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					                                                                   Mathematics Pacing Guide
                                                                      Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                        Supporting Grade Level Content Expectations          Vocabulary
Integrated and                   Employability/Career Skills                                                                    Assessable vocabulary =
Ongoing                                                                                                                            regular font
                    A-17 Careers                                                                                                Instructional vocabulary =
                     Explore Professions and Related Salaries                                                                     italicized font
                       - Accountant                                                                                             box plot
                       - Banker                                                                                                 formula
                       - Engineer                                                                                               graphing
                       - Teacher                                                                                                histogram
                       - Sales                                                                                                  Internet
                       - Artist                                                                                                 LIST
                       - Architect                                                                                              mean
                       - Mathematician                                                                                          median
                                                                                                                                mode
                    A-18 Personal Management                                                                                    scatterplot
                     Develop Personal Management Skills                                                                        spread sheet
                       - Budgeting (income, spending…)                                                                          table
                       - Calculate sports statistics                                                                            trace
                                                                                                                                window
                    A-19 Teamwork                                                                                               Y=
                     Develop Skills for Interacting with Others                                                                zoom
                       - Negotiations                                                                                           analyze
                       - Cooperative learning                                                                                   compare
                       - Respect for others                                                                                     conjecture
                       - Conflict resolution                                                                                    convey
                                                                                                                                describe
                                                                                                                                devise
                                         Technology                                                                             discuss
                                                                                                                                evaluate
                    A-16 Use, Transfer, and Apply Appropriate Technology                                                        explain
                     Investigate the Use of Calculators                                                                        interpret
                       - Determine key sequence                                                                                 algorithm
                            add
                            subtract
                            divide
                            multiply
Grade 8 Mathematics Pacing Guide – Revised May 2008                           1
     Timing                      Content & Processes (MCF)                Supporting Grade Level Content Expectations   Vocabulary
                            fraction
                            percent
                            decimal
                            square roots
                            exponents
                            reciprocals
                       Use Computer Spreadsheets to Solve Problems
                        - Develop spreadsheet instructions




Grade 8 Mathematics Pacing Guide – Revised May 2008                   2
                                                                    Mathematics Pacing Guide
                                                                       Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                           Supporting Grade Level Content Expectations                Vocabulary
Unit 1:                        Number Sense and Numeration                                                                               additive identity property
September                                                                                                                                   of zero
                    A-9 Concepts and Properties of Numbers                                                                               associative property of
Topic:              Develop an understanding and investigate properties of                                                                  addition
                    numbers in measuring and counting activities.                         Understand Real Number Concepts                associative property of
Number Systems
                                                                                                                                            multiplication
and Number                                                                                                                               commutative property of
Sense                  Extend their understanding of numeration systems to    N.ME.08.01 Understand the meaning of a square root of
                                                                                                                                            addition
                        include decimal numeration, scientific numeration      a number and its connection to the square whose area is
                                                                                                                                         commutative property of
Timing: 2 weeks         and non-decimal numeration systems. (IV.1.MS.2)        the number; understand the meaning of a cube root and        multiplication
                        (IV.1.HS.2)                                            its connection to the volume of a cube.                   consecutive
                                                                                                                                         cube root
                                                                                                                                         derived quantities
                    A-10 Representation and Uses of Numbers                                                                              distributive property
                    Produce and translate among equivalent expressions.                                                                  exponential growth
                                                                                                                                         integers
                       Determine use of rational approximations.                                                                        irrational number
                        (IV.2.MS.3) (IV.2.HS.3)                                                                                          means and extremes
                                                                                                                                         multiplicative identify
                       Apply estimation strategies. (IV.2.MS.4) (IV.2.HS.4)   N.FL.08.05 Estimate and solve problems with square           (property of one)
                                                                               roots and cube roots, using calculators.                  negative exponent
                                                                                                                                         prime
                                                                                                                                         property
                                                                               N.FL.08.06. Find square roots of perfect squares and
                                                                                                                                         proportion
                                                                               approximate the square roots of non-perfect squares by
                                                                                                                                         Pythagorean Theorem
                                                                               locating between consecutive integers, e.g.,   13C is     rational number
                                                                               between 11 and 12.                                        real number
                       Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5)                                                               repeating decimal
                                                                                                                                         scaling
                    A-11 Number Relationships                                                                                            scientific notation
                     Explain the meaning of powers and roots of numbers                                                                 square root
                       and use calculators to compute powers and square                                                                  squaring
                       roots. (IV.3.MS.4) (IV.3.HS.4)                                                                                    terminating decimal
                                                                                                                                         truncate
                                                                                                                                         unit rate



