BOCES Curriculum Outline for Integrated Algebra

PNWBOCES Curriculum Outline for Integrated Algebra

May 18, June 21, July 5-6, 2006

Time frame includes instructional days, review, and tests

Real Number SystemTime Frame: 6 days

Content Indicators:

A.N.1Identify 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. Students will understand meanings of operations and procedures, and how they relate to one another.

A.A.29Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form

A.A.30Find the complement of a subset of a given set, within a given universe

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

Process Indicators:

A.PS.1Use a variety of problem solving strategies to understand new mathematical content

A.PS.4Use multiple representations to represent and explain problem situations (e.g., verbally, numerically, algebraically, graphically) Students will apply and adapt a variety of appropriate strategies to solve problems.

A.PS.5Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic)

A.PS.10Evaluate the relative efficiency of different representations and solution methods of a problem

A.CM.12Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale

A.CN.8 Develop an appreciation for the historical development of mathematics

A.CM.3Present organized mathematical ideas with the use of appropriate standard notations, including the use of symbols and other representations when sharing an idea in verbal and written form.

Vocabulary:

Closure Property
Associative Property
Commutative Property
Distributive Property
Identity Property
Inverse property
Equivalent
Number Theory / Real Numbers
Irrational Numbers
Rational Numbers
Natural Numbers (Counting)
Integer
Field
Group
Connection / Subset
Set
Set Builder Notation
Universal Set
Element
Finite Sample Space
Union of sets
Venn Diagram
Complement of a subset / Denominator
Numerator
Fraction
Radical
Multiple Representations
Simplest Form Decimal
Absolute Value
Procedure

Resources:

Textbook / Performance Indicator(s) / Section # or Page #

Amsco: Integrated Algebra I

/ A.A.29, A.A.30, A.A.31 / 2-7
A.N.1 / 2-2
McDougal Littell: Algebra I
ISBN: 978-061859402-3 / A.A.29, A.A.30, A.A.31 / p.71-72
A.N.1 / p.73-79 (question #’s 53-56), 89-93, 96-101, 103-108, 120, 123, 189(#’s40-43), 939 (#’s38-45)

Glencoe: Algebra – NY Version

ISBN: 0-07-8733162 / A.A.29 / 6-1
A.A.30 / 14-3
A.A.31 / 6-3
A.N.1 / 1-4, 1-5, 1-6
A.RP.11 / p. 70, 775
A.PS.4 / p. 43-49

Algebraic Expressions, Equations and Inequalities14 days

Content Indicators:

A.A.1Translate a quantitative verbal phrase into an algebraic expression

A.A.2Write a verbal expression that matches a given mathematical expression

A.N.6 Evaluate expressions involving absolute value(s), and exponential expression(s)

A.A.3 Distinguish the difference between an algebraic expression and an algebraic equation

A.A.4Translate verbal sentences into mathematical equations or inequalities

A.A.5 Write algebraic equations or inequalities that represent a situation

A.A.22Solve all types of linear equations in one variable

A.A.24Solve linear inequalities in one variable

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.25Solve equations involving fractional expressions Note: Expressions which result in linear equations 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.23Solve literal equations for a given variable

Process Indicators:

A.CM.8 Reflect on strategies of others in relation to one’s own strategy

A.CM.10 Use correct mathematical language in developing mathematical questions that elicit, extend, or challenge other students’ conjectures

A.CM.11Represent word problems using standard mathematical notation

A.CN.1 Understand and make connections among multiple representations of the same mathematical idea

A.R.4Select appropriate representations to solve problem situations

A.R.5Investigate relationships between different representations and their impact on a given problem

Vocabulary:

