                                       yard
- Time                                                                                         mile
- Temperature                                                                                  Mg
- Perimeter                                                                                    g
- Area                                                                                         kg
- Volume                                                                                       Ml
- Angle                                                                                        L
- Circumference                                                                                kl
- Capacity                                                                                     Mm
- Money                                                                                        cm
dm
   Estimate Measurements with Accuracy                                                            m
(II.3.MS.3)                                                                                    km
- Length                                                                                       prism
- Distance                                                                                     - square
- Angles                                                                                       - triangular
- Area                                                                                         - cube
- Volume                                                                                       Nets
- Mass                                                                                         Perimeter
- Weight                                                                                       Square inches
- Time                                                                                         Square feet
- Temperature                                                                                  Surface area of
cubes

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Timing                        Content & Processes (MCF)                       Supporting Grade Level Content Expectations      Vocabulary

   Interpret Measurement (II.3.MS.4)                                                                    Surface area of
- Interpretational recognition of relationships                                                           rectangular
prism
   Apply Proportional Reasoning (II.3.MS.5)           -    Convert between basic units of measurement   Volume of cubes
- Indirect measurements                                 within a single measurement system, e.g.,    Volume of
- Inferences                                            square inches to square feet. M.UN.06.01          rectangular
- Precision                                        -    Compute the volume and surface area of            prism
- Degree of accuracy                                    cubes and rectangular prisms given the       line
lengths of their sides, using formulas.
M.TE.06.03
   Solve Problems (II.3.MS.6)

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)             Supporting Grade Level Content Expectations               Vocabulary

Unit 6                               Number Sense and Numeration
Equivalent ratios
Topic: Ratios and           6-11 Number Relationships                                                                               rate
proportions                  Ratios and Rates (IV.3.MS.2)                   -   Find equivalent ratios by scaling up or            ratio
- Measurement                                    scaling down. N.ME.06.11                           unit rate
Timing: 2 weeks                 - Objects                                    -   Solve applied problems involving rates,            scaling up or down
including speed, e.g., if a car is going 50 mph,   scale factor
how far will it go in 3½ hours? A.PA.06.01

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Mathematics Pacing Guide

Timing                       Content & Processes (MCF)                   Supporting Grade Level Content Expectations            Vocabulary

Unit 7                            Numerical and Algebraic Operations
and Analytical Thinking                                                                         Sales tax
Topic: Applying                                                                                                                       tips
Percent                    6-12 Operations and their Properties                   -   Solve word problems involving percentages       rate
 Solve Problems (V.1.MS.4)                                in such contexts as sales taxes and tips, and   percent
Timing: 2 weeks                                                                       involving positive rational numbers.            rational numbers
N.FL.06.13                                      percentage
-   Solve applied problems that use the four        composite number
operations with appropriate decimal             fractions
numbers. N.FL.06.15                             prime
triangular and
square numbers
Number Sense and Numeration                                                                       number lines
integers
6-10 Representation and Uses of Numbers                                                                    decimal
 Apply Geometric Representatives (IV.2.MS.1)          -   Order rational numbers and place them on        estimate
- Fractions                                            the number line. N.ME.06.05                     equivalent
- Prime and composite                                                                                  equivalent fractions
- Triangular and square numbers                                                                           and ratios
- Number line
- Rational numbers
- Integers

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                   Supporting Grade Level Content Expectations            Vocabulary

Unit 8                            Probability and Discrete Mathematics
Combinations
Topic: Probability          6-14 Probability                                                                                          Dependent Events
 Describe Outcomes (VI.1.MS.1)                        -   Express probabilities as fractions, decimals   Empirical
Timing: 3 weeks                 - Likely                                               or percentages between 0 and 1; know that 0    equally likely events
- Unlikely                                             probability means an event will not occur,     independent events
- Give qualitative or quantitative descriptions        and that probability 1 means an event will     certain event
of degrees of likeliness                           occur. D.PR.06.01                              iterations
-   Compute probabilities of events from simple    Likely measure of
experiments with equally likely outcomes,         certainty
e.g., tossing dice, flipping coins, spinning   networks
spinners, by listing all possibilities and     permutations
finding the fraction that meets given          Experimental
conditions. D.PR.06.02                            probability
recurrence
   Describe Probability (VI.1.MS.2)                   -   Express probabilities as fractions, decimals   sets
- Certainty                                            or percentages between 0 and 1; know that 0    simple event
- Impossible                                           probability means an event will not occur,     theoretical
- Odds                                                 and that probability 1 means an event will     Unlikely events
occur. D.PR.06.01                              equally likely
-   Compute probabilities of events from simple       outcomes
experiments with equally likely outcomes,      outcome and
e.g., tossing dice, flipping coins, spinning      probability
spinners, by listing all possibilities and     favorable outcomes
finding the fraction that meets given          theoretical
conditions. D.PR.06.02                            probability
possible outcomes
   Conduct Experiments (VI.1.MS.3)                    -   Compute probabilities of events from simple       simulations
- Dependent events                                     experiments with equally likely outcomes,      survey
- Independent events                                   e.g., tossing dice, flipping coins, spinning   chances
- Empirical (chance) events                            spinners, by listing all possibilities and     intersecting
- Theoretical (mathematical) events                    finding the fraction that meets given          impossible event
- Experiments                                          conditions. D.PR.06.02                         certain event
 empirically                                                                                      Experiment

