Oroville Union High School District
Mathematics Curriculum

Mathematics - Algebra I

Algebra I

COURSE TITLE: Algebra I

LENGTH OF COURSE:    One Year

TYPE OF CREDIT: Mathematics (10 Credits)
    
GRADE LEVEL:    9-12

PREREQUISITES:

Grade of C or better in Pre-Algebra level, and/or teacher recommendation

TEXTBOOKS:

Math 1 (Algebra 1) Second Edition Version 6.0, CPM Educational Program, 2000:
Math 1 Vol. 1 Units 0-6, ISBN 1-885145-76-4 M1-764
Math 1 Vol. 2 Units 7-13, ISBN 1-885145-67-5 M1-675

Algebra 1: Applications and Connections, California Edition, Glencoe/McGraw-Hill, 2002, ISBN 0-07-824774-8

SUPPLEMENTARY INSTRUCTIONAL MATERIALS:

PLATO, PLATO Learning Inc., 2000, and updates.

Math 1 (Algebra 1) Parent Guide with Review 2nd. ed., CPM Educational Program, 2001, ISBN 1-885145-88-8

Mathematics: Applications and Connections, Course 1, California Edition, Glencoe/McGraw-Hill, 2002, ISBN 0-07-824784-5.

Mathematics: Applications and Connections, Course 2, California Edition, Glencoe/McGraw-Hill, 2002, ISBN 0-07-824788-8

Mathematics: Applications and Connections, Course 3, California Edition, Glencoe/McGraw-Hill, 2002, ISBN 0-07-824768-3

Number Power 1: Addition, Subtraction, Multiplication, and Division, Contemporary Books, 2000, ISBN 0-8092-2380-5

Number Power 2: Fractions, Decimals, and Percents, Contemporary Books, 2000, ISBN 0-8092-2377-5

Number Power 3: Algebra, Contemporary Books, 2000, ISBN 0-8092-2388-0

Number Power 4: Geometry, Contemporary Books, 2000, ISBN 0-8092-2382-1

Number Power 5: Graphs, Charts, Schedules, and Maps, Contemporary Books, 2000, ISBN 0-8092-2381-3

Number Power 6: Word Problems, Contemporary Books, 2000, ISBN 0-8092-2378-3

Number Power 7: Problem-Solving and Test-Taking Strategies, Contemporary Books, 2000, ISBN 0-8092-2386-4

Number Power 8: Analyzing Data, Contemporary Books, 2000, ISBN 0-8092-2384-8

Number Power 9: Measurement, Contemporary Books, 2000, ISBN 0-8092-9891-0

Number Power: Calculator Power, Contemporary Books, 2000, ISBN 0-8092-2385-6

Number Power: Pre-Algebra, Contemporary Books, 2000, ISBN 0-8092-2387-2

Number Power: Number Power Review, Contemporary Books, 2000, ISBN 0-8092-2379-1


COURSE DESCRIPTION:

Algebra I is a course that will meet the district's algebra graduation requirement and prepares students for the California High School Exit Exam. Students should have a solid background in the basic skills of arithmetic including fractions, integers, and equation-solving. Areas of emphasis include the study of rational numbers, factoring, polynomials, ordered pairs and graphing, radicals, and quadratic equations.

In the CPM approach to algebra I, students explore and develop the ideas in each unit by completing the guided investigations (recommended in-class problems), much like lab experiments in a science class. The majority (but not all) of class time is spent working the guided problems with a partner or as part of a study team of four students. Solutions to the previous day's problem set are provided to the study teams so that the students may check their work and have examples available. Teachers circulate among the study teams, listening to student conversations and observing student work so that they know when and how to intervene. Direct teaching or whole class discussion is used to summarize, help connect ideas, clarify confusion or ambiguities in a question, and refocus or redirect students when a substantial portion of the class needs such assistance. Students are responsible to be active participants in their learning by keeping an organized notebook, reviewing homework, writing unit summaries and creating personal course tool kits.

BOARD ADOP TION DATE: June 20, 2001.


