Oroville Union High School District
Mathematics Curriculum

Mathematics - Pre-Algebra

Pre-Algebra

COURSE TITLE: Pre-Algebra

LENGTH OF COURSE:    One Year

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

PREREQUISITES:

Grade of C or better in Foundations for Algebra, and/or teacher recommendation

TEXTBOOKS:

Pre-Algebra: A Transition to Algebra and Geometry, California Edition, Glencoe/McGraw-Hill, 2002, ISBN 0-07-824772-1

Pre-Algebra, Globe-Fearon, 2001, ISBN 0-130-23633-0

SUPPLEMENTARY INSTRUCTIONAL MATERIALS:

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

Mathematics: Applications and Connections, Course 1, California Edition, Glencoe/McGraw-Hill, 2002, ISBN 0-07-82478-5

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:

Students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and propor-tion, compute percents of increase and decrease, and compute simple and compound
interest. They graph linear functions and understand the idea of slope and its relation to ratio.

BOARD ADOPTION DATE: JUNE 20, 2001
AMENDED: SEPTEMBER 18, 2002


Number Sense 1.0
Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, propor-tions, and percentages:

    Scientific Notation
The learner will be able to read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 1.1; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems [Textbook].  Chapter 9: GP-54-58, 61, 66, 82
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  6-9.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta6 Place Value, Decimals, & Scientific Notation (course); }ta9 Factoring and Exponential Notation (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Numeration ; Skill: Exponential Notation D Grade 8.
  
    Rational Numbers
The learner will be able to add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 1.2; CA HSEE Math Blueprint, December 2000, 3 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  2-4A, 2-4, 2-5A, 2-5, 2-7A, 2-7, 2-8, 4-2, 4-2B, 5-3, 5-4, 5-5, 6-3, 6-4, 6-5A, 6-5.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 1: GO-5, 6, 15, 25, 35, 51-53, 66, 68, 77, 87, 89, 93, 101, 108; Chapter 2: FT-4, 5, 19-22, 24?27, 31-35, 40, 44, 45, 46, 48-52, 62, 65-68, 74, 76-79, 84, 87-100, 102, 103, 106-111, 113, 114, 117, 125; Chapter 3: MD-7-9, 18-20, 40-47, 49-51, 53 59, 61, 62, 64, 65, 67-72, 86-92, 94, 97, 99, 107, 119-123, 125, 127-132, 135, 139-142; Chapter 4: GC-25, 60, 72, 82, 83, 127, 128, 132; Chapter 5: MC-1, 17, 18, 21-23, 32, 59, 62, 63, 76, 77, 91, 97, 100, 112-114, 125, 126 Chapter 6: RS-46, 60, 130; Supporting Problems: Chapter 6: RS-11-14, 16-20, 22-32, 40, 43-46, 49, 60, 61, 64, 75, 77, 78, 105, 106, 118, 119, 128, 135, 141; Chapter 7: CT-1, 3, 14, 16, 19, 21, 22, 25, 30, 32-34, 36-39, 41, 44, 56-60, 63, 64, 71, 72, 76, 77, 85, 86, 88, 98-102, 107115, 117-120, 130, 149; Chapter 8: GS-1, 6, 7, 13-19, 22-26, 28, 29, 32, 37-39, 46, 48-50, 58, 86, 128, 130-133, 145; Chapter 9: GP-21, 23, 25, 34-37, 47, 48, 50, 51, 63-65, 72-76, 78-80, 86-89, 98; Chapter 10: SC-I1, 12, 23, 39, 52, 60, 61, 74, 96, 97.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta11 Addition and Subtraction of Rational Numbers (course); }ta12 Multiplication and Division of Rational Numbers (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Rational Numbers; Skills: Addition and Subtraction of Rational# Grade 8, Multiplication and Division of Rational# Grade 8.
  
    Fractions, Decimals, & Percents
The learner will be able to convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 1.3; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 1-8, 3-4, 3-5, 4-6, 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7, 5-9, 6-1, 6-2, 6-3, 6-4, 6-5A, 6-5, 6-6, 6-6B, 6-7, 6-8, 7-1, 7-2, 7-4, 7-5, 7-6, 7-8, 8-1, 9-1, 9-4, 9-5, 9-6, 9-7, 9-8, 9-9, 9-10, 10-2, 12-1, 12-2, 12-5, 12-7, 12-8, 13-3.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-57; Chapter 3: MD-25, 26, 77-83, 86, 93, 109-1I5, 126, 133, 136; Chapter 4: GC-73, 83; Chapter 5: MC-98; Chapter 6: RS-23, 48; Chapter 7: CT-70, 79; Supporting Problems: Chapter 6: RS-18, 23, 48; Chapter 7: CT-26, 42, 69, 70, 79, 96, 108, 109, 160, 166, 167; Chapter 8: GS-35, 40-42; Chapter 10: SC-75.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta7e The Interior Decorator; }ta7f Going Both Ways; blm7a Decimal Fractions 1; blm7b Decimal Fractions 2; blm8c Percent Concepts 1; blm8d Percent Concepts 2.
  
    Rational & Irrational Numbers
The learner will be able to differentiate between rational and irrational numbers.
Strand Scope Source
Number Sense Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 1.4
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  13-3.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 6: RS-53; Supporting Problems: Chapter 7: CT-96.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    Terminating & Repeating Decimals
The learner will be able to know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.
Strand Scope Source
Number Sense Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 1.5.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  5-1, 6-1.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 7: CT-24.
- PLATO Learning Inc., 2000, Modules: [Software].  blm7a Decimal Fractions 1; blm7b Decimal Fractions 2.
  
    Percentage Calculations
The learner will be able to calculate the percentage of increases and decreases of a quantity.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 1.6; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  9-10.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 5: MC-7; Chapter 6: RS-63, 108, 132, 141, 143; Chapter 7: CT-81-84, 87, 98-103, 108-121, 123, 158, 159, 161, 166; Supporting Problems: Chapter 9: GP-45, 59, 68, 69, 77, 86, 102; Chapter 10: SC-42, 85.
- PLATO Learning Inc., 2000, Modules: [Software].  blm8f Problem Solving 6; }ta15b Window Shopping.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Percents; Skills: Appreciation, Depreciation Grade 8.
  
    Problem Solving: Interest, Etc.
The learner will be able to solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 1.7; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  8-8, 8-9, 9-5, 9-9, 9-10, 14-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 6: RS-63, 76, 91 Chapter 7: CT-81-84, 87, 94-103, 108-121, 126, 150; Chapter 8: GS-40-42, 45-47, 56; Supporting Problems: Chapter 8: GS-59, 70, 72; Chapter 10: SC-25, 75.
- PLATO Learning Inc., 2000, Modules: [Software].  Same lessons previously identified.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unti: Percents; Skill: Story Problems-Percents B Grade 7, Skill: Discount Tax Interest Commission Grade 8.
  

Number Sense 2.0
Students calculate and solve problems involving addition, subtraction, multiplication, and division.

    Negative Whole-Number Exponents
The learner will be able to understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 2.1; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  4-8, 4-9.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-80, 111; Chapter 3: MD-9, 20, 53-56, 59, 62, 64, 65, 67-72; Chapter 6: RS-77, 118; Chapter 7: CT-62, 124, 153 154; Supporting Problems: Chapter 7: CT-49, 51, 52, 54, 55, 133.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Numeration; Skill: Exponential Notation E Grade 9.
  
    Fractions: Factoring
The learner will be able to add and subtract fractions by using factoring to find common denominators.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 2.2; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  5-5.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 5: MC-97, 98; Supporting Problems: Chapter 6: RS-46, 60, 130,105.
- PLATO Learning Inc., 2000, Modules: [Software].   }ta9 Factoring and Exponential Notation (course); }ta11 Addition and Subtraction of Rational Numbers (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Fractions; Skill: Subtract Fractions-Mixed Numbers Grade 5, Add Fractions-Mixed Numbers-B Grade 8.
  
