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 2006Download Link: