Chapter 1 Data Representation and Communication

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Chapter 1 Data Representation and Communication Powered By Docstoc
					Instruction Period


                                                                                                      JEFFERSON COUNTY SCHOOLS
                     Dates Taught


                                                                                                         Sixth Grade Mathematics
                                       TN Department of Education
                                                                                                   Student Performance   Building blocks for the   Essential Vocabulary      Common                 Materials/
                                       CONTENT STANDARD/ GLE           Checks for Understanding
                                                                                                      Indicators (SPI)       new standards            *teacher word       Assessment item           Resources



                                     FIRST NINE WEEKS
                                    GLE 0606.1.2 Apply and            0606.1.6 Model              SPI 0606.1.1
                                    adapt a variety of appropriate    situations by devising      Make conjectures
                                    strategies to problem solving,    and carrying out            and predictions
                                    including estimation, and         experiments and             based on data.
                                    reasonableness of the solution.   simulations.
         1                          (Introduced)                              (Introduced)        (Introduced)                                                                              Chapter 1

                                                                                                                    SPI 0506.3.2
                                                                                                                    Evaluate multi-step
                                                                                                                    numerical
                                                                                                                    expressions
                                                                                                                    inolving fractions
                                                                                                                    using order of
                                                                                                                    operations.
                                                                                                                    SPI 0506.3.1
                                                                                                                    evaluate algebraic
                                                                                                                    expressions
                                                                                                                    involving decimals
                                                                                                                    and fractions using
                                                                                                                    order of operations.
                                                                                                                            * 0506.3.1
                                                                     0606.3.3 Recognize                             Evaluate an
                                                                     the use of juxtaposition                       expression by
                                                                     (such as 3x, ab) to       SPI 0606.3.2     Use substituting non-
                                                                     stand for multiplication, order of operations  negative rational
                                                                     and the convention in     and parentheses to   number values for
                                                                     these cases of writing    simplify expressions letter variables in
         1                          GLE 0606.3.3                     numbers to include grouping symbols and exponents.
                                                    Extend order of operationsbefore letters. and solve problems. the expression.                                                                   Chapter 1
                                                                                       SPI 0506.2.3 Select
                                                                                       a reasonable
    GLE 0606.3.2 Interpret and                                                         solution to a real-
    represent algebraic                                                                world division
    relationships with variables in                                                    problem in which
    expressions, simple equations                                                      the remainder must
1   and inequalities.                                                                  be considered.        Chapter 1
                                      0606.1.5 Illustrate
                                      properties of operations
                                      by showing that two
                                      expressions are
                                      equivalent in a given      SPI 0606.1.4
                                      context (e.g., using an         Select the
                                      area model for            representation that
                                      distributive property,     models one of the
                                      and grouping/set         arithmetic properties
                                      models for                   (commutative,
                                      commutative and              associative, or
1                                     associative properties).       distributive).                          Chapter 1
                                                          SPI 0506.2.5 Solve
                                                          addition and
                                                          subtraction
                                                          problems involving
                                                          both fractions and
                                                          decimals.
                                                           * 0506.2.3 Use
                                                          visual models,
                                                          benchmarks, and
                                                          equivalent forms to
                                                          add and subtract
                                                          commonly used
                                                          fractions and
                                                          decimals.
                                                          * 0506.2.5 Make
                                                          reasonable
                                                          estimates of
                                                          fractions and
                                                          decimal sums and
                                                          differences.
                                                          SPI 0506.2.4 Solve
                                                          problems involving
                                                          the division of two-
                                                          and three-digit
                                                          numbers by one-
                                                          and two-digit whole
                                   SPI 0606.2.3           numbers.
                                   Solve problems         *0506.2.7
                                   involving the          Understand
                                   addition, subtraction, placement of the
