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.




                                                                                                                            6
                                                                                                                         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
             answers.
             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.




                                                                            9
    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




                                                                                             11
                                                                                                                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




                                                                                                                            12
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.




                                                                                               13
                                          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.




                                                      14
                                                             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




                                                                               15
                                                     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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