Grade 8 Mathematics Pacing Guide – Revised May 2008                              3
                                                                    Mathematics Pacing Guide
                                                                       Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                            Supporting Grade Level Content Expectations          Vocabulary
Unit 2:                         Number Sense and Numeration
September and
October             A-9 Concepts and Properties of Numbers
                    Develop an understanding and investigate properties of
Topic: Number       numbers in measuring and counting activities.                           Understand Real Number Concepts
Systems and
Number Sense           Extend their understanding of numeration systems to     N.ME.08.02 Understand meanings for zero and negative
                        include decimal numeration, scientific numeration       integer exponents.
Timing: 3 weeks         and non-decimal numeration systems. (IV.1.MS.2)
                        (IV.1.HS.2)

                    A-10 Representation and Uses of Numbers
                    Produce and translate among equivalent expressions.

                       Incorporate decimal representations of rational and     N.ME.08.03 Understand that in decimal form, rational
                        irrational numbers. (IV.2.MS.1) (IV.2.HS.1)             numbers either terminate or eventually repeat, and that
                                                                                calculators truncate or round repeating decimals; locate
                       Evaluate exponential expressions. (IV.2.MS.2)           rational numbers on the number line; know fraction
                        (IV.2.HS.2)                                             forms of common repeating decimals, e.g.
                                                                                         1        1
                                                                                 0.1      ;0.3 
                       Determine use of rational approximations.                        9        3.
                        (IV.2.MS.3) (IV.2.HS.3)

                       Apply estimation strategies. (IV.2.MS.4) (IV.2.HS.4)    N.ME.08.04 Understand that irrational numbers are
                                                                                those that cannot be expressed as the quotient of two
                                                                                integers, and cannot be represented by terminating or
                                                                                repeating decimals; approximate the position of familiar
                                                                                irrational numbers, (e.g., 2, 3, ) on the number line.
                       Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5)


                    A-11 Number Relationships
                    Investigate relationships, and represent and compare very
                    large and small numbers.
Grade 8 Mathematics Pacing Guide – Revised May 2008                               4
     Timing                      Content & Processes (MCF)                       Supporting Grade Level Content Expectations   Vocabulary

                       Compare and order integers and rational numbers
                        using relations of equality and inequality.
                        (IV.3.MS.1) (IV.3.HS.1)

                       Explain the meaning of powers and roots of numbers
                        and use calculators to compute powers and square
                        roots. (IV.3.MS.4) (IV.3.HS.4)




Grade 8 Mathematics Pacing Guide – Revised May 2008                          5
                                                                    Mathematics Pacing Guide
                                                                       Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                            Supporting Grade Level Content Expectations         Vocabulary
Unit 3:                         Number Sense and Numeration
October
                    A-10 Representation and Uses of Numbers
Topic:              Produce and translate among equivalent expressions.                             Solve Problems
Calculations
Using Real and         Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5)      N.MR.08.08 Solve problems involving percent increases
Complex                                                                         and decreases.
Numbers             A-11 Number Relationships
                    Investigate relationships, and represent and compare very   N.FL.08.09 Solve problems involving compounded
Timing: 3 weeks     large and small numbers.                                    interest or multiple discounts.

                       Express numerical comparisons as ratios and rates.
                        (IV.3.MS.2) (IV.3.HS.2)                                 N.MR.08.07 Understand percent increase and percent
                                                                                decrease in both sum and product form, e.g. 3% increase
                                                                                of a quantity x is x + .03x = 1.03x. Understand the
                                                                                concept of non-linear functions using basic examples
                       Apply their understanding of number relationships in
                        solving problems. (IV.3.MS.5) (IV.3.HS.5)               N.FL.08.09 Solve problems involving compounded
                                                                                interest or multiple discounts.




                                                                    Mathematics Pacing Guide
                                                                       Grade 8 (Algebra)
Grade 8 Mathematics Pacing Guide – Revised May 2008                               6
     Timing                      Content & Processes (MCF)                            Supporting Grade Level Content Expectations          Vocabulary
Unit 4:                         Number Sense and Numeration
November
                    A-10 Representation and Uses of Numbers
Topic:              Produce and translate among equivalent expressions.                             Solve Problems
Calculations
using Real and         Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5)      N.MR.08.10 Calculate weighted averages such as course
Complex                                                                         grades, consumer price indices, and sports ratings.
Numbers             A-11 Number Relationships
                    Investigate relationships, and represent and compare very
Timing: 2 weeks     large and small numbers.

