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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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