Mathematics Curriculum Salem City Schools Grade 8

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Mathematics Curriculum

  Salem City Schools

        Grade 8



    Revised Summer 2006
  Time Allotted                      Topic                      SOL             Chapter(s)
First Six Weeks   Organizing Data                          8.1, 8.3, 8.12    Chapters 1, 2,
                  Measures of Central Tendency                               3, 7 and 10
                  Line Plots
                  Stem and Leaf Diagrams
                  Box and Whisker Plots
                  Bar and Line Graphs
                  Scatter Plots
                  Integer Operations
                  Absolute Value
Second Six        Order of Operations                      8.1, 8.4, 8.15,   Chapters 1, 3,
Weeks             Coordinate System                        8.17              4, 5, 6, 8, and
                  Exponential Notation                                       10
                  Scientific Notation
                  Formulas
                  Variable and Algebraic Expressions
                  One and Two Step Equations
                  Inequalities
Third Six Weeks   One and Two Step Equation/Inequalities   8.3, 8.14,        Chapters 4, 5,
                  Functions                                8.15, 8.16,       6, 7, and 8
                  Relations                                8.17, 8.18
                  Ratio and Proportions
                  Unit Rates
                  Scale Drawings

Fourth Six        Decimals and Percents                    8.1, 8.2, 8.5,    Chapters 1, 3,
Weeks             Number Sense                             8.10              9, and 10
                  Rational and Real Numbers
                  Probability
                  Perfect Squares
                  Square Roots
                  Pythagorean Theorem
Fifth Six Weeks   Geometry                                 8.6, 8.7, 8.8,    Chapters 12
                  Area/Perimeter                           8.9
                  Surface Area
                  Volume
                  Three Dimensional
                  Transformations
Sixth Six Weeks   More Functions                           8.11, 8.13,      Chapters 6 and
                  Probability                              8.14, 8.18, (all 8
                  Matrices                                 for SOL
                  Polynomials                              Review)
                  SOL Review




                                                 2                                   Revised Summer 2006
        These documents reflect alignment of the Mathematics curriculum in the Salem City Schools with
the Standards of Learning for the Commonwealth of Virginia. Efforts have been made to include
suggestions for:

           Use of manipulatives for classroom instruction.
           Applying technology to accomplish the goals of a standard.
           Integration of mathematics instruction with other curricular areas.
           Classroom assessments.

        The format of these materials is similar to Mathematics Standards of Learning Curriculum
Framework published by the Virginia Department of Education in 2002. Unit/Topic/Strand refers to the six
basic learning strands adopted by Virginia in support of the National Council of Teachers of Mathematics
Standards adopted in 1989. The strands are synonymous with the Blueprint Categories used for reporting
purposes on Standard of Learning tests grades 3 and 5. These strands/categories are:

           Number and Number Sense
           Computation and Estimation
           Measurement
           Geometry
           Probability and Statistics
           Patterns, Functions and Algebra

       Each objective has a recommended implementation schedule. Teacher notes and instructional
pedagogy that are implied in the objective are included along with Essential Understandings, and student
outcomes are listed under Essential Knowledge Skills. Notes for enrichment and extensions, particularly to
other curricular areas, are included under Essential Understandings. The cover page for each grade level is
a suggested teaching sequence for the standards. The standards are listed sequentially within the curriculum
document. The instructor is reminded that the standards are implemented with close attention given to
review or spiraling to former lessons. Math extensions are given by number (no SOL prefix).

         The implementation of mathematics standards does not rest entirely on the mathematics content
addressed at a grade level. Concepts become part of a student's knowledge when developed with the aid of
real life applications taken from other curricular areas. The use of technology and hence the implementation
of Computer/Technology Standards (C/T) enables access to and manipulation of data from all resources.

       Sample assessments are placed under Student Check for Understanding. Efforts have been made to
use multiple choice formats to support student practice for Standards of Learning tests. There are
suggestions for alternative assessments. Resources include reference to the student text and other classroom
resources that a teacher may have at their disposal.

