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Oroville Union High School District |
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Mathematics Curriculum |
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Mathematics - Algebra A |
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Algebra A Content Standards
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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. |
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Instructional Resources |
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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,).
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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. |
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Instructional Resources |
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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).
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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. |
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Instructional Resources |
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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.).
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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.
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Assessment Resources |
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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.
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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. |
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Instructional Resources |
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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.).
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PLATO Learning Inc., 2000, Modules: [Software]. Pre-Algebra:
Variables,
Binomials;
Beginning Algebra:
Polynomial Sum and Difference,
Polynomial Product.
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Assessment Resources |
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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.
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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. |
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Instructional Resources |
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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 1-6: 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.
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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.
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Assessment Resources |
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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.
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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. |
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Instructional Resources |
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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). Teacher notes: Math 1 also includes generating equations from data and introduces other types of functions. "(inequalities).
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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.
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Assessment Resources |
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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.
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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. |
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Instructional Resources |
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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). 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.
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PLATO Learning Inc., 2000, Modules: [Software]. Intermediate Algebra:
Slope-Intercept Form;
Advanced Algebra:
Lines and Slopes.
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Assessment Resources |
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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.
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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. |
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Instructional Resources |
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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.).
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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.
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Assessment Resources |
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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.
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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. |
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Instructional Resources |
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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.
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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.
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Assessment Resources |
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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.
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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. |
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Instructional Resources |
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CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]. Units 0-6: 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.
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PLATO Learning Inc., 2000, Modules: [Software]. Beginning Algebra:
Common Factors,
Factoring II,
Factoring Special Cases,
Factoring Trinomials I,
Factoring Trinomials II,
Review: Polynomials/Factoring.
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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. |
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Instructional Resources |
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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). Teacher notes: Sample problems listed. Word problems and investigations are
at the core of the CPM program.
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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
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Assessment Resources |
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Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software]. Unit: Number Sentences; Skill: Rates Grade 8.
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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. |
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Instructional Resources |
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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). Teacher notes: Often references to formal language appear in teacher notes. "Input" and "output" are used interchangeably with to domain and range.
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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.
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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. |
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Instructional Resources |
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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). 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.
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PLATO Learning Inc., 2000, Modules: [Software]. Pre-Algebra:
Variables,
Systems of Equations - Pre-Algebra;
Intermediate Algebra:
Linear Equations: 2 Variables. |
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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. |
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Instructional Resources |
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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).
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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.
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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. |
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Instructional Resources |
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CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]. Unit 3: introduction (BC-45, 56, 57).
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PLATO Learning Inc., 2000, Modules: [Software]. Advanced Algebra:
Parabolas,
Ellipses and Hyperbolas. |
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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. |
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Instructional Resources |
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CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems [Textbook]. Unit 3: introduction (BC-45, 56, 57). |
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PLATO Learning Inc., 2000, Modules: [Software]. Advanced Algebra:
Parabolas,
Ellipses and Hyperbolas.
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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. |
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Instructional Resources |
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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;
Teacher notes: Students are regularly
asked to justify why something is true throughout the course ("Explain your answer ").
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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. |
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Instructional Resources |
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 1:
Postulates and Theorems.
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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. |
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Instructional Resources |
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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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. |
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Instructional Resources |
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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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. |
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Instructional Resources |
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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.
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.
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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. |
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Instructional Resources |
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PLATO Learning Inc., 2000, Modules: [Software]. Geometry and Measurement 2:
Postulates and Theorems. |
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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. |
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Instructional Resources |
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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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. |
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Instructional Resources |
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| · |
PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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