    Rational Numbers: Exponent Rules
The learner will be able to multiply, divide, and simplify rational numbers by using exponent rules.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 2.3; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  4-8, 6-3, 6-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 8: GS-1, 36, 43, 44 Chapter 9: GP-7-10, 19, 23, 26-30, 33, 35, 40, 43, 47, 52, 74, 81, 89, 95-97; Supporting Problems: Chapter 7: CT-13, 49, 61, 62.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta9 Factoring and Exponential Notation (course); }ta12 Multiplying and Dividing Rational Numbers (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Numeration ; Skill: Exponential Notation E Grade 9.
  
    Integers: Square & Not Square
The learner will be able to use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 2.4; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  13-1.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 7: CT-49-55, 65-70; Chapter 8: GS-12-18, 21-26, 28-30, 48-50; Supporting Problems: Chapter 7: CT-73-75, 133; Chapter 8: GS-135; Chapter 9: GP-20, 70.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Irrational Numbers; Skill: Radicals and Roots Grade 7.
  
    Absolute Value of a Number
The learner will be able to understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
Strand Scope Source
Number Sense Master CA: Mathematics Content Standards, December 1997, Grade 7, Number Sense 2.5; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  2-1.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  
- PLATO Learning Inc., 2000, Modules: [Software].  }ta22 Integers and Their Opposites (course).
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.
  

Algebra and Functions 1.0
Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.

    Expressions, Equations, & Inequaliti
The learner will be able to use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 1.1; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-3, 1-8, 1-9, 7-7, 8-8.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-1, 5, 8, 15, 23, 30, 35, 36, 38, 54, 55, 59-61, 69, 80, 81, 86, 104, 119, 121-124; Chapter 3: MD-52, 60, 94; Chapter 4: GC-40-44, 53-55, 58, 61, 76-81, 90-92; Chapter 5: MC-5, 8, 20, 24-29, 31, 44-49, 65; Chapter 7: CT-122; Chapter 8: GS-33, 113; Supporting Problems: Chapter 4: GC-49, 62, 70, 71, 99, 112, 124, 126, 135, 136, 141, 143; Chapter 6: RS-24, 25, 62, 74, 110-114, 120 125, 138, 143, 146; Chapter 7: CT-3, 12, 72, 92, 104, 153, 154, 163, 165, 170; Chapter 8: GS-5, 11, 13-18, 20, 22, 24-26, 28-29, 32; 67, 69, 71, 89, 90, 93-96, 103, 110. 117-119; Chapter 9: GP-22: Chapter 10: SC-4, 10, 26, 70.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta25 Simple Equations (course); }ta27 Solving Simple Equations Using Transformation (course); }ta30 Introduction to Algebraic Inequalities (course); }ta31 Solving Inequalities Using Transformations (course); }ta34 Systems of Equations (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Expressions/Equations; Skills: Equations: Writing/Number Relation Problems Grade 8, Number Relation Problems Grade 8.
  
    Order of Operations
The learner will be able to use the correct order of operations to evaluate algebraic expressions such as 3(2xÊ +Ê 5) 2.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 1.2; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-2, 4-2.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-8, 23, 121-124; Chapter 3: MD-118; Chapter 4: GC-2-8, 23, 26?28, 50-52, 63, 71, 84, 96, 102, 114, 139; Chapter 5: MC-56, 58, 73, 75, 76, 79-89, 92, 99, 101, 102, 123; Supporting Problems: Chapter 6: RS-75, 131, 148 Chapter 7: CT-43; Chapter 8: GS-37; Chapter 9: GP-34; Chapter 10: SC-88, 89.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta8 Properties and Order of Operations (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Expressions/ Equations; Skills: Equations: Order of Operations Grade 9, Expressions: Evaluation and Simplifying Grade 9.
  
    Simplifying Numerical Expression
The learner will be able to simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.
Strand Scope Source
Algebra and Functions Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 1.3.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-4, 1-5, 2-5, 2-7, 5-3, 14-2, 14-5.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-48, 118, 119, 121-124; Chapter 3: MD-18, 19, 26-34, 38, 39, 53-56, 64, 67-72, 74, 87-91, 94-96, 98-105, 134, 140, 141; Chapter 4: GC-14?19, 26-31, 33, 36, 40-44, 53-56, 58, 61, 62, 64, 65, 70, 76, 85, 95, 107-111, 117, 138, 142; Chapter 5: MC-19, 27, 56, 57, 73, 79-88, 99 102, 122; Supporting Problems: Chapter 4: GC-10, 24, 45, 86, 120, 122, 123, 140; Chapter 6: RS-4, 16, 128, 148; Chapter 7: CT-41, 43, 48, 139, 141.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta8 Properties and Order of Operation (course).
  
