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III. Inequalities (4 Days) VII. Solving Quadratic ... · PDF fileSolving Quadratic Equations by Factoring ... Writing Linear Equations (6 Days) ... Intersection of two Sets Interval

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    Smithtown Central School District 8 Honors Integrated Algebra Curriculum

    August 2007

    I. Review of Real Number System (7 Days)

    II. Algebraic Expressions and Linear Equations (10 Days)

    III. Inequalities (4 Days)

    IV. Exponents and Monomials (9 Days)

    V. Polynomials (6 Days)

    VI. Factoring (7 Days)

    VII. Solving Quadratic Equations by Factoring (6 Days)

    VIII. Ratio, Proportion and Percent (11 Days)

    IX. Algebraic Fractions/Rational Expressions (8 Days)

    X. Plane and Solid Geometry (7 Days)

    XI. Transformational Geometry (Take Home Packet)

    XII. Functions (10 Days)

    XIII. Radicals (7 Days)

    XIV. Right Triangle Trigonometry (5 Days)

    XV. Graphing Linear Equations (7 Days)

    XVI. Writing Linear Equations (6 Days)

    XVII. Systems of Equations and Inequalities (8 Days)

    XVIII. Graphing Quadratic Equations (8 Days)

    XIX. Probability (9 Days)

    XX. Statistics (10 Days)

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    Math 8 Honors CurriculumMath 8 Honors CurriculumMath 8 Honors CurriculumMath 8 Honors Curriculum (Updated August 2007)

    I.I.I.I. Review of Real Number System (8Review of Real Number System (8Review of Real Number System (8Review of Real Number System (8 days) days) days) days) Technology: graphing calculator

    Number Sets (real, whole, integers, rationals, irrationals) Review of integer & rational number operations Properties (commutative, associative, distributive, identities,

    inverses and closure) A.N.1A.N.1A.N.1A.N.1 Order of operations (including integers, decimals, fractions) Evaluating expressions (including absolute value &

    exponents) A.N.6 A.N.6 A.N.6 A.N.6 Set Theory (no more than three sets)

    a. Elements of a Set A.A.29 A.A.29 A.A.29 A.A.29 Set Builder Notation

    Example Set Builder Notation: {x | x is a counting number}

    Interval Notation Example Interval Notation:

    [ )12,3 (-3 is included 12 is not) b. Kinds of Sets

    Finite, Infinite, Empty, Null c. Operations with Sets

    Complement of a given subset A.A.30 A.A.30 A.A.30 A.A.30 Intersection of sets A.A.31 A.A.31 A.A.31 A.A.31 Union of sets A.A.31 A.A.31 A.A.31 A.A.31

    Binary Operations and properties of real numbers

    Performance Indicators: A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields, but students should be engaged in the ideas.

    A.N.6 Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s) A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form A.A.30 Find the complement of a subset of a given set, within a given universe

    A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)

    Resources: Integrated Mathematics Course 1 Textbook; Chapters 1, 7, 19, 20-5 Algebra 1 Concepts and Skills Textbook; Chapters 2, 9, 12.6 Internet: www.regentsprep.org ; www.jmap.org ; http://illuminations.nctm.org ; www.unitedstreaming.com http://www.math.com/school/subject3/lessons/S3U3L4GL.html (explanation of right triangle terminology and practice problems) http://www.quia.com/pop/37541.html (rational & irrational numbers - practice identifying rational and irrational #s)

    Vocabulary

    Absolute Value

    Additive Inverse

    Associative

    Closure

    Binary Operations

    Commutative

    Complement

    Distributive

    Element

    Empty Set

    Equation

    Evaluate

    Expression

    Finite Sample Space

    Group

    Identities

    Infinite Sample Space

    Infinite Set

    Integers

    Intersection of two Sets

    Interval Notation

    Irrational

    Multiplicative Inverse

    Null Set

    Rational

    Real Numbers

    Reciprocals

    Set Builder Notation

    Solve

    Subset

    Symmetric

    Union

    Universal Set

    Universe

    Whole Numbers

    Zero Property

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    II.II.II.II. Algebraic ExpressionsAlgebraic ExpressionsAlgebraic ExpressionsAlgebraic Expressions and and and and Linear EquationsLinear EquationsLinear EquationsLinear Equations ((((10101010 days) days) days) days) Technology: Excel & graphing calculator

    Translating Phrases, Sentences A.A.3 A.A.3 A.A.3 A.A.3

    a. Verbal Phrase to Algebraic Expression A.A.1 A.A.1 A.A.1 A.A.1 b. Write a Verbal Phrase given an Algebraic Expression A.A.2 A.A.2 A.A.2 A.A.2 c. Verbal Sentence to Algebraic Equation A.A.4 A.A.4 A.A.4 A.A.4