                                   multiplication, and    decimal point in     equation, solution,
                                   division of            calculations of      solving and equation,
                                   decimals.(Introduced) multiplication and    defining the variable   Chapter 1
                                   SPI 0606.3.3
                                   Write equations that
                                   correspond to given
                                   situations or
                                   represent a given
    GLE 0606.3.1 Write and         mathematical                                term, sequence,
    solve two-step equations and   relationship.                               arithmetic sequence,
1   inequalities. (Introduced)     (Introduced)                                geometric sequence      Chapter 1
                            statistics, data,
                            frequency table, scale,
                            interval, line graph,
    SPI 0606.3.7            scatter plot, line plot,
    Use algebraic           cluster, outlier, range,
    expressions and         measures of central
    properties to analyze   tendency, mean,
    numeric and             median, mode, stem-
    geometric patterns.     and-leaf plot, stem,
                            leaf, bar graph,
1                           histogram                  Chapter 1
                                                           SPI 0506.5.3
                                                           Calculate
                                                           measures of central
                                                           tendency to
                                                           analyze data.
                                                           *05065.5 Evaluate
                                                           how different
                                                           measures of central
                                                           tendencies
                                                           describe data.
                                                                     *0506.5.6
                                                           Identify the outliers
                                                           and determine their
                                  0606.5.8 Connect         effect on mean,
                                  data sets and their      median, mode and
                                  graphical                range.
                                  representations (such    SPI 0506.5.2 Make
                                  as bar graphs, circle,   predictions based
                                  graphs, and stem-and-    on various data
                                  leaf plots).             representations,
                                                           including double
                                  0606.5.9 Determine       bar and line
                                  the sample space for a   graphs.
                                  given situation.         *0506.5.3 Design
                                                           investigations to
GLE 0606.5.2 Interpret            0606.5.11 Select the     address a question
representations of data from      appropriate measure of   and consider how
surveys and polls, and describe   center to describe a     data collection
sample bias and how data          data set.                methods affect the
representations can be                                     nature of the data
misleading.                                                set.                    Chapter 2
                                                                                  SPI 0506.2.1 Read
                                                                                  an dwrite nimbers
                                                                                  from millions to
                                                                                  millionths in various
                                                                                  contexts.
                                                                                  *0506.2.10 Use
                                                                                  exponential
                                                                                  notation to
                                                                                  represent repeated
                                                                                  multiplication of
                                                                                  whole numbers.
                                                                                       SPI 0506.2.2
                                                                                  Write the prime
                                                                                  factorization of
                                                                                  numbers throush
                                                                                  50 using bother
                                                                                  exponenial and
                                                                                  standard notation.
                                                            SPI 0606.1.3      Use   *0506.2.1 Identify
                                                            concrete, pictorial,  prime numbers up
                                                            and symbolic          to 50.
                                                            representation for    *0506.2.2 Use the
                                                            integers.             prime factorization
                                                                              SPI of two whole
                                                            0606.2.7      Locate  nujbers to
                                                            positive rational     determine greatest
                                    0606.2.10 Explore       numbers on the        common factor,
                                    contexts that can be    number line.          least common
    GLE 0606.2.5 Develop            described with negative                SPI    multiple.               integer, graph,
    meaning for integers; represent numbers (such as        0606.2.8      Locate  *0506.2.4 Use           positive integer,
    and compare quantities with     money, elevation, and integers on the         divisibility rules to   negative integer,
1   integers.                       temperature).           number line.          factor numbers.         absolute value      Chapter 3

                                    0606.2.10 Explore         SPI 0606.1.2
                                    contexts that can be      Judge the
    GLE 0606.2.5 Develop            described with negative   reasonableness of
    meaning for integers; represent numbers (such as          the results of rational
    and compare quantities with     money, elevation, and     number estimates
1   integers.                       temperature).             and/or computations.                                            Chapter 3
                                   0606.3.10 Understand
                                   that in an ordered pair
                                   (x, y), the x represents
                                   horizontal location and
                                   y represents vertical
                                   location.                                            coordinate plane,
                                                                                        coordinate grid, x-
                                   0606.3.11 Identify the     SPI 0606.3.9              axis, y-axis,
                                   quadrant of the            Graph ordered pairs       origin, ordered
                                   coordinate system in       of integers in all four   pair, x-
    GLE 0606.3.6 Understand        which a point lies.        quadrants of the          coordinate, y-
    and use the Cartesian                                     Cartesian coordinate      coordinate,
1   coordinate system.                                        system.                   quadrants           Chapter 3