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Timing                        Content & Processes (MCF)                 Supporting Grade Level Content Expectations            Vocabulary

-   Mathematically                                                                                  Organized list
 Theoretical

   Explain Differences Between Probabilities
(VI.1.MS.4)

   Solve Problems (VI.1.MS.5)
- Conduct experiments and simulation             -   Compute probabilities of events from simple
- Examine and explain results                        experiments with equally likely outcomes,
e.g., tossing dice, flipping coins, spinning
spinners, by listing all possibilities and
finding the fraction that meets given
conditions. D.PR.06.02

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                         Supporting Grade Level Content Expectations           Vocabulary

Unit 9                                 Data Analysis and Statistics
coordinate
Topic: Statistics and       6-6 Collection, Organization, and Presentation of                                                               descriptive
Analyzing Data              Data                                                                                                            statistics
 Collect and Explore Data (III.1.MS.1)                                                                         graph
Timing: 2 weeks                 - Observation                                                                                               - bar
- Measurement                                                                                               - circle
- Survey                                                                                                    extrapolate
- Sampling techniques                                                                                       frequency
- Simulation                                                                                                interpolate
line graph
   Organize Data (III.1.MS.2)                                                                                  mean
- Tables                                                                                                    median
- Charts                                                                                                    mode
- Graphs                                                                                                    pictograph
 bar                                                                                                    range
 circle                                                                                                 sample
 line                                                                                                   survey
 pictograph                                                                                             tally
 box and whisker                                                                                        organize list
 stem and leaf                                                                                          tree diagram
- Spreadsheets                                                                                              Venn diagram
- Databases

   Present Data Using a Variety of Representations      -    Understand that graphs and tables can
(III.1.MS.3)                                              suggest relationships between quantities.
- Compare and evaluate different                          A.RP.06.08
presentations of the same data                  -    Represent simple relationships between
- Give examples of how data can be biased                 quantities, using verbal descriptions, formulas
or equations, tables, and graphs, e.g.
perimeter-side relationship for a square,
distance-time graphs, and conversions such as
feet to inches. A.RP.06.10

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Timing                        Content & Processes (MCF)                    Supporting Grade Level Content Expectations   Vocabulary

   Solve Problems (III.1.MS.4)
- Identify everyday situations that rely on
data
- Design and implement strategies to obtain,
organize, and present data

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Mathematics Pacing Guide

Timing                       Content & Processes (MCF)                   Supporting Grade Level Content Expectations               Vocabulary