    Algebraic Terminology
The learner will be able to use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.
Strand Scope Source
Algebra and Functions Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 1.4.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-3, 1-5, 1-6, 1-9, 14-1, 14-2.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 4: GC-39, 41, 103; Chapter 5: MC-3, 8; Supporting Problems: Chapter 10: SC-31, 33.
- PLATO Learning Inc., 2000, Modules: [Software].   }ta21 Expressions (course).
  
    Graphing Quantitative Relationships
The learner will be able to represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 1.5; CA HSEE Math Blueprint, December 2000, 3 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 8-8, 8-9.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 1: GO-21-24, 40, 41, 52, 89, 90, 96; Chapter 2: FT-2, 3, 12-17, 28, 29, 36-39, 41, 42, 47, 48, 54-56, 59-61, 69-71, 80-82, 105, 111, 114, 118, 119, 121-124, 126; Chapter 5: MC-68, 74, 93, 94, 103-109; Supporting Problems: Chapter 3: MD-63, 106 Chapter 4: GC-68; Chapter 5: MC-9; Chapter 6: RS-13, 89; Chapter 7: CT-92, 136, 162, 170; Chapter 9: GP-4, 6, 17, 18, 44, 83, 84, 94.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta33 Graphing Equations (course); }ta35 Graphing Inequalities (course).
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, Graphing Equations B Grade 8.
  

Algebra and Functions 2.0
Students interpret and evaluate expressions involving integer powers and simple roots.

    Simplifying Expressions: Exponents
The learner will be able to interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 2.1; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  4-2, 4-8, 4-9, 14-1, 14-2, 14-3, 14-4, 14-5A, 14-5.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-35, 46, 80, 111, 118, 126; Chapter 6: RS-29-31, 77, 78, 118; Chapter 7: CT-49-51, 55, 61, 153, 154; Chapter 8: GS-1, 36, 43, 44; Chapter 9: GP-7-I0, 19, 23, 26-30, 33, 35, 40-43, 47, 52, 74, 81, 89, 95-97; Supporting Problems: Chapter 7: CT-74, I24; Chapter 9: GP-89, 96, 97.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta8 Factoring and Exponential Notation (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Numeration; Skill: Exponential Notation D Grade 8, Exponential Notation E Grade 9.
  
    Monomials
The learner will be able to multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 2.2; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  4-8, 4-9, 14-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 4: GC-53-56, 58, 59, 6I, 62, 64, 65, 85, 95, 107-111, 117, 120-125, 138, 142; Supporting Problems: Chapter 2: FT-35, 46, 80, 111, 118, 126; Chapter 6: RS-29-31, 77, 78, 118; Chapter 7: CT-49-51, 55, 61, 153, 154; Chapter 8: GS-1, 36, 43, 44; Chapter 9: GP-7-10, 19, 23, 26-30, 33, 35, 40-43, 47, 52, 74, 81, 89, 95-97.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Numeration; Skill: Exponential Notation E Grade 9.
  

Algebra and Functions 3.0
Students graph and interpret linear and some nonlinear functions.

    Graphing Functions
The learner will be able to graph functions of the form y = nx 2 and y = nx 3 and use in solving problems.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 3.1; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  8-3B.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-80, 111, 121; Chapter 5: MC-68, 69, 93, 103-109; Chapter 9: GP-3-6, 17, 18, 93, 94; Supporting Problems: Chapter 4: GC-97, 115; Chapter 6: RS-89.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta26 Functions (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Algebraic Concepts; Skill: Functions-Exponential Grade 10.
  