    Solving Linear Equations A.A.21 & A.A.22 & A.A.25 A.A.21 & A.A.22 & A.A.25 A.A.21 & A.A.22 & A.A.25 A.A.21 & A.A.22 & A.A.25 a. Check whether a given number is a solution to an equation or inequality b. Two step equations c. Variables on both sides d. Combining like terms e. Parenthesis (Distributive Property) f. Fractions/Decimals including coefficients g. Fractional equations by clearing the denominator

    Word Problems A.A.5 A.A.5 A.A.5 A.A.5 & A.A.6A.A.6A.A.6A.A.6 a. Larger/Smaller Numbers b. Consecutive Integers

    Include even and odd consecutive integers c. Perimeter Problems d. Angles of a Triangle

    Literal Equations A.A.23 A.A.23 A.A.23 A.A.23 a. Including Formulas: Area, Perimeter, Circumference, Volume, CelsiusFahrenheit, etc.

    Vocabulary

    Coefficient

    Consecutive

    Constant

    Decrease

    Difference

    Equation

    Evaluate

    Expression

    Increase

    Inverse operation

    Like terms

    Literal Equation

    Phrase

    Product

    Quantity

    Quotient

    Sentence

    Simplify

    Solve

    Statement

    Sum

    Translate

    Twice

    Variables

    Performance Indicators: A.N.6 Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s) A.A.1 Translate a quantitative verbal phrase into an algebraic expression A.A.2 Write a verbal expression that matches a given mathematical expression A.A.3 Distinguish the difference between an algebraic expression and an algebraic equation A.A.4 Translate verbal sentences into mathematical equations or inequalities A.A.5 Write algebraic equations or inequalities that represent a situation A.A.21Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable A.A.22 Solve all types of linear equations in one variable A.A.23 Solve literal equations for a given variable

    A.A.25 Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable.

    Resources: Integrated Mathematics Course 1 Textbook; Chapter 3-1, 3-2, 3-4, 3-5, 4, 10 Algebra 1 Concepts and Skills Textbook; Chapters 1.5, 3, Internet: www.regentsprep.org ; www.jmap.org ; http://illuminations.nctm.org ; www.unitedstreaming.com http://www.math.com/school/subject2/lessons/S2U1L3GL.html (words to math - explanation and interactive problems) ; http://www.mathgoodies.com/lessons/vol7/equations.html (equations) www.quia.com/cb/62631.html (Algebra Jeopardy)

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    III. III. III. III. InequalitiesInequalitiesInequalitiesInequalities (4 d (4 d (4 d (4 days)ays)ays)ays)

    Linear Inequalities a. Translating verbal sentences into inequalities A.A.4A.A.4A.A.4A.A.4 b. Write algebraic inequalities that represent a situation A.A.5A.A.5A.A.5A.A.5 c. Determine if a given value is a solution

    to an inequality A.A.21A.A.21A.A.21A.A.21 d. Solve Linear Inequalities in one variable A.A.24 A.A.24 A.A.24 A.A.24 e. Graph solution on a number line A.G.6A.G.6A.G.6A.G.6 f. Word Problems A.A.6A.A.6A.A.6A.A.6

    Compound Inequalities a. Translate verbal sentences into compound inequalities b. Write compound inequalities that represent a situation

    Graphing using Interval Notation Example Interval Notation:

    [ )12,3 means -3 x < 12 Graphing using Set Builder Notation

    Example Set Builder Notation: {x | -3 x < 12}

    Performance Indicators: A.A.4 Translate verbal sentences into mathematical equations or inequalities A.A.5 Write algebraic equations or inequalities that represent a situation A.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable A.A.21Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable A.A.24 Solve linear inequalities in one variable A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form

    A.G.6 Graph linear inequalities

    Resources: Integrated Mathematics Course 1 Textbook; Chapters 10-10, 18-5 Algebra 1 Concepts and Skills Textbook; Chapters 6.1, 6.2, 6.3, 6.4, 6.8, 7.6 Technology: Graphing Calculator Internet: www.regentsprep.org ; www.jmap.org ; http://illuminations.nctm.org ; www.unitedstreaming.com

    Vocabulary < less than

    < less than or equal to

    > greater than

    > greater than or equal to

    At least

    At most

    Closed Circle

    Compound Inequality

    Exceeds

    Inequality Symbols

    Interval Notation

    Linear Inequality

    Maximum of

    Minimum of

    Open Circle

    Set Builder Notation

    Solution Set

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