Unit 10                                Geometry and Measurement
Coordinate
Topic: Geometric            6-4 Position                                                                                                     plane/system
Positions                    Identify and Describe Position of Objects                                                                   Coordinates
(II.2.MS.1)                                                                                               origin
Timing: 3 weeks                 - Latitude and longitude                                                                                  plane
- Compass directions                                                                                      rotations
- Cartesian coordinates                                                                                   width
- Midpoints                                                                                               x and y axis
x and y coordinate
    Describe Objects in Terms of Their Orientation    -   Use paper folding to perform basic geometric       angle rotation
and Relative Position (II.2.MS.2)                     constructions of perpendicular lines,              center of rotation
- Parallel                                            midpoints of line segments and angle               image
- Perpendicular                                       bisectors, and justify informally. G.SR.06.05      prime notation
- Collinear                                                                                              Y
- Coincident                                                                                             similar
- Directions                                                                                             skew lines
 N, S, E, W, NE, SE, SW, NW                                                                         vertices
- Right/left                                                                                             constructions
- Symmetry                                                                                               line
 bilateral                                                                                          line segment
 radial                                                                                             midpoints of a line
 asymmetrical                                                                                          segment
(lines of)
    Describe Transformations of Objects               -   Understand the basic rigid motions in the             reflections
(II.2.MS.3)                                           plane (reflections, rotations, translations),      Transversal
- Translation/slide                                   relate these to congruence, and apply them to      Dimensions
- Reflection/flip                                     solve problems. G.TR.06.03                         Tessellations
- Rotation/turn                                   -   Understand and use simple compositions of          Rotational
 half turn                                      basic rigid transformations, e.g., a translation      symmetry
 quarter turn                                   followed by a reflection. G.TR.06.04
- Dilation
 enlargement
 reduction
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Timing                        Content & Processes (MCF)                 Supporting Grade Level Content Expectations            Vocabulary

    Locate the Position of Points or Objects        -   Plot ordered pairs of integers and use ordered
Described by Two or More Conditions                 pairs of integers to identify points in all four
(II.2.MS.4)                                         quadrants of the coordinate plane.
- Cardinal                                          A.RP.06.02
- Ordinal

    Solve Problems (II.2.MS.5)                      -   Understand the basic rigid motions in the
plane (reflections, rotations, translations),
relate these to congruence, and apply them to
solve problems. G.TR.06.03

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                Supporting Grade Level Content Expectations      Vocabulary

Unit 11                                 Data Analysis and Statistics
coordinate plane
Topic: Graphing              6-8 Inferences and Predictions                                                                    coordinate
 Make and Test Hypotheses (III.3.MS.1)                                                           outcomes
Timing: 2 weeks                  - Estimate                                                                                    predictions
- Predict                                                                                     ordered pairs
origin
   Design Experiments to Model and Solve                                                         quadrants
Problems (III.3.MS.2)                                                                         x and y axis
- Sampling                                                                                    x and y coordinates
- Simulations                                                                                 Tessellations
- Controlled investigations                                                                   Rotational
symmetry
   Evaluate Problems (III.3.MS.3)
- Explain, analyze, and critique data
 written
 oral

   Make Predictions and Decisions Based on Data
(III.3.MS.4)
- Patterns
- Analyze source
- Analyze method used to gather data

   Solve Problems Using Data Analysis Strategies
(III.3.MS.5)
- Inferences
- Predictions

Patterns, Relationships, and Functions

6-2 Variability and Change
 Identify and Describe Change (I.2.MS.1)
- Relationships of variables
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Timing                         Content & Processes (MCF)                     Supporting Grade Level Content Expectations          Vocabulary

-   Charting and graphing variables
-   Manipulate variables
-   Interpret graphs

   Generalize a Rule that Describes a Pattern of
Change (I.2.MS.2)
- Input/output
- Independent and dependent
- Transforming geometric shapes
 slips
 flips
 turns
 combinations

   Explore Change and Interdependency
(I.2.MS.3)
- Conducting experiments
- Using technology
-   Represent simple relationships between
   Represent Variability or Change (I.2.MS.4)               quantities using verbal descriptions, formulas
- Ordered pairs                                          or equations, tables, and graphs
- Tables                                                     perimeter-side relationship for a
- Graphs                                                        square distance time graphs and
- Equations                                                     conversions such as feet to inches
(A.RP.06.10)
   Differentiate Between Functions and Relations
(I.2.MS.5)
- Explore and classify examples of
relationships
 linear
 inverse patterns of growth or decay
 noncontinuous functions

   Use Variables and Relationships to Problem           -   Solve problems involving linear functions
Solve (I.2.MS.6)                                         whose input values are integers; write the
equation; graph the resulting ordered pairs
of integers. A.PA.06.09

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Timing                         Content & Processes (MCF)                Supporting Grade Level Content Expectations         Vocabulary

Numerical and Algebraic Operations
and Analytical Thinking

6-13 Algebraic and Analytical Thinking
 Represent Algebraic Concepts (V.2.MS.2)
- Geometric
- Physical models
- Tables/graphs
- Multiple representations

   Solve Linear Equalities and Inequalities        -   Understand that adding or subtracting the
(V.2.MS.3)                                          same number to both sides an equation
- Algebraic                                         creates a new equation that has the same
- Geometric                                         solution. A.FO.06.12
-   Solve equations of the form ax + b = c. A.FO.
06.14

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                      Supporting Grade Level Content Expectations        Vocabulary

Unit 12                            Numerical and Algebraic Operations
and Analytical Thinking                                                                         Linear
Topic: Linear Equations                                                                                                                linear functions
and Functions                6-12 Operations and their Properties                                                                      function f(x)=
 Use Manipulatives and Diagrams (V.1.MS.1)                                                               formula
Timing: 2 weeks                  - Operations and their inverses                                                                       linear equations
- Integers                                                                                            non-linear
- Rational numbers                                                                                    variable equations
 fractions                                                                                        algebraic equation
 decimals                                                                                         variable
 percents
- Powers
- Relate to symbolic representation

   Investigate Properties of Operations (V.1.MS.3)
- Commutative
- Associative
- Distributive
- Zero
- One
- Identify

   Solve Problems (V.1.MS.4)
-    Solve word problems involving percentages in
such contexts as sales taxes and tips, and
involving positive rational numbers.
N.FL.06.13
-    Solve applied problems that use the four
operations with appropriate decimal numbers.
N.FL.06.15

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Timing                         Content & Processes (MCF)              Supporting Grade Level Content Expectations       Vocabulary

6-13 Algebraic and Analytical Thinking
 Analyze Problems (V.2.MS.4)                 -    Solve problems involving linear functions
- Strategies                                   whose input values are integers; write the
- Valid solutions                              equation; graph the resulting ordered pairs of
integers. A.PA.06.09

   Explore Problems (V.2.MS.5)               -    Solve applied problems involving rates,
- Contemporary uses                            including speed. A.PA.06.01
- Technology
- Algebraic and analytic reasoning

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                  Supporting Grade Level Content Expectations      Vocabulary

Unit 13                                Geometry and Measurement
Angle
Topic: Geometry –           6-3 Shape and Shape Relationships                                                                    degrees
Shapes and Relationships     Analyze Properties and Attributes (II.1.MS.1)                                                      vertex
- Line                                                                                           acute angle
Timing: 3 weeks                 - Rays                                                                                           right angle
- Segments                                                                                       obtuse angle
- Angles                                                                                         straight angle
- Points on a gird                                                                               circle graph
- Parallel                                                                                       vertical angle
- Perpendicular                                                                                  congruent angle
- Intersection                                                                                   supplementary
- Congruent                                                                                         angles
- Similar                                                                                           complementary
- Symmetric                                                                                         angles
- Equal sides                                                                                    triangle
- Equal angles                                                                                   acute triangle
- Complimentary                                                                                  right triangle
- Supplementary                                                                                  obtuse triangle
- Tessellate                                                                                     congruent
segments
   Classify Shapes (II.1.MS.2)                                                                      scalene triangle
- Linear                                                                                         isosceles triangle
 line                                                                                       equilateral triangle
 segment                                                                                    parallelogram
 parallel                                                                                   rhombus
 perpendicular                                                                              trapezoid
- Plane                                                                                          similar figures
 5, 6, 8 sided figures                                                                         measurement
 square                                                                                 pentagon
 rectangle                                                                              hexagon
 rhombus                                                                                heptagon

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Timing                         Content & Processes (MCF)                    Supporting Grade Level Content Expectations         Vocabulary

 trapezoid                                                                                  octagon
 kite                                                                                       nonagon
 parallelogram                                                                              decagon
 angles                                                                                         regular polygon
-   Solids                                                                                           concave and
 cube                                                                                              convex polygon
 sphere                                                                                            tessellation
 pyramid                                                                                           transformation
 cone                                                                                           line symmetry
 cylinder                                                                                       line of symmetry
 rectangular and triangular prism                                                                  reflection
construction
   Derive Generalizations about Shapes to Develop                                                        rotational
Classifications (II.1.MS.3)                                                                              symmetry
triangle
   Construct Familiar Shapes (II.1.MS.4)                                                                    inequalities
- Linear                                         -    Draw patterns (of faces) for a cube and         alternate interior
 right                                            rectangular prism that, when cut, will cover       angles angle
 obtuse                                           the solid exactly (nets). M.PS.06.02               bisectors
 acute angles                                -    Use paper folding to perform basic geometric    corresponding
 lines                                            constructions of perpendicular lines,              angles and
 rays                                             midpoints of line segments and angle               corresponding
 segments                                         bisectors, and justify informally. G.SR.06.05      sides
 bisector                                                                                         exterior and
 diagonals                                                                                           interior angles
- Plane                                                                                               parallel lines
 quadrilaterals                                                                                   line segment
 square                                                                                      midpoint of a line
segment
 rectangle
opposite interior
 triangles
angles
 right
perpendicular
 equilateral
lines
 isosceles                                                                                   point
 scalene                                                                                     properties
 obtuse                                                                                      Transformation
 acute                                                                                       translation
 circles
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Timing                         Content & Processes (MCF)                     Supporting Grade Level Content Expectations            Vocabulary