    Plotting Values of Volumes
The learner will be able to plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).
Strand Scope Source
Algebra and Functions Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 3.2.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  4-2, 12-7A, 12-7.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 9: GP-3-6, 17, 18, 94.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    Graphing Linear Functions
The learner will be able to graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 3.3; CA HSEE Math Blueprint, December 2000, 3 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  8-3, 8-6, 8-7, 8-7B, 8-8.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-36, 38, 39, 41, 54-56, 59-61, 69-71, 80-82, 114, 116, 118, 119, 121, 126; Chapter 5: MC-9; Chapter 10: SC-1-7, 14-19, 27-38, 44, 47-50, 55-59, 63, 78-86, 90-95, 100; Supporting Problems: Chapter 3: MD-85.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta26 Functions (course).
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.
  
    Plotting Values of Quantities
The learner will be able to plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 3.4; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  8-6B.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 5: MC-68, 69, 74, 93, 94, 103-109; Chapter 7: CT-170; Chapter 8: GS-33; Chapter 9: GP-83; Chapter 10: SC-14-18, 21, 44, 57-59, 66-70, 78, 79, 90-95, 100.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta26 Functions (course).
  

Algebra and Functions 4.0
Students solve simple linear equations and inequalities over the rational
numbers.

    Two-Step Linear Equations & Inequali
The learner will be able to solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 4.1; CA HSEE Math Blueprint, December 2000, 3 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  7-2A, 7-2, 7-6.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 2: FT-19, 34, 35, 48, 63, 137; Chapter 5: MC-1, 10, 13-16, 20, 24-31, 33, 35-41, 41, 44-46, 48-55, 65, 66, 70-72, 80-86, 89, 92, 95, 96, 111, 115-120; Chapter 6: RS-11, 21-26, 28, 49, 61, 88, 103, 110-114, 131, 134-139, 146, 148; Supporting Problems: Chapter 7: CT-2-6, 8, 10-12, 19, 22, 29, 33, 34, 36-41, 56, 57, 72, 80, 86, 88, 90, 92, 127, 128, 134, 138, 139, 142, 143, 150, 163-165; Chapter 8: GS-10, 11, 58, 136, 144; Chapter 9: GP-22, 38, 60, 76, 77, 85, 99, 100; Chapter 10: SC-11, 41, 53, 76, 88.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta27 Solving Equations Using Transformations (course); }ta31 Solving Inequalities Using Transformations (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Expressions/Equations; Skill: Equations: Two Step Grade 8.
  
    Multistep-Problem Solving
The learner will be able to solve multistep problems involving rate, average speed, distance, and time or a direct variation.
Strand Scope Source
Algebra and Functions Master CA: Mathematics Content Standards, December 1997, Grade 7, Algebra and Functions 4.2; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  3-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 5, MC-127; Chapter 6: RS-139; Supporting Problems: Chapter 5: MC-47; Chapter 7: CT-126, 144-148, 171; Chapter 9: GP-39, 83, 84.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta36 Solving Inequalities with Two Variables (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Number Theory; Skill: Inverse and Direct Variations Grade 10; Unit: Expressions & Equations; Skill; Distance, Rate, Time Grade 7.
  

Measurement and Geometry 1.0
Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.

    Measurement Systems
The learner will be able to compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement and Geometry 1.1; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  7-8, 8-3, 14-3.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 3: MD-73, 75, 96; Chapter 5: MC-3, 4, 34, 60; Chapter 6: RS-4-5; Chapter 7: CT-135; Supporting Problems: Chapter 2: FT-22; Chapter 5: MC-34, 60; Chapter 9: GP-83, 84.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta16 Measurement (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Measurement; Skills: Mass & Capacity-C Grade 8, Length-B Grade 8, Time-D Grade 8, Units of Measurement-D Grade 8, Temperature-D Grade 8.
  
    Drawings & Models Made to Scale
The learner will be able to construct and read drawings and models made to scale.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement and Geometry 1.2; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  11-7.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 8: GS-51-54, 60-69, 71, 74-82, 87-100, 107-116, 120-127; Supporting Problems: Chapter 7: CT-28, 78, 159; Chapter 9: GP-3, 6.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Number Sentences; Skill: Scale Drawings Grade 7.
  