Equation
Evaluate
Formula
Expression
Variable
Symbol
Inequality / Interpretations
Communicate
Organize
Translate
Analyze
Formulate
Strategy
Explain
Systematic Approach
Communicate
Comprehension
Conclusion
Conjecture
Decoding
Standard mathematical Notation
Technical Writing
Numerically
Verbally / Algebraic Problem
Arithmetic Operations
Algebraic Expression
Algebraic Equation
Coefficient
Linear Equation in one variable
Solution Set
Linear Inequality in one variable
Literal equation
Verbal ExpressionAlgebraically
Verbal Sentence
Satisfies the equation
Means
Extremes / Diagram
Profit
Discount
Percent of increase/decrease
Product
Proportion
Quotient
Ratio
Sum

Resources:

Textbook / Performance Indicator(s) / Section # or Page #
Educational Design: New York Math A – Semesters 1 and 2 / A.A.1 / Chapter 4, Section 5, p. 178 18
A.A.4 / Chapter 4, Section 6, p. 183-187
A.N.6 / p. 52, Lakeland packet of handouts
A.A.22 / Chapter 4, Section 2-4, 7-8, p. 162-177, 189-199
A.A.25 / Section 9, p. 200-205, Lakeland packet of handouts
A.A.6 / Chapter 5, Section 1-7, p. 213-263
Chapter 6, Section 4, p. 290-293
Lakeland packet of handouts
A.A.23 / Chapter 5, Section 8, p. 264-267
Lakeland packet of handouts
Glencoe/McGraw Hill (Merrill): Integrated Mathematics Course 1 / A.A.1 / p. 71-77
A.A.2 / p. 71-77
A.N.6 / p. 41-49
A.A.3 / p. 74-79
A.A.4 / p. 78-79, p. 113-115
A.A.5 / p. 88-89
A.A.22 / p. 88-89, p. 94-101
A.A.24 / p. 116-120
A.A.6 / p. 94-101, p. 123-124
A.A.25 / p. 82
A.A.21 / p. 82 46-51
A.A.23 / p. 110-112
Glencoe: Algebra 1 – NY State / A.A.2 / p. 8-9 11-18, 31-42
A.A.3 / p. 16-17
A.A.4 / p. 124 13-20
A.N.6 / p.71 (34-56 all)
A.A.25 / p. 146 (26 – 39) all
A.A.6 / p. 139 ( 39-50) all
p. 146-147 (48 -54) all
A.A.23 / p. 16-19 (1-25) all
A.A.5 / p. 124-125 (21, 22,45 -51 all)
A.A.21 / p. 16-19 (1-25) all
A.A.24 / Chapter 6 Sections 6.1 – 6.3
p. 318 - 337
A.CM.11 / Section 3.2, p. 131-132; Section 3.4, p. 142-148; Section 3.5 p. 153-154
McDougal Littell – Algebra 1 / A.CM.8 / Section 3.5, p. 160-162
A.CM.11
A.R.5

Operations with Polynomials9 days

Content Indicators:

A.A.13Add, subtract, and multiply monomials and polynomials

A.A.12Multiply and divide monomial expressions with a common base, using the properties of exponents Note: Use integral exponents only

A.A.14Divide a polynomial by a monomial or binomial, where the quotient has no remainder

A.N.4Understand and use scientific notation to compute products and quotients of numbers

Process Indicators:

A.CM.4 Explain relationships among different representations of a problem

Vocabulary:

Coefficient

Integral Coefficient

Integral Exponent
Lead Coefficient
Exponential Expression / Monomial
Binomial
Trinomial
Polynomial / Exponent
Properties of Exponents
Common Base
Scientific notation

Resources:

Textbook / Performance Indicator(s) / Section # or Page #
Amsco: Mathematics A (2002) / A.A.12, A.A.13, A.A.14, A.N.4 / p. 235-268
Amsco: Integrated Mathematics Course 1 (3rd ed) / A.N.4 / p. 292-296
A.A.12 / p. 297-299
A.A.13 / p. 266-286
A.A.14 / p. 299-301
Glencoe/McGraw Hill: Integrated Mathematics Course 1 (1995) / A.A.1 / p. 71-77
A.A.2 / p. 71-77
A.N.6 / p. 41-49
A.A.3 / p. 74-79
A.A.4 / p. 78-79, p. 113-115
A.A.5 / p. 88-89
A.A.22 / p. 88-89, p. 94-101
A.A.24 / p. 116-120
A.A.6 / p. 94-101, p. 123-124
A.A.25 / p. 82
A.A.21 / p. 82 46-51
A.A.23 / p. 110-112
Educational Design: Mathematics A Semester 1 and 2 / A.CM.4 / Section 3.1 p. 108; 3.2 p. 113; 3.4 p. 126; 3.5 p. 132; 3.6 p. 139; 3.7 p. 140-146; Review 1-3 p. 151-152
Section 10.3 p. 504-505, 510; 10.4 p. 513
A.A.13 / Section 3.1, pp. 104-108
Section 3.2, pp. 109-113
Section 3.6, pp. 133-137
Section 3.7, pp. 142-146
Section 10.3, pp. 506 – 510
Section 10.4 pp. 511-518
Section 10.5, pp. 515-518
A.A.12 / Section 3.1, p. 104-108
Section 3.2, pp. 109-113
Section 3.3, pp. 114-119
Section 3.4, pp. 12—126
Section 3.7, pp. 142-146
A.A.14 / Section 3.8, pp. 147-150
A.N.4 / Section 3.5, pp. 127-132
Glencoe: Algebra - NY State
ISBN -0-07-873316-2 / A.A.13 / Chapter 1, Section 8.4, p. 406-424,
p.432-471
A.A.12 / Chapter 1, Section 8.4, p. 406-424
A.A.14 / Chapter 1, Section 8.4, p. 666-671
A.N.4 / Chapter 1, Section 8.4, p. 425-430
Amsco: Integrated Mathematics Course 1 (2nd ed) / A.A.13 / Chapter 8, Section 8.1 to 8.4, p. 232 -242
Chapter 9, Section 9-1 to 9-5, p. 256-270
A.A.12 / Chapter 8, Section 8-5, p. 243-244
Section 8-6, p. 244-246
Section 8-7 p. 246 - 248
A.A.14 / Chapter 9, Section 9-6, 9-7,
p. 270-274
A.N.4 / Chapter 8, Section 8-8, p. 249-251
Section 8-9, p. 251 -253

Factoring and Quadratics9 days

Content Indicators:

A.A.19Identify and factor the difference of two perfect squares

A.A.20Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)

A.A.27Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots

A.A.28Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression

A.A.8Analyze and solve verbal problems that involve quadratic equations

Process Indicators:

A.PS.1 Use a variety of problem solving strategies to understand new mathematical content

A.PS.4 Use multiple representations to represent and explain problem situations (e.g., verbally, numerically, algebraically, graphically)

A.PS.5 Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic)

A.PS.10Evaluate the relative efficiency of different representations and solution methods of a problem

A.CM.12Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale

A.CN.8Develop an appreciation for the historical development of mathematics

Vocabulary:

Factoring
Greatest Common Factor
Difference of two perfect squares / Integral Roots
Roots of an equation
Quadratic Equation
Solution set(s)
Zeroes of a function

Resources:

Textbook / Performance Indicator(s) / Section # or Page #
Glencoe/McGraw Hill: Algebra 1 – New York Math A Edition / A.A.19 / Chapter 10 – Section 4 (pages 581-586)
A.A.20 / Chapter 10 – Section 3 (pages 574-580)
A.A.27 / Chapter 10 – Section 6 (pages 594-600)
A.A.8 / Chapter 10 – Section 6 (pages 594-600)
Glencoe/McGraw Hill: Algebra 1 – New York Math A Edition – Study Guide Masters / A.A.19 / 10-4 (page 72)
A.A.20 / 10-3 (page 71)
A.A.27 / 10-6 (page 74)
A.A.8 / 10-6 (page 74)
Glencoe/McGraw Hill: Algebra 1 – New York Math A Edition – Practice Masters / A.A.19 / 10-4 (page 72)
A.A.20 / 10-3 (page 71)
A.A.27 / 10-6 (page 74)

Amsco: Preparing for the Regents Examination – Mathematics A (2002)