Algebra I Content Standards
Symbolic reasoning and calculations with symbols are central in algebra. In the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem solving situations.

    Arithmetic Properties of Numbers
The learner will be able to identify and use the arithmetic properties of subsets of integers, rational, irrational and real numbers. This includes closure properties for the four basic arithmetic operations where applicable.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 1.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Unit 0: diamond problems (GS-3 thru Unit 8); Unit 1: integer operations (SQ-8 & SQ-28, esp. SQ-18 & SQ-39), Unit 2: Substitution (KF-30 ff.), Distributive Property (KF-53-84 ff.), order of operations (KF-93 ff,); Unit 11: CM-119 ff. in units 12 and 13. Teacher notes: Properties and operations developed using algebra files and used in context. Teacher notes are important to understand the purpose of some roblems.
  
    Properties of Numbers: True or False
The learner will be able to use properties of numbers to demonstrate whether assertions are true or false.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 1.1.
Instructional Resources
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-6, 1-7A, 1-7, 1-8, 2-3, 2-4, 2-5, 2-6, 2-7, 3-1, 3-2, 3-3, 3-5, 3-6, 7-2.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Adding and Subtracting Integers (additive inverse); Beginning Algebra: Integer Sum (additive inverse), Monomial Sum and Difference (distributive, additive inverse), Binomial Sum and Difference (additive inverse), Polynomial Product (distributive over addition), Factoring II (distributive over subtraction).
  
    Rules of Exponents
The learner will be able to understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 2.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 1: operations with integers (SQ as above); Unit 2, irrational numbers, roots (KF-103 thru 111); Unit 3, non-linear functions (BC-64 thru 71, 87); Unit 4: common term factoring (CP-51 ff.), solving equations as an inverse operation (CP-63 & 64 ff.); Unit 8: trinomial factoring (AP-4, 10, 19 ff.); Unit 9: square roots (BP-6, 57 ff., esp. BC-70, 96); Unit 10: exponents (YS-25 ff., esp. YS-26, 40, 43 and homework in units 11-13); Unit 11: solve equations with square roots (CM-29, 107 ff. units 12 and 13 homework).
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-1, 1-3, 1-5, 1-6, 2-3, 2-7, 2-8A, 2-8, 6-6, 9-1, 9-2, 9-5, 12-5.
- PLATO Learning Inc., 2000, Modules: [Software]
Math Fundamentals: Dividing Fractions 1, Dividing Fractions 2; Pre-Algebra: Adding and Subtracting Integers, Exponents - Pre-Algebra, Square Roots - Pre-Algebra; Beginning Algebra: Integer Sum, Integer Difference, Exponents - Beginning Algebra, Quotient and Power, Square Roots - Beginning Algebra.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Fractions; Skill: Reciprocals Grade 8; Unit: Irrational Numbers; Skill: Radicals and Roots Grade 7; Unit: Numeration; Skill: Exponential Notation-E Grade 9.
  
    Absolute Values
The learner will be able to solve equations and inequalities involving absolute values.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 3.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 11: CM-74 thru 77, 83-89, 95-100 ff.; Unit 12: GG-76 thru 80 ff., GG-124; Unit 13: various homework problems. Teacher Notes: In Math 3 (Algebra 2) absolute value is treated with families of functions and carried on in Math 4 (Math Analysis) with modelin and iecewise functions.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
7-6
- PLATO Learning Inc., 2000, Modules: [Software]
Beginning Algebra: Absolute Value, Solving Equations.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Algebraic Concepts; Skill: Absolute Value Grade 9.
  
    Simplifying Expressions
The learner will be able to simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 4.0; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 1: like terms (SQ-67 ff.); Unit 2: Distributive Property (KF-53-84 ff.); Unit 4: simplifying to solve equations (throughout, esp. CP-77 ff.); Unit 9, equations with fractions (BP-46 ff.); Units 10-12, working with rational expressions (esp. YS-53 ff., YS-64, CM-39 ff., GG-15 thru_ 19, GG-30 ff.) Unit 12: Inequalities (GG-58 ff. thru Unit 13). Teacher notes: Used in solving equations throughout the course.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-5, 3-3, 3-4, 3-5, 7-3.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Variables, Binomials; Beginning Algebra: Polynomial Sum and Difference, Polynomial Product.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unti: Algebraic Concepts; Skills: Inequalities-A Grade 7, Inequalities-B Grade 8; Unit: Expressions/Equations; Skill: Expressions: Evaluation and Simplifying Grade 9.
  