                       Apply their understanding of number relationships in
                        solving problems. (IV.3.MS.5) (IV.3.HS.5)               N.FL.08.11 Solve problems involving ratio units, such as
                                                                                miles per hour, dollars per pound, or persons per square
                                                                                mile.




Grade 8 Mathematics Pacing Guide – Revised May 2008                               7
                                                                      Mathematics Pacing Guide
                                                                         Grade 8 (Algebra)

     Timing                       Content & Processes (MCF)                            Supporting Grade Level Content Expectations                     Vocabulary
Unit 5:                     Patterns, Relationships, and Functions                                                                              binomial
November and                                                                                                                                    coefficient
December            A-1 Patterns                                                    Understand the Concept of Non-linear Functions              constant
                    Analyze, interpret, and predict patterns.                                   using Basic Examples                            continuous
Topic: Functions                                                                                                                                degree
                       Use models to make predictions and decisions.            A.RP.08.01 Identify and represent linear functions,            dependent variable
Timing: 3 weeks         (I.1.MS.3) (I.1.HS.3)                                    quadratic functions, and other simple functions including      direct variation
                                                                                 inversely proportional relationships (y = k/x); cubics (y =    domain
                       Explore and describe visual and numeric patterns,        ax3); roots (y = x ); and exponentials (y = ax, a > 0);
                                                                                                                                                equation
                        including linear expressions, near-linear patterns and                                                                  expression
                                                                                 using tables, graphs, and equations.
                        symmetric and spatial patterns. (I.1.MS.4) (I.1.HS.4)                                                                   exponential function
                                                                                                                                                function
                                                                                 A.PA.08.02 For basic functions, e.g. simple quadratics,
                    A-2 Variability and Change                                                                                                  function notation
                                                                                 direct and indirect variation, and population growth,
                    Explore variability and change.                                                                                             hyperbole
                                                                                 describe how changes in one variable affect the others.
                                                                                                                                                independent variable
                       Differentiate between functions and relationships        A.PA.08.03 Recognize basic functions in problem
                                                                                                                                                indirect variation
                        such as linear vs. not linear or continuous vs. non-                                                                    inverse function
                                                                                 context, e.g. area of a circle is r2, volume of a sphere is   inversely proportional
                        continuous. (I.2.MS.5) (I.2.HS.5)                        4/3 r3, and represent them using tables, graphs, and             relationship
                                                                                 formulas                                                       linear
                       Solve real-world problems. (I.2.MS.6) (I.2.HS.6)
                                                                                                                                                linear function
                                                                                 A.RP.08.04 Use the vertical line test to determine if a        linear equalities
                                                                                 graph represents a function in one variable.                   linear inequalities
                                Number Sense and Numeration
                                                                                                                                                monomial
                    A-11 Number Relationships                                                                                                   non-continuous
                                                                                 Recognize, Represent, and Apply Common Formulas                nonlinear function
                                                                                                                                                ordered pairs
                       Express numerical comparisons as ratios and rates.       A.FO.08.07 Recognize and apply the common formulas:            perimeter area
                        (IV.3.MS.2) (IV.3.HS.2)                                  (a + b)2 = a2 + 2 ab + b2                                      polynomial relationship
                                                                                 (a – b)2 = a2 – 2 ab + b2                                      proportional
                       Explain the meaning of powers and roots of numbers       (a + b) (a – b) = a2 – b2; represent geometrically.            quadratic function
                        and use calculators to compute powers and square
                                                                                                                                                range
                        roots. (IV.3.MS.4) (IV.3.HS.4)
                                                                                                                                                rate of change
                                                                                                                                                root
                            Probability and Discrete Mathematics                                                                                scale factor
Grade 8 Mathematics Pacing Guide – Revised May 2008                                8
     Timing                      Content & Processes (MCF)                        Supporting Grade Level Content Expectations                    Vocabulary
                    A-14 Probability                                        A.FO.08.08 Factor simple quadratic expressions with            sequence simultaneous
                                                                            integer coefficients, e.g., x2 + 6x + 9, x2 + 2x – 3, and x2      linear equations
                       Generate and interpret probability distributions.   – 4; solve simple quadratic equations, e.g., x2 = 16 or x2     slope
                        (VI.1.MS.2) (VI.1.HS.2)                             = 5 (by taking square roots); x2 – x – 6 = 0, x2 – 2x = 15     square root function
                                                                            (by factoring); verify solutions by evaluation.                trinomial
                                                                                                                                           term
                                                                                                                                           vertical line test
                                                                                                                                           x-intercept
                                                                                                                                           y-intercept