                                                              SPI 0606.1.3      Use
                                                              concrete, pictorial,
                                                              and symbolic
                                                              representation for        opposites,
1                                                             integers.                 additive inverse   Chapter 3

                                                              SPI 0606.1.3      Use
                                                              concrete, pictorial,
                                                              and symbolic
                                                              representation for
1                                                             integers.                                    Chapter 3

                                   0606.1.11 Model
                                   algebraic expressions
                                   with manipulatives,
                                   technology, and pencil
                                   and paper.
                                                              SPI 0606.1.5
                                    0606.3.7 Move fluently    Model algebraic
    GLE 0606.3.1 Write and          between different         expressions using
    solve two-step equations and    representations (such     algebra tiles.
    inequalities.                   as verbal, tabular,                          SPI
                             GLE numerical, algebraic,        0606.3.4      Rewrite
    0606.3.4 Use expressions,       and graphical) of         expressions to
    equations and formulas to solve equations and             represent quantities      expression, zero
1   problems.                       expressions.              in different ways.        pairs              Chapter 4
                                                                                 SPI 0506.3.3 Find
                                                                                 the unknown in
                                                                                 single-step
                                                                                 equations involving
                                                                                 fractions and mixed   inverse
                                                                                 numbers.              operations,
                                   0606.3.6 Use                                  * 0506.3.2 Use        Subtraction
                                   equations to describe                         variables             Property of
                                   simple relationships                          appropriately to      Equality, Addition
                                   shown in a table or     SPI 0606.3.6          represent numbers     Property of
                                   graph.                  Solve two-step linear whose values are      Equality,
                                                           equations using       not yet known.        coefficient,
                                   0606.3.8 Represent      number sense,             *0506.3.3 Solve   Division Property
    GLE 0606.3.1 Write and         patterns using words,   properties, and       single-step linear    of Equality, two-
    solve two-step equations and   graphs, and simple      inverse operations.   equations using       step equation,
1   inequalities.                  symbolic notation.                            inverse operations.   inequality         Chapter 4
                                                          SPI 0506.2.9
                                                          Compare whole
                                                          numbers, decimals
                                                          and fractions using
                                                          the symbols <,>,
                                                          and =.
                                                          * 0506.2.9 Explore
                                                          numbers less than
                                                          0 by extending the
                                                          number line
                                                          through familiar
                                                          applications (e.g.,
                                                          temperatures,
                                                          below zero, owing
                                                          money, measuring
                                                          elevation below sea
                                                          levels.
                                                          SPI 0506.3.4 Given
                                                          a set fo values,
                                                          identify those that
                                                          make an inequality
                                                          a true statement.
                                                             * 0506.3.4 Solve
                                                          single-step linear
                                                          inequalities and       terminating decimals,
                                                          graph solutions on     repeating decimals,
    GLE 0606.3.5 Use multiple      SPI 0606.3.1           a number line.         bar notation, ratio,
    representations including      Represent on a            * 0506.3.5          percent, common         function, function
    symbolic algebra to model      number line the        Determine if a         denominator, least      table, domain,
    and/or solve contextual        solution of a linear   given value is a       common denominator      range, linear
    problems that involve linear   inequality.            solution to a linear   (LCD), rational         equation, ordered
1   relationships.                                        equation/inequality.   numbers                 pair               Chapter 4
                                    0606.2.1 Efficiently
                                    compare and order
                                    fractions, decimals and   SPI 0606.2.3
                                    percents; determine       Solve problems
                                    their approximate         involving the
                                    locations on a number     addition, subtraction,
                                    line.                     multiplication, and
                                                              division of decimals.
                                    0606.2.8 Recognize
                                    that a terminating       SPI 0606.2.5
                                    decimal equals a         Transform numbers
                                    fraction with a          from one form to
                                    denominator that is a    another (fractions,     SPI 0506.2.7
                                    power of ten.            decimals, percents,     Recognize
    GLE 0606.2.3 Understand                                  and mixed numbers). equivalent
    and use ratios, rates and       0606.2.9 Recognize                               representations for
    percents. (Introduced)          that the decimal form of SPI 0606.2.6            the same number.
                                    a rational number        Solve problems            SPI 0506.2.8
        GLE 0606.2.4 Understand     either terminates or     involving ratios, rates Write terminating
    and convert between fraction,   repeats.                 and percents.           decimals in the
    decimal, and percent forms of                                                    form of fractions or
1   rational numbers.                                                                mixed numbers.                                   Chapter 5
                                                                                                            Compatable numbers,
                                                                                                            GCF (Greatest
                                                                                                            Common Factor),
                                                                                                            multipliative inverse,
                                                                                                            reciprocal,
                                                                                                            Multiplication Property
2    SECOND NINE WEEKS                                                                                      of Equality
                                                              SPI 0606.2.1
                                                              Solve problems
                                                              involving the
                                                              multiplication and
                                                              division of fractions.