    Multistep Problem Solving
The learner will be able to solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 5.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Unit 1: guess and check tables (SQ-45 ff.); Unit 4 guess and check tables, solving equations, multi-step (throughout, esp. CP-1, CP-27, box after CP-37, CP-77 ff., CP-99 ff.); Unit 5: equations with ratios (throughout); Units 9 & 12, equations from diagrams (throughout, esp. GG-1 ff., GG-113 ff.); Units 1-13: unit theme problems, other application problems, and Gold Medal problems. Teacher notes: The CPM curriculum emphasizes problem solving and algebraic representation, including multi-step problems that require students to organize and explain their work.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
3-3, 3-4, 3-5, 6-4, 6-5, 7-3, 7-4.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Linear Equations: 1 Variable, Linear Inequalities: 1 Variable, Using Math Sentences, Part 1; Beginning Algebra: Simple Equations, Solving Equations; Intermediate Algebra: Linear Equations and Inequalities.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Expressions/Equations; Skills: Equations-Two Step Grade 8, Story Problems Grade 8.
  
    Graphing a Linear Equation
The learner will be able to graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 6.0; CA HSEE Math Blueprint, December 2000, 2 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Unit 3: graphing functions (throughout, esp. BC-1, 9, 42, 47); Unit 5: horizontal & vertical lines (EF-66); Unit 6: two-point graphing (WR-31); Units 7, 10 & 13: intercepts (BR-13, YS-65, 66, 98, RS-65); Unit 12: Inequalities (GG-87 thru 91, 99-104 ff.) Teacher notes: Math 1 also includes generating equations from data and introduces other types of functions. "(inequalities).
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
5-4A, 5-4, 6-4, 6-5A, 6-5, 7-8.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Linear Equations: 2 Variables, Systems of Equations - Pre-Algebra; Beginning Algebra: Inequalities I, Inequalities II; Intermediate Algebra: Points in a Plane, Linear Equations and Inequalities, Slope and Y-Intercept, Slope-Intercept Form; Advanced Algebra: Inequalities.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Real Numbers and the Coordinate Plane; Skill: Graphing Equations-A Grade 7.
  
    Point-Slope Formula
The learner will be able to verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 7.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Units 3, 5, 6, verify (BC-12 ff., EF-67, WR-22); Unit 6: y-intercept (WR-29); Unit 7: verify (BR-9), slope, slope-intercept form (throughout, esp. BR-25, 52); Unit 9: equation from two points (BP-83 thru BP-86); Unit 10: YS-58, 99; Unit 11:CM-18, 52, 93; Unit 13: equation from graph (RS-8), line of best fit (RS-11 ff.); RS-27, 49, 90, 102, 105 . Teacher notes: Equation writing uses slope-intercept formula, including writing equations of lines given the slope of a line and a point on the line as well as given two points on a line.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
6-2. 6-3, 6-6.
- PLATO Learning Inc., 2000, Modules: [Software]
Intermediate Algebra: Slope-Intercept Form; Advanced Algebra: Lines and Slopes.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Real Numbers and the Coordinate Plane; Skill: Equations of a Line Grade 9.
  
    Parallel and Perpendicular Lines
The learner will be able to understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 8.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Units 7: parallel (BR-49, 73, 83); Unit 11: CM-101; Unit 12: QG-94, 110, 122; Unit 13: RS-28, 61, 102.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
6-6, 8-1.
- PLATO Learning Inc., 2000, Modules: [Software]
Intermediate Algebra: Parallel and Perpendicular Lines - Intermediate Algebra; Advanced Algebra: Parallel and Perpendicular Lines - Advanced Algebra, Review: Graphs. Geometry and Measurement 2 Slope
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Geometry; Skill: Lines, Segments, Points and Rays Grade 7.
  
