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

• View
220

3

Embed Size (px)

### Text of III. Inequalities (4 Days) VII. Solving Quadratic ... · PDF fileSolving Quadratic Equations...

• + 1

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)

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)

• 2

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

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

• 3

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)

• 4

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

• 5  