Grade 8 Mathematics Pacing Guide – Revised May 2008                           9
                                                                      Mathematics Pacing Guide
                                                                         Grade 8 (Algebra)

     Timing                       Content & Processes (MCF)                        Supporting Grade Level Content Expectations                Vocabulary
Unit 6:                     Patterns, Relationships, and Functions
January
                    A-1 Patterns                                                Recognize, Represent, and Apply Common Formulas
Topic: Binomials    Analyze, interpret, and predict patterns.
                                                                               A.FO.08.07 Recognize and apply the common formulas:
Timing: 3 weeks        Analyze and generalize number sequences.               (a + b)2 = a2 + 2 ab + b2
                        (I.1.MS.1) (I.1.HS.1)                                  (a – b)2 = a2 – 2 ab + b2
                                                                               (a + b) (a – b) = a2 – b2; represent geometrically.
                       Solve real-world problems. (I.1.MS.5) (I.1.HS.5)
                                                                               A.FO.08.08 Factor simple quadratic expressions with
                                                                               integer coefficients, e.g., x2 + 6x + 9, x2 + 2x – 3, and x2
                                Number Sense and Numeration                    – 4; solve simple quadratic equations, e.g., x2 = 16 or x2
                                                                               = 5 (by taking square roots); x2 – x – 6 = 0, x2 – 2x = 15
                    A-10 Representation and Uses of Numbers                    (by factoring); verify solutions by evaluation.

                       Incorporate decimal representations of rational and
                        irrational numbers. (IV.2.MS.1) (IV.2.HS.1)

                    A-11 Number Relationships

                       Explain the meaning of powers and roots of numbers
                        and use calculators to compute powers and square
                        roots. (IV.3.MS.4) (IV.3.HS.4)


                             Numerical and Algebraic Operations
                                 and Analytical Thinking

                    A-12 Operations and Their Properties
                    Investigate algebraic operations and their properties.

                       Present and explain geometric and symbolic models
                        for operations with real numbers and algebraic
                        expressions. (V.1.MS.1) (V.1.HS.1)

Grade 8 Mathematics Pacing Guide – Revised May 2008                              10
     Timing                      Content & Processes (MCF)                      Supporting Grade Level Content Expectations   Vocabulary
                       Compute with real numbers and algebraic
                        expressions. (V.1.MS.2) (V.1.HS.2)

                       Describe the properties of operations and generalize
                        about their properties. (V.1.MS.3) (V.1.HS.3)

                    A-13 Algebraic And Analytic Thinking

                       Represent algebraic concepts with matrices,
                        diagrams, graphs, etc. (V.2.MS.2) (V.2.HS.2)




Grade 8 Mathematics Pacing Guide – Revised May 2008                            11
                                                                     Mathematics Pacing Guide
                                                                        Grade 8 (Algebra)

     Timing                       Content & Processes (MCF)                          Supporting Grade Level Content Expectations                Vocabulary
Unit 7:                     Patterns, Relationships, and Functions
January &
February            A-1 Patterns                                                    Understand and Represent Quadratic Functions
                    Analyze, interpret, and predict patterns.
Topic:                                                                           A.RP.08.05 Relate quadratic functions in factored form
Understand and         Analyze and generalize number sequences.                 and vertex form to their graphs, and vice versa; in
Represent               (I.1.MS.1) (I.1.HS.1)                                    particular, note that solutions of a quadratic equation are
Quadratic                                                                        the x-intercepts of the corresponding quadratic function.
Functions              Analyze, interpret, and translate among
                        representations such as tables and graphs. (I.1.MS.2)    A.RP.08.06 Graph factorable quadratic functions,
Timing: 3 weeks         (I.1.HS.2)                                               finding where the graph intersects the x-axis and the
                                                                                 coordinates of the vertex; use words “parabola” and
                       Use models to make predictions and decisions.            “roots”; include functions in vertex form and those with
                        (I.1.MS.3) (I.1.HS.3)                                    leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9;
                                                                                 y = – x2; y = – (x – 3)2.
                       Explore and describe visual and numeric patterns,
                        including linear expressions, near-linear patterns and
                        symmetric and spatial patterns. (I.1.MS.4) (I.1.HS.4)    Recognize, Represent, and Apply Common Formulas