-   Solid                                                                                                transversal
 cube                                                                                               triangle
 sphere                                                                                                inequalities
 cylinder                                                                                           ray
 pyramid                                                                                            orientation
 cone                                                                                               pre-image
 rectangular prisms                                                                                 slide
 triangular prisms                                                                                  view: front, side,
 views                                                                                                 top
 front                                                                                          net
 side
 back
-   Tools
 ruler
 protractor
 compass

   Combine, Dissect, and Transform Shapes            -    Understand the basic rigid motions in the
(II.1.MS.5)                                            plane (reflections, rotations, translations),
- Use tangrams                                         relate these to congruence, and apply them to
- Use pentominoes                                      solve problems. G.TR.06.03
-    Understand and use simple compositions of
basic rigid transformations, e.g., a translation
followed by a reflection. G.TR.06.04

   Generalize and Verify Common Properties of        -    Understand and apply basic properties of
Shapes (II.1.MS.6)                                     lines, angles, and triangles, including:
- Similar                                               triangle inequality
- Congruent                                             relationships of vertical angles,
- Parallel                                                complementary angles, supplementary
- Perpendicular                                           angles
 congruence of corresponding and alternate
interior angles when parallel lines are cut
by a transversal, and that such
congruencies imply parallel lines
 locate interior and exterior angles of any
triangle and use the property that a
Sixth Grade Mathematics Pacing Guide – May 2008 Revision                      30
Timing                         Content & Processes (MCF)            Supporting Grade Level Content Expectations       Vocabulary

exterior angle of a triangle is equal to the
sum of the remote (opposite) interior angles
 know that the sum of the exterior angles of
a convex polygon is 360. G.GS.06.01
-    Understand that for polygons, congruence
means corresponding sides and angles have
equal measures. G.GS.06.02

   Solve Problems (II.1.MS.7)

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Mathematics Pacing Guide

Timing                        Content & Processes (MCF)                     Supporting Grade Level Content Expectations      Vocabulary

Unit 14                           Probability and Discrete Mathematics
combinations
Topic: Discrete              6-15 Discrete Mathematics                                                                              dependent
Mathematics                   Count Permutations and Combinations                                                                  events
(VI.2.MS.1)                                                                                        empirical
Timing: 2 weeks                  - Manipulatives                                                                                    equally likely
- Diagrams                                                                                         events
- Fundamental Theorem of Counting                                                                  independent
- Pascal’s Triangle                                                                                events
- Fibonacci Sequence                                                                               iterations
likely
   Use Sets and Set Relationships to Explore and                                                      measure of
Solve Simple Algebraic and Geometric                                                               certainty
Problems (VI.2.MS.2)                                                                               networks
- Venn diagrams                                                                                    permutations
- Attribute blocks                                                                                 probability
recurrence
   Solve Problems Involving Networks                                                                  sets
(VI.2.MS.3)                                                                                        simple event
- Delivery routes                                                                                  theoretical
- Paths between points                                                                             unlikely
- Recurrence                                                                                       events
- Iterations                                                                                       triangular numbers
square numbers
   Explore Recurrent Relations and Iterations                                                         patterns
(VI.2.MS.4)                                                                                        Venn diagram
- Triangular numbers
- Square numbers
- Patterns

   Develop and Analyze Algorithms (VI.2.MS.5)
- Design an algorithm to accomplish a task
- Create and solve logic problems

Sixth Grade Mathematics Pacing Guide – May 2008 Revision                          32
Timing                         Content & Processes (MCF)              Supporting Grade Level Content Expectations   Vocabulary

   Solve Problems (VI.2.MS.6)
- Existence (whether or not there is a
solution)
- Counting (how many solutions)
- Best solution
- Strategies used

Sixth Grade Mathematics Pacing Guide – May 2008 Revision                   33

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