    Measures Expressed as Rates & Produc
The learner will be able to use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement and Geometry 1.3; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 1-5, 2-6, 2-7, 3-3, 3-8, 4-2, 4-9, 5-9, 6-2, 6-5, 6-9, 7-7, 8-2, 8-4, 8-7, 8-8, 9-5, 10-3, 10-3B, 13-1, 13-3.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 7: CT-143-148; Supporting Problems: Chapter 6: RS-116, 137; Chapter 7: CT-126, 170, 171; Chapter 9: GP-83, 84; Chapter 10: SC-79.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Number Sentences; Skill: Rates Grade 8.
  

Measurement and Geometry 2.0
Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:

    Formulas: Perimeter, Surface, & Volu
The learner will be able to use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement and Geometry 2.1; CA HSEE Math Blueprint, December 2000, 3 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  3-5, 6-7, 7-4, 12-1A, 12-1, 12-2, 12-3, 12-5, 12-7, 13-1, 13-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-20, 39, 64, 65, 67, 80, 86; Chapter 2: FT-64; Chapter 3: MD-22, 23, 37; Chapter 6: RS-33-41, 50-59, 65; Chapter 7: CT-129-132, 137, 151, 161; Chapter 8: GS-75-82, 89-92, 94-97, 100, 103-107, 109-112, 114-127, 129, 131, 137-138, 143; Chapter 9: GP-1, 2, 5, 11, 15, 16, 20, 27, 28, 32, 45, 46, 67-71, 77, 93, 94, 100, 101.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta29 Formulas (course); }ta18d Perimeter Practice; }ta20 Area and Volume (course); blm9g Area Measurement; blm9h Volume and Capacity Measurement.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Measurement; Skills: Skills: Area of a Triangle Grade 6, Surface Area Grade 6, Area of a Circle Grade 7, Area of a Trapezoid Grade 7, Perimeter-C Grade 7, Volume of a Cylinder Grade 7, Volume of Rectangular Prisms Grade 7, Area of a Parallelogram-B Grade 8, Area of a Rectangle-D Grade 8, Circumference-B Grade 8, Volume of a Cone Grade 8, Volume of a Pyramid Grade 8. .
  
    Area of Complex & Irregular Figures
The learner will be able to estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement and Geometry 2.2; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  3-5A, 3-5, 12-1A, 12-1, 12-2, 12-4, 12-5, 12-6.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 8: GS-81, 83, 87, 98, 100, 101, 127, 131, 134, 137-144.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    Measuring 3-Dimensional Objects
The learner will be able to compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement and Geometry 2.3; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  12-5, 12-8B.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 6: RS-66-72, 80-87, 92-101, 109, 126, 140; Chapter 8: GS-52, 53, 55, 60-63, 65, 67, 69, 71, 74-82, 84, 142; Chapter 9: GP-15-17, 27-31, 45, 46, 68, 69, 94, 101.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Measurement; Skill: Volume of Rectangular Prisms Grade 7, Surface Area of a Prism Grade 8.
  
    Measurement: Change of Scale
The learner will be able to relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft 2 ] = [144 in 2 ], 1 cubic inch is approximately 16.38 cubic centimeters-meters or [1Ê in 3 ] = [16.38 cm 3 ]).
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement and Geometry 2.4; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  3-5, 7-8, 12-1A, 12-1, 12-1.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 5: MC-34; Chapter 8: GS-77; Chapter 9: GP-32, 94.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta16 Measurement (course).
  

Measurement and Geometry 3.0
Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures.

    Elements of Geometric Figures
The learner will be able to identify and construct basic elements of geometric figures (e.g., altitudes, mid-points, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.
Strand Scope Source
Measurement and Geometry Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Measurement & Geometry 3.1
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  2-6, 7-5, 11-1, 11-1B, 11-7, 11-8, 12-1, 13-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 6: RS-33-38, 42; Chapter 8: GS-68; Supporting Problems: Chapter 6: RS-59.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta18 Polygons (course); }ta19 Circles (course).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Geometry [Software].  
  
    Coordinate Graphs
The learner will be able to understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement & Geometry 3.2; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  3-5B, 11-9, 13-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: GO-75, 76, 84, 85, 90, 86; Supporting Problems: Chapter 7: CT-159; Chapter 8: GS-34; Chapter 10: SC-29, 30, 72.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Geometry; Skills: Coordinate Geomety-C Grade 7, Coordinate Geometry-D Grade 8, Transformations Grade 8; Unit: Real Numbers and the Coordinate Plane; Skills: Distance Formula Grade 9, .
  