                                                              SPI 0606.2.2
                                                              Solve problems
                                                              involving the
                                                              addition, subtraction,
                                                              multiplication, and
    GLE 0606.1.2 Apply and                                    division of mixed
    adapt a variety of appropriate                            numbers.
    strategies to problem solving,                                              SPI
    including estimation, and                                 0606.3.6      Solve
    reasonableness of the solution.                           two-step linear
                                GLE   0606.1.2 Recognize      equations using
    0606.3.4 Use expressions,         when an estimate is     number sense,          SPI 0506.2.6 Add
    equations and formulas to solve   more appropriate than   properties, and        and subtract proper    perimeter, formula,
    problems.                         an exact answer in a    inverse operations.    and improper           area, circle, center,
                                      variety of problem                             fractions as well as   circumference,
2                                     situations.                                    mixed numbers          diameter, pi, raidius   Chapter 6
                                                       SPI 0506.4.2
                                                       Decompose
                                                       irregular shapes to
                                                       find perimeter and
                                                       area.
                                                       * 0506.4.2 Find the
                                                       area of a convex
                                                       polygon by
                                                       decomposing it into
                                                       triangles/rectangles.
                                                         SPI 0506.4.6
                                                       Record
                                                       measurements in
                                                       context to
    0606.4.11 Relate the                               reasonable degree
    circumference of a                                 of accuracy using
    circle with the perimeter                          decimals and/or
    of a polygonal figure.                             fractions.
                                                       *0506.4.9 Correctly
    0606.4.12 Derive the                               interpret significant
    meaning of Pi using                                digits in the
    concrete models and/or                             accuracy of
    appropriate technology.                            measurements and
                                                       associated
    0606.4.16 Solve                                    calculations.
    contextual problems                                 *0506.4.10
    involving area and                                 Recognize that
    circumference of                                   measurements are        equivalent ratios, ratio,
    circles, surface areas                             never exact.            rate, unit rate,
    and volumes of prisms,        SPI 0606.4.4         * 0506.4.11             proportion, cross
    pyramids, cones, and           Calculate with      Understand the          product, scale, scale
    cylinders.                  circumferences and     usefulness of           drawing, scale factor,
2                                  areas of circles.   approximations.         scale model               Chapter 6
    0606.2.4 Understand
    ratio as a fraction used
    to compare two
    quantities by division.

    0606.2.5 Recognize
    a:b, a/b, and “a to b” as
    notations for ratios.

    0606.2.6 Recognize
    common percentages
    as ratios based on
    fractions whose
    denominators are 2, 3,
    4, 5, or 10.