    System of Two Linear Equations
The learner will be able to solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 9.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Units 2 & 3: preproblems (KF-116, BC-4); Unit 4: CP-92; Unit 6: throughout, esp. solution to a system (WR-3, 95), substitution (WR-41), y-form (WR-43), applications (WR-51, 52, 59, 60 ff.); Unit 7: slope (throughout, esp. BR-10, 12, 16, 23-26, 33-37, 49-53), graph interpretation (Big Race problems, BR-1, 2, 11, ff., 90, 91), substitution (BR-71 ff., 81), applications (BR-12, 16, 65, 87, 93, 99), write equations from graph (BR-98); Unit 11: elimination (CM-14, 15, 24-28, ff. (CM-50, 64, 80, 90, 103, 116, 121, 135); Unit 12: GG-10, 49; inequalities GG-102 thru 105, 109, 123; Unit 13: RS-16, 25, 39, 61, 97. Teacher notes: Several problems in units 7-12 involve several equations at once.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
8-1, 8-2, 8-3, 8-4, 8-5.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Linear Equations: 2 Variables; Beginning Algebra: Inequalities I, Inequalities II; Intermediate Algebra: Linear Systems of Equations and Inequalities, Linear Systems, Systems - Substitute, Systems - Addition, Word Problems, Review: Linear Systems; Math Problem Solving: Video Rental: Intermediate Algebra: Math Problem-Solving, Running a Race: Intermediate Algebra: Math Problem-Solving.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Expressions/Equations; Skill: Equations: Two Variables Grade 8, Equations: Systems Grade 9; Unit: Real Numbers and the Coordinate Plane; Skill: Graphing Equations-B Grade 8, Sets/Subsets/Solution Sets Grade 8.
  
    Monomials and Polynomials
The learner will be able to add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 10.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Unit 1: combining like terms (SQ-65, 67 ff.); Unit 2: Mult. monomials (KF-53 ff.), Distributive Property (KF-53 thru 84 ff.); Unit 3: practice (BC-73, 76); Unit 4: in context of writing equations (CP-3, 15, ff.); Unit 5: in context of solving proportions (EF-33, 68, 89, 124); Unit 6: practice (WR-33, 48), multiplying binomials (WR-70 thru 73 ff.); Unit 8: AP-89; Unit 11: CM-42, 44, 54; Unit 12: GG-23.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
9-1, 9-2, 9-5A, 9-5, 9-6A, 9-6, 9-7, 9-8, 12-4.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Monomials, Binomials; Beginning Algebra: Monomial Sum and Difference, Monomial Product and Quotient, Binomial Sum and Difference, Polynomial Sum and Difference, Polynomial Product, Polynomial Quotient; Math Problem Solving: Video Rental: Intermediate Algebra: Math Problem-Solving.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Algebraic Concepts; Sills: Polynomials: Addition Grade 9, Polynomials: Division Grade 9, Polynomials: Multiplication Grade 9, Polynomials: Subtraction Grade 9.
  
    Factoring Techniques
The learner will be able to apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 11.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Units 0-8: diamond problems (GS-3 ff.); Units 2-6: multiplying algebraic expressions (KF-53, Distributive Property KF-78), CP-52, WR-70 thru 72, WR-82, perfect squares WR-96; Unit 8: factoring quadratics (AP-2 thru 4, 10 thru 12, 18 thru 21), monomial factoring (AP-31), difference of squares (AP-50 ff., AP-57, 58), summary of methods (AP-59), complete factoring (AP-70), application (AP-79); Unit 9: F.O.I.L. (BP-90); Unit 10: trinomials where a $ 1 (YS-1 thru 3 ff., 17); Unit 12: GG-36; Units 11-13 practice in homework.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
10-1, 10-2, 10-3, 10-4, 10-5, 10-6, 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7, 12-8.
- PLATO Learning Inc., 2000, Modules: [Software]
Beginning Algebra: Common Factors, Factoring II, Factoring Special Cases, Factoring Trinomials I, Factoring Trinomials II, Review: Polynomials/Factoring.
  