    Pythagorean Theorem
The learner will be able to know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement & Geometry 3.3; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  13-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 8: GS-1-8, 13-18, 21-26, 28-30, 48-50, 55, 57, 85, 99; Supporting Problems: Chapter 8: GS-57, 85, 102, 130-133, 140-141; Chapter 10: SC-65.
- PLATO Learning Inc., 2000, Modules: [Software].  }gm2g The Pythagorean Theorem (8th grade level).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Geometry; Skills: Triangles-C Grade 9, PythagoreanTtheorem Grade 9.
  
    Congruence of Geometrical Figures
The learner will be able to demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
Strand Scope Source
Measurement and Geometry Master CA: Mathematics Content Standards, December 1997, Grade 7, Measurement & Geometry 3.4; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  11-1B, 11-3, 11-5.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 6: RS-1, 8, 99.
- PLATO Learning Inc., 2000, Modules: [Software].  }gm1d Congruent Angles (8th grade level).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Geometry; Skills: Congruence-B Grade 7, Congruence(SAS/ASA) Grade 8.
  
    2-Dimensional Patterns
The learner will be able to construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.
Strand Scope Source
Measurement and Geometry Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Measurement & Geometry 3.5.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  12-5, 12-6.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 8: GS-51-54, 60-69, 71, 74-82, 87-100, 107-116, 120-127, 137-144.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    3-Dimensional Geometric Objects
The learner will be able to identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).
Strand Scope Source
Measurement and Geometry Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Measurement & Geometry 3.6.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  11-1.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 8: GS-51-54, 60-69, 71, 74-82, 87-100, 107-116, 120-127, 137-144.
- PLATO Learning Inc., 2000, Modules: [Software].  blm9d Common 3-Dimensional Figures.
  

Statistics, Data Analysis, & Prob. 1.0
Students collect, organize, and represent data sets that have one or more vari-ables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program.

    Displays for Data Sets
The learner will be able to know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.
Strand Scope Source
Statistics, Data Analysis, & Probabi Master CA: Mathematics Content Standards, December 1997, Grade 7, Statistics, Data Analysis, and Probability 1.1; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-10, 10-1, 10-3, 10-3B, 11-2.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 1: GO-46-49, 61-63, 70, 71, 83, 102-104; Supporting Problems: Chapter 1: GO-2, 3, 21, 41; Chapter 3: MD-21; Chapter 6: RS-107, 129.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta37 Organizing Data (course); }ta40a The Counting Principle and Probability (tree diagram).
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Data Interpretation; Skills: Tables-E Grade 7, Tables-F Grade 8; Unit: Probability & Statistics; Skill: Statistics Grade 10.
  
    Numerical Variables on Scatterplots
The learner will be able to represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
Strand Scope Source
Statistics, Data Analysis, & Probabi Master CA: Mathematics Content Standards, December 1997, Grade 7, Statistics, Data Analysis, and Probability 1.2; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  8-2.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 1: GO-83, 98-100; Chapter 10: SC-94; Supporting Problems: Chapter 9: GP-49.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    Data Set Quartiles
The learner will be able to understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.
Strand Scope Source
Statistics, Data Analysis, & Probabi Master CA: Mathematics Content Standards, December 1997, Grade 7, Statistics, Data Analysis, and Probability 1.3; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  6-6A, 6-6, 6-6B, 10-2.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Primary Problems: Chapter 1: GO-27, 36, 45, 54, 58-60, 72-74, 78, 81, 97; Chapter 2: FT-34, 43, 72, 74, 75, 85, 101; Chapter 3: MD-60; Chapter 4: GC-9, 87; Chapter 5: MC-61; Supporting Problems: Chapter 6: RS-90, 107.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Probability & Statistics; Skill: Statistics Grade 10.
  

Mathematical Reasoning 1.0
Students make decisions about how to approach problems.