                       Solve real-world problems. (I.1.MS.5) (I.1.HS.5)         A.FO.08.08 Factor simple quadratic expressions with
                                                                                 integer coefficients, e.g., x2 + 6x + 9, x2 + 2x – 3, and
                                                                                 x2 – 4; solve simple quadratic equations, e.g., x2 = 16 or
                                Number Sense and Numeration                      x2 = 5 (by taking square roots); x2 – x – 6 = 0, x2 – 2x =
                                                                                 15 (by factoring); verify solutions by evaluation.
                    A-11 Number Relationships
                                                                                 A.FO.08.09 Solve applied problems involving simple
                       Distinguish between prime and composite numbers;         quadratic equations.
                        identify factors, multiples, common factors and
                        multiples, and relatively prime numbers; and apply
                        divisibility tests to numbers. (IV.3.MS.3) (IV.3.HS.3)




Grade 8 Mathematics Pacing Guide – Revised May 2008                               12
                                                                      Mathematics Pacing Guide
                                                                         Grade 8 (Algebra)

     Timing                     Content & Processes (MCF)                         Supporting Grade Level Content Expectations                Vocabulary
Unit 8:                     Numerical and Algebraic Operations
February                        and Analytical Thinking                            Understand Solutions and Solve Equations,
                                                                                 Simultaneous Equations, and Linear Inequalities
Topic:              A-13 Algebraic and Analytic Thinking
Recognize,          Analyze and model problems using algebraic notation.     A.FO.08.10 Understand that to solve the equation f(x) =
Represent, and                                                               g(x) means to find all values of x for which the equation is
Apply Common           Identify variables and express their relationships   true; e.g., determine whether a given value, or values from
Formulas                algebraically. (V.2.MS.1) (V.2.HS.1)                 a given set, is a solution of an equation (0 is a solution of
                                                                             3x2 + 2 = 4x + 2, but 1 is not a solution).
Timing: 3 weeks        Represent algebraic concepts with matrices,
                        diagrams, graphs, etc. (V.2.MS.2) (V.2.HS.2)         A.FO.08.11 Solve simultaneous linear equations in two
                                                                             variables, by graphing, by substitution and by linear
                       Solve equations and inequalities. (V.2.MS.3)         combination; estimate solutions using graphs; include
                        (V.2.HS.3)                                           examples with no solutions and infinitely many solutions.

                       Solve linear systems. (V.2.MS.3) (V.2.HS.3)          A.FO.08.12 Solve linear inequalities in one and two
                                                                             variables, and graph the solution sets.
                       Solve problems using equations and inequalities.
                        (V.2.MS.5) (V.2.HS.5)                                A.FO.08.13 Set up and solve applied problems involving
                                                                             simultaneous linear equations and linear inequalities.

                               Number Sense and Numeration

                    A-10 Representation and Uses of Numbers

                       Solve real-world problems. (IV.2.MS.5)
                        (IV.2.HS.5)




Grade 8 Mathematics Pacing Guide – Revised May 2008                              13
                                                                      Mathematics Pacing Guide
                                                                         Grade 8 (Algebra)

     Timing                        Content & Processes (MCF)                          Supporting Grade Level Content Expectations                  Vocabulary
Unit 9:                            Geometry and Measurement                                                                                 bisector
March                                                                                   Understand and Use the Pythagorean Theorem          circle
                    A-3 Shape and Shape Relationships                                                                                       complimentary angles
                    Identify properties and describe relationships among          G.GS.08.01 Understand at least one proof of the           corresponding angles
Topic:
                                                                                                                                            cones
Understand and      shapes.                                                       Pythagorean Theorem; use the Pythagorean Theorem and
                                                                                                                                            congruent
Use the                                                                           its converse to solve applied problems, including         cube
Pythagorean            Use shape properties and relationships to solve           perimeter, area, and volume problems.                     cylinder
Theorem                 problems. (II.1.MS.7) (II.1.HS.7)                                                                                   dilation
                                                                                  G.LO.08.02 Find the distance between two points on the    edge
Timing: 2 weeks     A-4 Position                                                  coordinate plane, using the distance formula; recognize   face
                                                                                  that the distance formula is an application of the        horizontal stretch
                       Locate the position of points or objects described by     Pythagorean Theorem.                                      image
                        two or more conditions; locate all the points (locus)                                                               isometric view
                                                                                                                                            net
                        that satisfy a given condition. (II.2.MS.4) (II.2.HS.4)
                                                                                                                                            orthogonal view
                                                                                                                                            parabola
                                                                                                                                            perpendicular bisector
                                                                                                                                            plane figure
                                                                                                                                            prism
                                                                                                                                            projective view
                                                                                                                                            pyramid
                                                                                                                                            quadrilateral
                                                                                                                                            reflection
                                                                                                                                            reflectional symmetry
                                                                                                                                            rotational symmetry
                                                                                                                                            scale factor
                                                                                                                                            similarity
                                                                                                                                            slide
                                                                                                                                            solid figure
                                                                                                                                            sphere
                                                                                                                                            supplementary angles
                                                                                                                                            transformation
                                                                                                                                            translate
                                                                                                                                            vertex
                                                                                                                                            vertical stretch