    Simplification
The learner will be able to simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 12.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Unit 10: YS-53 thru 55 ff., YS-63 & 64; Unit 11: CM-7, 22, 31, 57, 51, 126: Unit 13: RS-82.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7, 12-8.
- PLATO Learning Inc., 2000, Modules: [Software]
Intermediate Algebra: Equivalent Forms, Rational Sum and Difference, Rational Product and Quotient.
  
    Rational Expressions & Functions
The learner will be able to add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 13.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Units 11 & 12: multiplication and division (CM-35 thru 39 ff., 51, 126, 131; GG-9s 45, 96; Units 12 & 13: addition and subtraction (GG-15 thru 19, 26-31 ff., 60, 62, 73,132; RS-34); mixed practice: Unit 12: GG-47, 82 (84-89), 92; Unit 13: RS- 100.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
12-2, 12-3, 12-5, 12-6, 12-7.
- PLATO Learning Inc., 2000, Modules: [Software]
Intermediate Algebra: Rational Expressions, Evaluating, Equivalent Forms, Rational Sum and Difference, Rational Product and Quotient, Unlike Denominators, Review: Rational Expression.
  
    Quadratic Equations
The learner will be able to solve a quadratic equation by factoring or completing the square.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 14.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Unit 13: RS-55 thru 58, 66-68, 83,
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
10-6, 11-2, 11-3, 11-4, 13-4, 13-5, 13-6.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Special Quadratic Equations; Beginning Algebra: Simple Quadratics, Quadratic Equations, Quadratic Formula.
  
    Rate, Work, & Percent Mixture Proble
The learner will be able to apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
Strand Scope Source
Algebraic Concepts Master CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 15.0; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]
Unit 4: writing equations to solve problems (throughout, esp. CP-15, 40, 54, 68, 92, 103 113-115); Unit 5: EF-81 ff., 118-19; Unit 6, WR-11, 20, 21, 51, 52 ff.; Unit 7: Big Race series (BR-1, 11, 21, 40, 47, 61, 79, 90, 91 and BR-65, 87, 93, 99); Unit 9: BP-28, 95, 110; Unit 12 (GG 1 thru 7, 51, 52, 61, 64, 65, 98, 111-121, 133-34, 133-34); Unit 13: RS-1, 12-14, 52, 53, 62, 64, 72, 78, 101. Teacher notes: Sample problems listed. Word problems and investigations are at the core of the CPM program. Students regularly solve word problems without categorizing them b "type."o
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
4-7, 12-8.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Using Math Sentences, Part 2; Beginning Algebra: Word Problems I, Word Problems II; Math Problem Solving: Beginning Algebra: Math Problem Solving: Planning for a Fishing Trip: Beginning Algebra, Tunnel through Bald Mountain: Beginning Algebra, Bean-Counting: Beginning Algebra. Intermediate Algebra: Math Problem Solving Video Rental: Intermediate Algebra Running a Race: Intermediate Algebra
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]
Unit: Number Sentences; Skill: Rates Grade 8.
  
    Concepts of a Relation and a Function
The learner will be able to understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 16.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 3: writing rules for functions (BC-19 thru 22, ff., esp. BC-87), discrete and continuous functions (BC-39), non-linear functions (BP-66 ff.), Unit 4: CP-102; Unit 6: families of functions (WR-1); Unit 7: writing rules (BR-2 ff., 12, 16); Unit 8: nature of equations (AP-71). Teacher notes: Often references to formal language appear in teacher notes. "Input" and "output" are used interchangeably with to domain and range.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
5-2, 5-5.
- PLATO Learning Inc., 2000, Lesson References: [Software]
Advanced Algebra: Functions and Their Graphs: Definitions of Functions, Graphs of Functions, More on Graphing Functions, Composite and Inverse Functions, Applications of Functions.
  