    0606.2.7 Connect
    ratio and rate to           SPI 0606.2.6
    multiplication and          Solve problems
    division.                   involving ratios, rates   percent, percent
                                and percents.             proportion, part, base,
2                               (continued)               percent equation
    0606.2.1 Efficiently
    compare and order
    fractions, decimals and
    percents; determine
    their approximate                                     survey, random
    locations on a number                                 sample, population,
    line.                   SPI 0606.2.4                  percent of change,
                            Solve multi-step              percent of increase,
    0606.2.2 Use area       arithmetic problems           percent of decrease,
    models to represent     using fractions,              sales tax, discount,
    multiplication of       mixed numbers, and            simple interest,
2   fractions.              decimals.                     principle, discount       Chapter 7 and 8
                                                                        SPI 0506.5.1
                                                                        Depict data using
                                                                        various
                                                                        representations,
                                                                        including decimal
                                                                        and/or fractional
                                                SPI 0606.5.1            data.
                        0606.5.9 Determine      Determine the           *0506.5.1 Construct
                       the sample space for a   theoretical probability and analyze double
                       given situation.         of simple and           bar and line
                                                compound events in graphs. *0506.5.2
                       0606.5.10 Distinguish    familiar contexts.      Represent data
                       between a random and                             using ordered pairs
                       nonrandom sample.                                in the first quadrant
                                                                        of the coordinate
                                                SPI 0606.5.3            system. *0506.5.4
                       0606.5.12 Predict the    Determine whether       Recognize the
                       characteristics of a     or not a sample is      differences in
                       population based on      biased.                 representing
                       the analysis of sample                           categorical and
2                      data.                                            numerical data.                                     Chapter 8

                                                                                                outcomes, simple,
                                                                                                event, probability,
                                                                                                random,
                                                                                                complementary
                                                                                                events, fair game, tree
                                                                                                diagram, sample
                                                                                                space, Fundamental
                                                                                                Counting Principal,
                                                                                                compound event,
                                                                                                independent event,
                                                                                                permutation,
                                                                                                combinations,
                                                                                                experimental
                                                                                                probability, theoretical,
                                                                                                probabality,dependent
3   THIRD NINE WEEKS                                                                            event
                                      0606.5.1
                                    Understand that the
                                    probability of an event
                                    is a number between
                                    zero and one that
                                    expresses the
                                    likelihood of its
                                    occurrence.

                                    0606.5.2 6.5.2
                                    Identify the probability
                                    of an event as the ratio
                                    of the number of its
                                    actual occurrences to
                                    the total number of its
                                    possible occurrences.

                                    0606.5.3 Express
                                    probabilities in different
                                    ways.

                                    0606.5.4 Understand
                                    the difference between
                                    probability and odds.

                                    0606.5.5 Analyze a
                                    situation that involves
                                    probability of an
                                    independent event.

    GLE 0606.5.1 Understand the 0606.5.6 Estimate
    meaning of probability and how the probability of simple
3   it is expressed.               and compound events           Chapter 9
                                      0606.3.10 Understand
                                     that in an ordered pair
                                     (x, y), the x represents
                                     horizontal location and
                                     y represents vertical
                                     location. 0606.4.1
                                     Investigate the sum of
                                     the angles in a triangle
                                     and a quadrilateral
                                     using various methods.
                                                                SPI 0606.4.1
                                     ü      0606.4.2            Identify, define or
                                     Relate the sum of the      describe geometric
                                     angles in a triangle to    shapes given a
                                     the sum of the angles      visual representation
                                     in polygons.               or a written
                                                                description of its
                                     0606.4.3 Verify the        properties.
                                     basic properties of
                                     triangles and              SPI 0606.4.2      Find
                                     quadrilaterals using a     a missing angle
                                     protractor and ruler.      measure in problems
                                                                involving
                                     0606.4.4 Classify          interior/exterior
                                     triangles by side          angles and/or their
                                     lengths (scalene,          sums.
                                     isosceles, and
                                     equilateral) and angle     SPI 0606.4.3
                                     measure (acute, right,     Solve problems
    GLE 0606.4.1 Understand          obtuse, isosceles and      using the Triangle
    and use basic properties of      equiangular).              Inequality Theorem.
    triangles, quadrilaterals, and
3   other polygons.                                                                                Chapter 10
3                                                                                        similar
                                0606.4.8 Understand
                                scaling, dilation and
                                their relation to
                                similarity.

                                0606.4.9 Analyze the
                                differences between
                                congruence and
                                similarity.



