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Oroville Union High School District |
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Mathematics Curriculum |
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Mathematics - Algebra I |
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Algebra I 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,); 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.
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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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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. |
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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.); 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).
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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. |
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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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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. |
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Instructional Resources |
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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.
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GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]. 7-6 |
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PLATO Learning Inc., 2000, Modules: [Software]. Beginning Algebra:
Absolute Value,
Solving Equations.
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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; Skill: Absolute Value 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.); 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.
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GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]. 1-5, 3-3, 3-4, 3-5, 7-3. |
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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 1-13: 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.
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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.
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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); 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).
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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. |
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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); 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.
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GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]. 6-2. 6-3, 6-6.
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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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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. |
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Instructional Resources |
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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.
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GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]. 6-6, 8-1.
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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
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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: Geometry; Skill: Lines, Segments, Points and Rays Grade 7.
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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.); 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.
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GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]. 8-1, 8-2, 8-3, 8-4, 8-5. |
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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; Unit 11: CM-42, 44, 54; Unit 12: GG-23.
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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. |
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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 0-8: 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.
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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. |
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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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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. |
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Instructional Resources |
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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.
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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. |
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PLATO Learning Inc., 2000, Modules: [Software]. Intermediate Algebra:
Equivalent Forms,
Rational Sum and Difference,
Rational Product and Quotient.
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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. |
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Instructional Resources |
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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.
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GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]. 12-2, 12-3, 12-5, 12-6, 12-7. |
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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.
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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. |
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Instructional Resources |
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CPM Mathematics 1, (Algebra 1) 2nd ed., v. 6.0, 2000., Problems: [Textbook]. Unit 13: RS-55 thru 58, 66-68, 83, |
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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. |
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PLATO Learning Inc., 2000, Modules: [Software]. Pre-Algebra:
Special Quadratic Equations;
Beginning Algebra:
Simple Quadratics,
Quadratic Equations,
Quadratic Formula.
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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); 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
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GLENCOE Algebra 1: Applications Connections, Glencoe/McGraw-Hill, 2002, Lesson References, Chapter-Section: [Textbook]. 4-7, 12-8. |
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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); 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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