    Independent & Dependent Variables
The learner will be able to determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 17.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 3: determine range (BC-8 and throughout), scaling axes (BC- 28 thru 30, ff.), domain defined (BC-59 & 60), understanding relationship (BC-61 & 62); Unit 9: domain for square root graphs (BP-15, 44, 65, 76); formal work: Unit 11 (CM-1 thru 3, 17, 29-30, 37-38, 61, 62, 74, 75, 122, 123); Unit 13 (RS-17, 63). Teacher notes: Students work with functions throughout the course, as they do in Math 2. Analysis of families of functions is a main thread in Math 3.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-9, 5-2, 5-3A, 5-3, 5-4, 5-5, 11-1, 11-3.
- PLATO Learning Inc., 2000, Modules: [Software]
Pre-Algebra: Variables, Systems of Equations - Pre-Algebra; Intermediate Algebra: Linear Equations: 2 Variables.
  
    Determining If a Relation Is a Function
The learner will be able to determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 18.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 3: writing rules for functions (BC-19 thru 22, ff., esp. BC-87), discrete and continuous functions (BC-39), non-linear functions (BP-66 ff.), Unit 4: CP-102; Unit 6: families of functions (WR-1); Unit 7: writing rules (BR-2 ff., 12, 16); Unit 8: nature of equations (AP-71).
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
5-5, 5-6.
- PLATO Learning Inc., 2000, Modules: [Software]
Advanced Algebra: Functions and Their Graphs: Definitions of Functions, Graphs of Functions, More on Graphing Functions, Composite and Inverse Functions, Applications of Functions.
  
    Quadratic Formula Proof
The learner will be able to know the quadratic formula and are familiar with its proof by completing the square.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 19.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 10: introduced (YS-75 thru 88) and used thereafter; Unit 13: RS-85 thru 89, 93-94.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
11-3, 13-6.
- PLATO Learning Inc., 2000, Modules: [Software]
Beginning Algebra: Quadratic Equations, Quadratic Formula.
  
    Quadratic Formula Applications
The learner will be able to use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 20.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 10: introduction (YS-75 thru 88, 95, 105), determining rational roots (YS-96, 100); Units 11-13: CM-55, 92, 94; GG-24, 48, 66 ff., 76 ff.; RS-37, 94.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
11-3.
- PLATO Learning Inc., 2000, Modules: [Software]
Beginning Algebra: Quadratic Equations, Quadratic Formula.
  
    Graphing Quadratic Functions
The learner will be able to graph quadratic functions and know that their roots are the x-intercepts.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 21.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 3: introduction (BC-45, 56, 57); Unit 8: graph, roots, Zero Product Prop. (AP-40 thru 46, 71, 93); Unit 9: BP-29; Unit 10: standard form YS-75; Unit 12: GG-66 thru 69; Unit 13: use roots to write equations (RS-20 thru 24, 31-33, 40-47 ff., shape of parabolas (RS-42, 99, 106).
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
11-2, 11-3.
- PLATO Learning Inc., 2000, Modules: [Software]
Advanced Algebra: Parabolas, Ellipses and Hyperbolas.
  
    Quadratic Formula & Factoring Techni
The learner will be able to use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 22.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 3: introduction (BC-45, 56, 57); Unit 8: graph, roots, Zero Product Prop. (AP-40 thru 46, 71, 93); Unit 9: BP-29; Unit 10: standard form YS-75; Unit 12: GG-66 thru 69; Unit 13: use roots to write equations (RS-20 thru 24, 31-33, 40-47 ff., shape of parabolas (RS-42, 99, 106).
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
11-2, 11-3.
- PLATO Learning Inc., 2000, Modules: [Software]
Advanced Algebra: Parabolas, Ellipses and Hyperbolas.
  
    Solving Physical Problems
The learner will be able to apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 23.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 8: AP-29; Unit 9: BP- 24 thru 26, 28, 37, 61; Unit 10: YS-104, 106; Unit 11: CM-45; GG-104, 109, 114; Unit 13: RS-12, 50, 77, 84, 9977, 95.
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
10-6, 11-1, 13-6.
- PLATO Learning Inc., 2000, Modules: [Software]
Beginning Algebra: Word Problems II; Advanced Algebra: Applications of Functions.
  