Grade 8 Mathematics Pacing Guide – Revised May 2008                                14
                                                                      Mathematics Pacing Guide
                                                                         Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                           Supporting Grade Level Content Expectations                  Vocabulary
Unit 10:
March               A-3 Shape and Shape Relationships                             Solve Problems About Geometric Figures                    area
                    Identify properties and describe relationships among                                                                    circumference
                    shapes.                                                       G.SR.08.03 Understand the definition of a circle; know    perimeter
Topic: Solve
                                                                                                                                            radius
Problems About                                                                    and use the formulas for circumference and area of a
                                                                                                                                            surface area
Geometric              Generalize the characteristics of shapes and apply        circle to solve problems.                                 volume
Figures                 their generalizations to classes of shapes. (II.1.MS.2)
                        (II.1.HS.2)                                               G.SR.08.04 Find area and perimeter of complex figures
Timing: 3 weeks                                                                   by sub-dividing them into basic shapes (quadrilaterals,
                       Construct familiar shapes using coordinates,              triangles, circles).
                        appropriate tools (including technology), sketching
                        and drawing two- and three dimensional shapes.            G.SR.08.05 Solve applied problems involving areas of
                        (II.1.MS.4) (II.1.HS.4)                                   triangles, quadrilaterals, and circles.

                       Combine, dissect, and transform shapes. (II.1.MS.5)
                        (II.1.HS.5)

                       Use shape properties and relationships to solve
                        problems. (II.1.MS.7) (II.1.HS.7)

                    A-5 Measurement

                    Use proportional reasoning and indirect measurements to
                    draw inferences. (II.3.MS.5) (II.3.HS.5)




Grade 8 Mathematics Pacing Guide – Revised May 2008                                15
                                                                      Mathematics Pacing Guide
                                                                         Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                            Supporting Grade Level Content Expectations              Vocabulary
Unit 11:                          Geometry and Measurement
April                                                                              Understand Concepts of Volume and Surface Area,
                    A-5 Measurement                                                             and Apply Formulas
Topic: Volume       Compare and analyze objects with a standard unit.
and Surface Area                                                                  G.SR.08.06 Know the volume formulas for generalized
                       Interpret measurements and explain how changes in         cylinders ((area of base) x height),generalized cones and
Timing: 2 weeks         one measurement affects another. (II.3.MS.4)              pyramids ( (area of base) x height) and spheres (
                        (II.3.HS.4)
                                                                                  (radius)3), and apply them to solve problems.
                       Use proportional reasoning and indirect
                                                                                  G.SR.08.07 Understand the concept of surface area and
                        measurements to draw inferences. (II.3.MS.5)
                                                                                  find the surface area of prisms, cones, spheres, pyramids,
                        (II.3.HS.5)
                                                                                  and cylinders.
                    A-3 Shape and Shape Relationships
                                                                                                       Visualize Solids
                    Identify properties and describe relationships among
                    shapes.
                                                                                  G.SR.08.08 Sketch a variety of two-dimensional
                                                                                  representations of three-dimensional solids, including:
                       Generalize the characteristics of shapes and apply        orthogonal views (top, front, and side), picture views
                        their generalizations to classes of shapes. (II.1.MS.2)   (projective or isometric) and nets, and use such two-
                        (II.1.HS.2)                                               dimensional representations to help solve problems.
                       Construct familiar shapes using coordinates,
                        appropriate tools (including technology), sketching
                        and drawing two- and three dimensional shapes.
                        (II.1.MS.4) (II.1.HS.4)

                       Use shape properties and relationships to solve
                        problems. (II.1.MS.7) (II.1.HS.7)




Grade 8 Mathematics Pacing Guide – Revised May 2008                                16
                                                                         Mathematics Pacing Guide
                                                                            Grade 8 (Algebra)