3                                                                               Chapter 10
                                                          SPI 0606.4.3
                                 0606.4.5 Model and       Solve problems
                                use the Triangle          using the Triangle
3                               Inequality Theorem.       Inequality Theorem.   Not in book

                                0606.4.7 Work with
                                transformations in a
                                plane and explore their
                                meanings through
                                drawings and
                                manipulatives.

    GLE 0606.4.2 Use the        0606.4.10 Describe
    concepts of translation,    the effect of a
    rotation, reflection, and   transformation on a 2-
    symmetry to understand      dimensional figure and
3   congruence in the plane.    the resulting symmetry.                         Chapter 10
                                                              SPI 0606.4.1
                                                              Identify, define or    SPI 0506.4.1 Solve
                                                              describe geometric     contextual
                                                              shapes given a         problems that
                                                              visual representation  require calculating
                                                              or a written           the area of
                                                              description of its     triangles and
    GLE 0606.4.3 Develop and                                  properties.            parallelograms.
    use formulas to determine the                                                     * 0506.4.1
    circumference and area of                                 SPI 0606.4.2      Find Develop the
    circles, and the area of                                  a missing angle        formula for the are
    trapezoids, and develop                                   measure in problems af a triangle by
    strategies to find the area of   0606.4.14 Relate the     involving              relating it to the
    composite shapes.                area of a trapezoid to   interior/exterior      area of a
                                     the area of a            angles and/or their    parallelogram or
3                                    parallelogram.           sums.                  rectangle.            Chapter 11
                                                                                   *0506.4.7
                                                                                   Understand, select
                                                                                   and use units of
                                                                                   appropriate size
                                                                                   and type to
                                                                                   measure angles,
                                                                                   lengths/distances,
                                                                                   area, surface area
                                                                                   and volume.
                                                                                   SPI 0506.4.3
                                                                                   Identify a three-
                                    0606.4.15 Find lengths                         dimentional object
                                    given areas or                                 from two-
                                    volumes, and vice                              dimentional
                                    versa.                                         representations of
                                                                                   that object and vice
                                    0606.4.17 Use                                  versa.
                                    manipulatives to                               * 0506.4.3 Build,
                                    discover the volume of SPI 0606.4.5            draw, and work with
                                    a pyramid is one-third  Determine the          prisms in
                                    the volume of the       surface area and       orthogonal views,
                                    related prism (the      volume of prisms,      projective views
                                    heights and base areas pyramids and            and nets.
                                    are equal).             cylinders.             *0506.4.6
                                                                                   Decompose prisms
    GLE 0606.4.4 Develop and        0606.4.18 Use           SPI 0606.4.6           to calculate surface
    use formulas for surface area   manipulatives to        Given the volume of area/volume.
    and volume of 3-dimensional     discover the volume of a cone/pyramid, find SPI 0506.4.4 Solve
    figures.                        a cone is one-third the the volume of the      problems involving
                                    volume of the related   related cylinder/prism surface area and
                                    cylinder (the heights   or vice versa.         volume of
                                    and base areas are                             rectangular prisms
3                                   equal).                                        and polyhedral
3   ALL YEAR LONG
GLE 0606.1.1 Use
mathematical language,
symbols, and definitions while
developing mathematical
reasoning.

GLE 0606.1.2 Apply and
adapt a variety of appropriate
strategies to problem solving,  0606.1.3 Recognize
including estimation, and       errors generated by
reasonableness of the solution. rounding.

GLE 0606.1.3 Develop              0606.1.4 Describe
independent reasoning to          how changes in one
communicate mathematical          quantity or variable
ideas and derive algorithms       result in changes in
and/or formulas.                  another.

GLE 0606.1.4 Move flexibly        0606.1.7
between concrete and abstract     Formulate questions,
representations of                design studies, and
mathematical ideas in order to    collect real world data.
solve problems, model
mathematical ideas, and           0606.1.8 Determine
communicate solution              an appropriate sample
strategies.                       to test an hypothesis.

GLE 0606.1.5 Use                  0606.1.9 Use age-
mathematical ideas and            appropriate books,
processes in different settings   stories, and videos to
to formulate patterns, analyze    convey ideas of
graphs, set up and solve          mathematics.
problems and interpret

				
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