    Aspects of a Logical Argument
The learner will be able to use and know simple aspects of a logical argument.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 24.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 0: GS-7(c & d), 13(g), 21-23; Unit 1: SQ-4, 85; Unit 2: KF-34, 90, 114; Unit 3: BC-22, 39, 45-47, 58, 72; Unit 4 guess and check tables throughout, CP-92; Unit 5: EF-18 & 19, 32, 46, 56, 57; Unit 6: WR-3, 10, 12, 29, 40, 51, 62; Unit 7: BR-10, 12, 16, 20 ff., 49, 73, 83, 99; Unit 8: AP-41 & 42, 50; Unit 9: BP-2, 3, 6, 15 ff., 16, 24, 58, 76, 77; Unit 10: YS-33, 96; Unit 11: CM-119; Unit 12: GG-27, 33, 40, 41, 87-89, 107; Unit 13: RS-2, 4, 13, 22, 23, 31, 33, 40, 77. Teacher notes: Students are regularly asked to justify why something is true throughout the course ("Explain your answer ").
  
    Inductive & Deductive Reasoning
The learner will be able to explain the difference between inductive and deductive reasoning and identify and provide examples of each.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 24.1.
Instructional Resources
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-2.
- PLATO Learning Inc., 2000, Modules: [Software]
Geometry and Measurement 1: Postulates and Theorems.
  
    Hypothesis and Conclusion
The learner will be able to identify the hypothesis and conclusion in logical deduction.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 24.2.
Instructional Resources
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-6.
- PLATO Learning Inc., 2000, Modules: [Software]
No PLATO modules are available for this learning expectation at this time.
  
    Counterexamples
The learner will be able to use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 24.3.
Instructional Resources
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-7, 2-5, 5-5, 6-5, 7-2.
- PLATO Learning Inc., 2000, Modules: [Software]
No PLATO modules are available for this learning expectation at this time.
  
    Properties of the Number System
The learner will be able to use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 25.0.
Instructional Resources
- CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]
Unit 2: KF-77, 95; Unit 4: CP-50, 78, 79, ff.,.99-100; Unit 5: EF-49, 77, 110; Unit 6: WR-14, 34, 45, 48, 91; Unit 7: BR-8, 72 ff.; Unit 9: BP-7, 29, 46, 97, 112; Unit 10: YS-14, 69, 95; Unit 11: CM-128; Unit 12: GG-14, 34, 75, 84, 107, 125; Unit 12: RS-17, 19, 55, 89. Teacher notes: There are numerous problems beyond those cited where, at the teacher's discretion, requiring showing and/or justifying steps in the solution would be appropriate.
- PLATO Learning Inc., 2000, Modules: [Software]
  
    Constructing Simple Valid Arguments
The learner will be able to use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 25.1.
Instructional Resources
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-7, 2-5, 5-5, 6-2, 9-1, 9-2, 10-1, 11-1, 11-2, 13-1, 13-2.
- PLATO Learning Inc., 2000, Modules: [Software]
Geometry and Measurement 2: Postulates and Theorems.
  
    Validity of an Argument
The learner will be able to judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 25.2.
Instructional Resources
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-3, 1-5, 1-6, 1-8, 3-3, 3-5, 13-2.
- PLATO Learning Inc., 2000, Modules: [Software]
No PLATO modules are available for this learning expectation at this time.
  
    Determining the Truth of a Statement
The learner will be able to given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, determine whether the statement is true sometimes, always, or never.
Strand Scope Source
Algebraic Concepts Introduce CA: Mathematics Content Standards, December 1997, Grades 8-12, Algebra 1, 25.3.
Instructional Resources
- GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]
1-8, 3-3, 7-6.
- PLATO Learning Inc., 2000, Modules: [Software]
No PLATO modules are available for this learning expectation at this time.
  

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