ISBN 1-56765-535-1 / A.A.19 / Chapter 4 (pages 114-115)
A.A.20 / Chapter 4 (pages 119-120)
A.A.27 / Chapter 4 (pages 123-137)
A.A.28 / Chapter 4 (pages 124-130)
A.A.8 / Chapter 4 (pages 140-145)
Educational Design: NYS Math A Regents Coach
ISBN 0-87694-843-3 / A.A.19 / Lesson 9 (pages 31- 35)
A.A.20 / Lesson 9 (pages 31- 35)
A.A.27 / Lesson 18 (pages 69-73)
A.A.8 / Lesson 18 (pages 69-73)
WestSea Publishing Co. Inc.: Regents High School Mathematics A
ISBN 0-937820-85-7 / A.A.19 / Unit 3 – Operations (page 42)
A.A.20 / Unit 3 – Operations (page 43)
A.A.27 / Unit 7 – Patterns/Functions (page 247-255)
A.A.8 / Unit 7 – Patterns/Functions (page 256-259)
Algebra PowerPoint: Teaching Made Easy as Pi – Written and Published by James Wenk / A.A.19 / Lesson 10-3a (slides 1-7)
A.A.20 / Lesson 10-5 (slides 1-8)
A.A.27 / Lesson 10-4 (slides 1-5)
Website – (Regents Prep) / A.A.19 /
`
A.A.27 /

McDougal Littell: Algebra 1 / A.A.19 / Section 10.7, p. 619-624
A.A.20 / Section 10.8, p. 625-632
A.A.27 / Section 10.4, p. 597-602
A.A.28 / Sections 10.5, 10.6, 10.7, 10.8 p. 604-631
A.A.8 / Sections 10.5, 10.6, 10.7, 10.8 p. 604-631
A.PS.10 / Sections 9.1 p. 505, 603, 610, 618
A.PS.5 / p. 573

Amsco: Integrated Algebra Course 1 (2nd ed)

/ A.A.19 / Chapter 13, Section 5, p. 418-420
A.A.20 / Chapter 13, Section 7, p. 423-428
A.A.27 / Chapter 20, Section 2, p. 681-685
A.A.28 / Chapter 20, Section 7, p. 702-704
A.A.8 / Chapter 20, Section 3, p. 685-688

Amsco: Integrated Algebra Course 1 (3rd ed)

/ A.A.19 / Section 18-5, p. 632-634
A.A.20 / Section 18-8, p. 641-644
A.A.27 / Section 21-2, p. 705-710
A.A.28 / Section 21-2, p. 705-710
A.A.8 / Section 21-6, p. 723-726

Educational Design: Mathematics A Semesters 1 and 2

/ A.PS.1 / p. 504-505

Internet Resources:

Rational Expressions and Equations10 days

Content Indicators:

A.A.15Find values of a variable for which an algebraic fraction is undefined

A.A.16Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms

A.A.18Multiply and divide algebraic fractions and express the product or quotient in simplest form

A.A.17Add or subtract fractional expressions with monomial or like binomial denominators

A.A.26Solve algebraic proportions in one variable which result in linear or quadratic equations

A.N.5Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation

Process Indicators:

A.CM.1Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem

A.CM.5Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid

Vocabulary:

Fractional Expression
Proportionality/direct variation / Lowest terms fraction
Undefined
Appropriate Unit
Conversion
error

Resources:

Textbook / Performance Indicator(s) / Section # or Page #
Merrill: Integrated Math Course III (Bumby, Klutch) / A.A.15 / p.21
A.A.16 / p.26-28
A.A.18 / p.26-28
A.A.17 / p. 30-32
A.A.26 / p.25
A.N.5 / p.40-43
Amsco: Integrated Math (3rd edition) (Dressler) Course I / A.A.15 / p.646
Glencoe: Algebra I, ISBN: 0-07-865113-1 c2005 / A.A.15 / Textbook p. 648-651
Handouts:
Study guide p. 711, 712
Skill practice p. 714
Reading to learn p. 715
A.A.16 / Textbook p. 648-651
Handouts:
Study guide p. 711, 712
Skill practice p. 714
Reading to learn p. 715
A.A.18 / Textbook p. 655-671
Handouts:
Study guide p. 717, 718, 723,
724, 729, 730
Skill practice p. 719, 720, 725, 726, 731, 732
Reading to learn p. 721, 727, 733
A.A.17 / Textbook p. 672-683
Handouts:
Study guide p. 735, 736, 741, 742
Skill practice p. 737, 738, 743, 744
Reading to learn p. 739, 745
A.A.26 / Textbook p. 684-689
Handouts:
Study guide p. 747, 748
Skill practice p. 749, 750
Reading to learn p. 757
A.N.5 / Textbook p. 690-695
Handouts:
Study guide p. 753, 754
Skill practice p. 755, 756
Reading to learn p. 757
A.CM.1/A.CM.2 / p. 653 56, 57; p. 664 45; p. 671 43; p. 676
50; p. 683 59; p. 688 43
Amsco: Integrated Mathematics Course I / A.A.16 / p.647-650
A.A.18 / p.650-655
A.A.17 / p. 655-657
A.A.26 / p.420-423
A.N.5 / p. 666-667
Merrill: Integrated Mathematics Course I / A.A.26 / p. 179-186
A.N.5 / p. 181, 185-186
Amsco: Mathematics A / A.A.39 / p. 589
A.A.33 / p. 601
A.A.37 / p. 608
Educational Design: Math A Semester 3 / A.A.38 / p. 381

Internet Resources:

Radical Expressions6 days

Content Indicators:

A.N.2Simplify radical terms (no variable in the radicand)

A.N.3 Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form

Process Indicators:

A.RP.10 Extend specific results to more general cases

Vocabulary:

Radical / Radicand / Like/Unlike radical terms

Resources:

Textbook / Performance Indicator(s) / Section # or Page #
McDougal Littell: Algebra 1 / A.N.2 / Chapter 9 Section 2, p. 511-516
A.N.3 / Chapter 12 Section 2, p. 716-721
Amsco: Integrated Mathematics Course 1 (2nd ed) / A.N.2 / Chapter 19, Section 4, p. 647-651
A.N.3 / Chapter 19, Section 10, 11, 12, p. 660-666
Amsco: Integrated Mathematics Course 1 (3rd ed) / A.N.2 / Chapter 20 Section 4, p. 691-693
A.N.3 / Chapter 20 Section 5, p. 693-696
Chapter 20 Section 6, p. 696-698
Chapter 20 Section 7, p. 698-700

Internet Resources:

Coordinate Plane and Graphical Analysis20 days

Content Indicators:

A.G.4Identify and graph linear, {quadratic (parabolic), absolute value, and exponential functions}

A.A.39Determine whether a given point is on a line, given the equation of the line

A.A.32Explain slope as a rate of change between dependent and independent variables

A.A.33Determine the slope of a line, given the coordinates of two points on the line

A.M.1Calculate rates using appropriate units (e.g., rate of a space shipversus the rate of a snail)

A.A.34Write the equation of a line, given its slope and the coordinates of a point on the line

A.A.35Write the equation of a line, given the coordinates of two points on the line

A.A.36Write the equation of a line parallel to the x- or y-axis

A.A.37Determine the slope of a line, given its equation in any form

A.A.38Determine if two lines are parallel, given their equations in any form

A.G.4Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions

A.G.10Determine the vertex and axis of symmetry of a parabola, given its graph (See A.A.41) Note: The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value.