        The intent of these materials is to provide a teacher guide for a basic mathematics course for each
grade in levels K-8. Suggestions for extending the mathematics or enriching the mathematics content are
directed to the teacher who has students that are prepared to do more advanced work. Extensions and
Connections were developed with the cooperation of the gifted program coordinator. Some of these
additions may provide an alternative challenge for students who have demonstrated mastery of the material.
Pretesting is recommended for assessing competence in a standard. Each standard must be addressed either
as a new topic or pretested to assure concept mastery required by the Standards of Learning.




                                                      3                                  Revised Summer 2006
STANDARD 8.1                                           STRAND: NUMBER AND NUMBER SENSE                                                          GRADE LEVEL 8

8.1          The student will
             a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of
                operations with real numbers;
             b) recognize, represent, compare, and order rational numbers expressed in scientific notation; and
             c) compare and order decimals, fractions, percents, and numbers written in scientific notation.

Time Allotted:           2 weeks
      UNDERSTANDING THE STANDARD                           ESSENTIAL UNDERSTANDINGS                            ESSENTIAL KNOWLEDGE AND SKILLS
                   (Teacher Notes)

  Expression is a word used to designate any            All students should                                The student will use problem solving, mathematical
   symbolic mathematical phrase that may contain                                                            communication, mathematical reasoning, connections, and
                                                          Understand that any real number can be           representations to
   numbers and/or variables. Expressions do not
                                                           shown on a number line.
   contain an equal sign.
                                                                                                             Simplify numerical expressions containing exponents
                                                          Understand that integers, positive and
  A numerical expression contains only numbers                                                               where the base is a rational number and the exponent is a
                                                           negative fractions, and positive and negative      positive whole number, using the order of operations and
   and the operations on those numbers.
                                                           decimals are rational numbers.                     properties of operations with real numbers.
  Expressions are simplified using the order of
                                                          Understand that an expression is like a phrase    Recognize, represent, compare, and order rational numbers
   operations and the properties for operations with
                                                           in that it has no equal sign.                      expressed in scientific notation, using both positive and
   real numbers, i.e., associative, commutative, and
   distributive properties.                               Understand that the order of operations            negative exponents.
                                                           describes the order to use to compute with        Compare and order fractions, decimals, percents, and
  The order of operations defines the order in which
                                                           rational numbers.                                  numbers written in scientific notation.
   operations are performed to simplify an
   expression.                                            Understand that numbers can be represented
                                                           as decimals, fractions, percents, and in
  The order of operations is as follows:
                                                           scientific notation.
    Complete all operations within grouping
       symbols. If there are grouping symbols             Understand and use strategies to simplify
       within other grouping symbols, do the               expressions and to compare and order
       innermost operation first.                          numbers.
    Evaluate all exponential expressions.
    Multiply and/or divide in order from left to
       right.
    Add and/or subtract in order from left to
       right.


 continued

                                                                                    4                                                                Revised Summer 2006
STANDARD 8.1 (continued)                                 STRAND: NUMBER AND NUMBER SENSE                GRADE LEVEL 8

  UNDERSTANDING THE STANDARD                                ESSENTIAL UNDERSTANDINGS   ESSENTIAL KNOWLEDGE AND SKILLS
                   (Teacher Notes)

 continued
  A power of a number represents repeated
   multiplication of the number. For example, (5)3
   means (5)  (5)  (5). The base is the number
   that is multiplied, and the exponent represents the
   number of times the base is used as a factor. In
   this example, (5) is the base, and 3 is the
   exponent.
  Scientific notation is used to represent very large
   or very small numbers.
  A number written in scientific notation is the
   product of two factors: a decimal greater than or
   equal to one but less than 10 multiplied by a
   power of 10 (e.g., 3.1  105 = 310,000 and 3.1 
   105 = 0.000031).
  Any real number raised to the zero power is 1.
   The only exception to this rule is zero itself.
  Scientific calculators, graphing calculators, and
   some four-function calculators follow the rules of
   order of operations.




                                                                         5                                 Revised Summer 2006
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