     Timing                       Content & Processes (MCF)                              Supporting Grade Level Content Expectations         Vocabulary
Unit 12:                          Geometry and Measurement
April & May                                                                                   Understand and Apply Concepts of
                    A-3 Shape and Shape Relationships                                          Transformation and Symmetry
Topic:              Identify properties and describe relationships among
Transformations     shapes.                                                        G.TR.08.09 Understand the definition of a dilation from
                                                                                   a point in the plane and relate it to the definition of
Timing: 2 weeks        Generalize the characteristics of shapes and apply         similar polygons.
                        their generalizations to classes of shapes. (II.1.MS.2)
                        (II.1.HS.2)                                                G.TR.08.10 Understand and use reflective and
                                                                                   rotational symmetries of two-dimensional shapes and
                       Combine, dissect, and transform shapes. (II.1.MS.5)        relate them to transformations to solve problems.
                        (II.1.HS.5)

                       Generalize about the common properties of similar,
                        congruent, parallel and perpendicular shapes and
                        verify their generalizations informally. (II.1.MS.6)
                        (II.1.HS.6)

                    A-4 Position
                    Identify location of objects, location relative to other
                    objects, and the effects of transformations.

                       Locate and describe objects in terms of their
                        orientation and relative position. (II.2.MS.2)
                        (II.2.HS.2)

                       Describe translations, reflections, rotations and
                        dilations using the language of transformations and
                        employ transformations to verify congruence of
                        figures. (II.2.MS.3) (II.2.HS.3)




                                   Data Analysis and Statistics
Grade 8 Mathematics Pacing Guide – Revised May 2008                                 17
     Timing                      Content & Processes (MCF)                           Supporting Grade Level Content Expectations   Vocabulary

                    A-6 Collection, Organization, and Presentation of Data

                       Explain how data can be skewed/biased. (III.1.MS.3)
                        (III.1.HS.3)

                       Implement strategies to obtain, organize, and present
                        data. (III.1.MS.4) (III.1.HS.4)


                                Number Sense and Numeration

                    A-10 Representation and Uses of Numbers

                       Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5)




Grade 8 Mathematics Pacing Guide – Revised May 2008                             18
                                                                       Mathematics Pacing Guide
                                                                          Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                           Supporting Grade Level Content Expectations                      Vocabulary
Unit 13: May                      Data Analysis and Statistics                                                                                 basic counting principal
                                                                                   Draw, Explain, and Justify Conclusions Based on             biased sample
Topic: Bias         A-6 Collection, Organization and Presentation of Data                                 Data                                 box plots
                    Collect, organize, and analyze data.                                                                                       coordinate graph
Timing: 2 weeks                                                                  D.AN.08.01 Determine which measure of central                 counting tree
                       Collect data through survey and observation.             tendency (mean, median, mode) best represents a data          cumulative frequency
                        (III.1.MS.1) (III.1.HS.1)                                set, e.g. salaries, home prices for answering certain         dependent event
                                                                                 questions, and justify the choice made.                       experimental probability
                       Organize data in various forms such as tables, charts,                                                                 extrapolations
                        and graphs. (III.1.MS.2) (III.1.HS.2)                    D.AN.08.02 Recognize practices of collecting and              five number summary
                                                                                 displaying data that may bias the presentation or analysis.   frequency table
                       Explain how data can be skewed/biased. (III.1.MS.3)                                                                    histogram
                        (III.1.HS.3)                                                                                                           independent event
                                                                                                                                               interpolations
                       Implement strategies to obtain, organize, and present                                                                  intersection
                        data. (III.1.MS.4) (III.1.HS.4)                                                                                        IQR (inter-quartile) range
                                                                                                                                               line graph
                    A-7 Description and Interpretation                                                                                         line of best fit
                    Examine, describe, and relate data.                                                                                        line plot
                                                                                                                                               lower quartile
                                                                                                                                               mean
                       Present and critically examine data from tables,
                                                                                                                                               measures of central
                        graphs, and charts. (III.2.MS.1) (III.2.HS.1)
                                                                                                                                                  tendency
                                                                                                                                               median
                       Calculate measures of central tendency. (III.2.MS.2)
                                                                                                                                               mode
                        (III.2.HS.2)
                                                                                                                                               organized list
                                                                                                                                               outcomes
                       Utilize data and their characteristics to draw and                                                                     population
                        support conclusions. (III.2.MS.3) (III.2.HS.3)                                                                         probability
                                                                                                                                               proportion
                       Question sources of data and collection techniques.                                                                    quartile
                        (III.2.MS.4) (III.2.HS.4)                                                                                              random
                                                                                                                                               range
                       Formulate problems to gather and interpret data.                                                                       relative frequency
                        (III.2.MS.5) (III.2.HS.5)                                                                                              repeated events
Grade 8 Mathematics Pacing Guide – Revised May 2008                               19
     Timing                      Content & Processes (MCF)                     Supporting Grade Level Content Expectations          Vocabulary
                                                                                                                             sample
                    A-8 Inference and Prediction                                                                             sampling
                    Develop and justify inferences and predictions.                                                          scatter plot
                                                                                                                             stem-and-leaf plot
                       Develop and test hypothesis. (III.3.MS.1)                                                            theoretical probability
                        (III.3.HS.1)                                                                                         trend union
                                                                                                                             upper quartile
                       Employ confidence intervals and curve fitting in                                                     Venn Diagram
                        analyzing data. (III.3.MS.2) (III.3.HS.2)