A.A.41Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10)

A.G.8Find the roots of a parabolic function graphically Note: Only quadraticequations with integral solutions

A.G.4Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions

A.G.3Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations

A.G.5Investigate and generalize how changing the coefficients of a function affects its graph

Process Indicators:

A.PS.6Use a variety of strategies to extend solution methods to other problems

A.PS.7Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving

A.PS.9 Interpret solutions within the given constraints of a problem

A.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, and objects created using technology as representations of mathematical concepts

A.R.8 Use mathematics to show and understand mathematical phenomena (e.g.,compare the graphs of the functions represented by the equations and )

Vocabulary:

Chart
Graph
Table / Function
Absolute Value Function
Parabolic Function
Quadratic Function / Technology
Constraint
Graphically
Parameter
Pattern
Refute
Mathematical Visual
Relation
x-intercept
y-intercept / Axis of symmetry
Coordinates
Line parallel to axes
Parabola
Parallel
Slope
Vertex
x-axis
y-axis
Ordered Pair
Roots of a Parabolic Function
Roots of a Quadratic Function
Zeros of a function
Solution Set

Resources:

Textbook / Performance Indicator(s) / Section # or Page #
Glencoe: Algebra 1 / A.A.32 / p. 258 ex. 6 (Rate of change)
A.M.1 / p. 261 39, 40, 53-55 (Rate of change)
A.A.33 / p. 260 15-34 (slope given 2 points)
A.A.34/A.A.35 / p. 284 11-33 (Writing Equations of Lines)
p. 289 15-26 (Writing Equations of Lines)
p. 290 53,54 (Writing Equations of Lines)
A.A.36 / p. 290 27, 28 (Equations parallel to axes)
A.G.3 / p. 229 4-9, 17-24 (Determine if a function)
p. 230 29-31 (Determine if a function)
A.G.4 / p. 559 27-32
A.G.5 / p. 531-532 (graphing calculator investigation)
A.G.8 / p. 536 11-16, 21-32 (Find roots graphically)
A.G.10/A.A.41 / p. 528 18-29 (Determine vertex and A.O.S. given graph/equation)
A.R.1 / p. 260-262 35, 36, 50-57, 61
A.R.8 / p. 278-279, p. 531-532

Glencoe: Geometry

/ A.A.36 / p. 143 28, 31 (Equations parallel to axes)
p. 148 36, 38, 41 (Equations parallel to axes)
Amsco: Mathematics A / A.G.3 / p. 779 1-11 (Determine if a function)
p. 780 15-2211 (Determine if a function)
A.G.10/A.A.41 / p. 785-787 17-29, 33, 35-38 (Determine vertex and A.O.S. given graph/equation)
Addison Wesley: Intermediate Algebra / A.A.32/A.M.1 / p. 101-102 53-67 (Rate of change)
A.G.4 / p. 567 1-28 (Graphing Exponential Functions)
Merrill Integrated Mathematics Course 2 / A.G.8 / p. 380 5-30 (Find roots graphically)
A.G.10/A.A.41 / p. 376 8-27 (Determine vertex and A.O.S. given graph/equation)
Handout / A.G.5

Systems of Equations and Inequalities 15 days

Content Indicators:

A.G.6Graph linear inequalities

A.G.7Graph and solve systems of linear equations and inequalities with rational coefficients in two variables (See A.A.10)

A.A.40 Determine whether a given point is in the solution set of a system of linear inequalities

A.A.10Solve systems of two linear equations in two variables algebraically (See A.G.7)

A.A.7Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables

A.G.9Solve systems of linear and quadratic equations graphically Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers.

A.A.11Solve a system of one linear and one quadratic equation in two variables, where only factoring is required Note: The quadratic equation should represent a parabola and the solution(s) should be integers.

Process Indicators:

A.PS.7 Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving

A.CN.2 Understand the corresponding procedures for similar problems or mathematical concepts

Vocabulary:

Counter Example
Solution Set / System of Linear Equations
Systems of Linear Inequalities / Quadratic-Linear System of Equations

References:

Textbook / Performance Indicator(s) / Section # or Page #
Glencoe: Algebra 1 / A.G.6 / p. 355-357 (graphing inequalities)
A.G.7 / p. 372 15-40 (graphing systems)
p. 375 1-10 (Graphing Calculator)
p. 397 12-28 (Graphing systems)
A.A.10 / p. 379 11-28 (Substitution)
p. 385 12-29 (Elimination)
A.G.9 / p. 553 1-6 (Graphing Calculator)
A.A.7 / p. 373 44-54 (Word Problems Systems)
p. 380 30, 31, 33, 34, 35, 36, 37
p. 385 30-36 (Word Problems Systems)
A.PS.7 / p. 391 27-38
Amsco: Mathematics A / A.G.6 / p. 640 (graphing inequalities)
A.A.10 / p. 656 1-20 (substitution)
p. 654 3-47 (Elimination)
p. 657 21-36 (either method)
A.G.9 / p. 793 3-27 (Quadratic-Linear systems graphically)
A.A.11 / p. 798 7-27, 37, 38
(Quadratic-Linear systems algebraically)
A.A.7 / p. 660-661 1-29 (Word Problems systems)
McDougal Littell: Algebra 1 / A.A.40 / p. 432-435
A.PS.7 / p. 421-422 10-45

Exponential Equations and Graphs5 days

Content Indicators:

A.A.9 Analyze and solve verbal problems that involve exponential growth and decay

Process Indicators:

A.RP.3 Recognize when an approximation is more appropriate than an exact answer

Vocabulary:

Conjecture
Constraint
Analyze / Quantitative Model
Exponential Growth and Decay / Exponential Function

References:

Textbook / Performance Indicator(s) / Section # or Page #
Glencoe: Algebra 1 / A.A.9 / Chapter 10, Section 5, 6
McDougal Littell: Algebra 1 (2007) / A.A.9 / Chapter 8, Section 5, 6
Holt, Rinehart, and Winston / A.A.9 / Chapter 6, p. 354-360
Prentice Hall Mathematics / A.A.9 / Chapter 8, p. 430-438

Right Triangle7 days

Content Indicators:

A.A.45Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides

A.A.42Find the sine, cosine, and tangent ratios of an angle of a righttriangle, given the lengths of the sides

A.A.44Find the measure of a side of a right triangle, given an acute angle and the length of another side

A.A.43Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle

Process Indicators:

A.R.6Use mathematics to show and understand physical phenomena (e.g., find the height of a building if a ladder of a given length forms a given angle of elevation with the ground)

A.CM.6 Support or reject arguments or questions raised by others about the correctness of mathematical work

Vocabulary:

Proof
Refute / Angle of elevation
Angle of depression / Angle
Acute Angle
Adjacent side/angles
Triangle / Right Angle
Right triangle
Hypotenuse
Legs of a right triangle
Trigonometry
Opposite side/angle
Pythagorean theorem
Cosine
Sine
Tangent

Resources:

Textbook / Performance Indicator(s) / Section # or Page #
Key Curriculum Press: Interactive Mathematics Program, Year 1
ISBN 1-55953-250-5 / A.A.42 / p.464-471
Key Curriculum Press: Interactive Mathematics Program, Year 2
ISBN 1-55953-263-7 / A.A.45 / p.226-233,p.283-286
A.A.42 / p.219-221
Merrill: Integrated Mathematics Course I / A.A.45 / p. 230-232
Merrill: Integrated Mathematics Course II / A.A.42 / p.501-502, 511-512
A.A.44 / p.507-510,p.514-515
A.A.43 / p. 507-510, p.514-515
Amsco: Course I / A.A.45 / p.717-722
Glencoe: Algebra
ISBN 0-07-873316-2 / A.R.6 / p. 609 41-47; p. 629 61, 62; p. 630 63-65

Area and Volume9 days

Content Indicators:

A.M.2Solve problems involving conversions within measurement systems, given the relationship between the units

A.G.1Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Note: Figures may include triangles, rectangles, squares, parallelograms, rhombi, trapezoids, circles, semi-circles, quarter-circles, and regular polygons (perimeter only).

A.G.2Use formulas to calculate volume and surface area of rectangular solids and cylinders

A.M.3Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure

Process Indicators:

A.RP.4Develop, verify, and explain an argument, using appropriate mathematical ideas and language