                       Formulate, communicate, and evaluate arguments.
                        (III.3.MS.3) (III.3.HS.3)

                       Make predictions and decisions based on data.
                        (III.3.MS.4) (III.3.HS.4)

                       Solve real-world problems. (III.3.MS.5) (III.3.HS.5




Grade 8 Mathematics Pacing Guide – Revised May 2008                           20
                                                                       Mathematics Pacing Guide
                                                                          Grade 8 (Algebra)

     Timing                      Content & Processes (MCF)                         Supporting Grade Level Content Expectations   Vocabulary
Unit 14:                          Data Analysis and Statistics
May & June
                    A-6 Collection, Organization and Presentation of Data
Topic:              Collect, organize, and analyze data.
Frequency
                       Collect data through survey and observation.
Timing: 3 weeks         (III.1.MS.1) (III.1.HS.1)

                       Organize data in various forms such as tables, charts,
                        and graphs. (III.1.MS.2) (III.1.HS.2)

                       Explain how data can be skewed/biased. (III.1.MS.3)
                        (III.1.HS.3)

                       Implement strategies to obtain, organize, and present
                        data. (III.1.MS.4) (III.1.HS.4)

                    A-7 Description and Interpretation
                    Examine, describe, and relate data.

                       Present and critically examine data from tables,
                        graphs, and charts. (III.2.MS.1) (III.2.HS.1)

                    A-8 Inference and Prediction
                    Develop and justify inferences and predictions.

                       Develop and test hypothesis. (III.3.MS.1)
                        (III.3.HS.1)

                       Employ confidence intervals and curve fitting in
                        analyzing data. (III.3.MS.2) (III.3.HS.2)

                       Formulate, communicate, and evaluate arguments.
                        (III.3.MS.3) (III.3.HS.3)

Grade 8 Mathematics Pacing Guide – Revised May 2008                               21
     Timing                      Content & Processes (MCF)                         Supporting Grade Level Content Expectations                  Vocabulary
                       Make predictions and decisions based on data.
                        (III.3.MS.4) (III.3.HS.4)

                       Solve real-world problems. (III.3.MS.5) (III.3.HS.5)

                                                                                     Understand Probability Concepts for Simple
                            Probability and Discrete Mathematics                              and Compound Events

                    A-14 Probability                                           D.PR.08.05 Find and/or compare the theoretical
                    Utilize knowledge of probability to make critical          probability, the experimental probability, and/or the
                    judgments of various situations.                           relative frequency of a given event.

                       Generate and interpret probability distributions.      D.PR.08.04 Apply the Basic Counting Principle to find
                        (VI.1.MS.2) (VI.1.HS.2)                                total number of outcomes possible for independent and
                                                                               dependent events, and calculate the probabilities using
                       Identify probability of compound or multiple events.   organized lists or tree diagrams.
                        (VI.1.MS.3) (VI.1.HS.3)
                                                                               D.PR.08.06 Understand the difference between
                       Utilize simulations and samplings to determine         independent and dependent events, and recognize
                        probability. (VI.1.MS.4) (VI.1.HS.4)                   common misconceptions involving probability, e.g. Alice
                                                                               rolls a 6 on a die three times in a row; she is just as likely
                                                                               to roll a 6 on the 4th roll as she was on any previous roll.

                                                                               D.PR.08.03 Compute relative frequencies from a table
                                                                               of experimental results for a repeated event. Interpret the
                                                                               results using relationship of probability to relative
                                                                               frequency.




Grade 8 Mathematics Pacing Guide – Revised May 2008                             22

				
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