    Problem Analysis
The learner will be able to analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
Strand Scope Source
Mathematical Reasoning Master CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 1.1; CA HSEE Math Blueprint, December 2000, 2 Test Items.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 2-6, 4-1.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-16, 18-21, 27-35, 42, 56, 108; Chapter 2: FT-5, 9-11; Chapter 3: MD-18, 57.
- PLATO Learning Inc., 2000, Modules: [Software].  blm3h Problem Solving 1; blm4o Problem Solving 2; blm5m Problem Solving 3; blm6s Problem Solving 4; blm7g Problem Solving 5; blm8f Problem Solving 6; blm9j Problem Solving 7.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Problem Solving; Skills: Irrelavant/Missing Information-A Grade 7, Irrelavant/Missing Information-B Grade 8.
  
    Mathematical Conjectures
The learner will be able to formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
Strand Scope Source
Mathematical Reasoning Master CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 1.2; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-4, 1-7, 2-4, 2-5, 2-6, 2-8.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 5: MC-23; Chapter 6: RS-44.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    Problem Disaggregation
The learner will be able to determine when and how to break a problem into simpler parts.
Strand Scope Source
Mathematical Reasoning Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 1.3.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  9-4B, 10-8.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-18-20; Chapter 8: GS-24, 25, 27, 28.
- PLATO Learning Inc., 2000, Modules: [Software].  Included in previously identified problem solving lessons.
  

Mathematical Reasoning 2.0
Students use strategies, skills, and concepts in finding solutions.

    Estimation
The learner will be able to use estimation to verify the reasonableness of calculated results.
Strand Scope Source
Mathematical Reasoning Master CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.1; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1. 1-8, 2-4, 3-6, 3-8, 5-3, 5-4, 5-5, 6-3, 6-4, 6-5, 6-7, 7-4, 9-4, 9-6, 9-10, 11-4, 12-2, 12-4, 12-5, 12-6, 13-4, 14-2, 14-4.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-18-20, 43, 65; Chapter 2: FT-126.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta3b Not Exactly.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unti: Numeration; Skills: Rounding and Estimation-E Grade 7, Rounding and Estimation-F Grade 8; Unit: Problem Solving; Skill: Evaluating Solutions-B Grade 8.
  
    Complex Problem Solving
The learner will be able to apply strategies and results from simpler problems to more complex problems.
Strand Scope Source
Mathematical Reasoning Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.2.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  2-6.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-18-20, 56; Chapter 3: MD-18; Chapter 5: MC-14, 23, 47, 88, 118.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO's problem solving strategies at simple levels are used in more complex problems.
  
    Estimation & Logical Reasoning
The learner will be able to estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
Strand Scope Source
Mathematical Reasoning Master CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.3; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-6, 1-8, 2-4, 2-5A, 2-5, 2-7A, 2-7, 2-8, 3-4, 3-6, 3-7, 3-8, 5-3, 5-4, 5-6, 5-8, 6-3, 6-4, 6-5, 6-7, 7-2A, 7-2, 7-5A, 7-5, 7-6, 8-3, 8-5, 8-7, 9-4, 9-4B, 9-9.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-14; Chapter 5: MC-93, 94.
- PLATO Learning Inc., 2000, Modules: [Software].  Included in previously identified problem solving lessons.
  
    Conjectures: Inductive & Deductive
The learner will be able to make and test conjectures by using both inductive and deductive reasoning.
Strand Scope Source
Mathematical Reasoning Master CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.4; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 1-4, 1-5, 1-8, 2-4, 2-5, 2-6, 2-7, 2-8, 3-1, 3-2, 3-5, 3-6, 4-1, 4-4, 4-4B, 4-6A, 4-8, 4-9, 5-3, 5-4, 5-5, 5-7, 5-8, 5-9, 5-9B, 6-2, 6-3, 6-4, 6-5, 6-7, 6-8, 7-1, 7-6, 8-2, 8-6B, 8-9, 9-3A, 9-3, 9-7, 9-9, 10-10, 11-3, 11-3B, 11-4, 11-6, 11-8, 12-1, 12-2, 12-5, 12-6, 12-7A, 12-7, 12-8, 12-8B, 13-2, 13-4, 13-5, 13-6A, 13-6, 13-6B, 13-7, 14-2, 14-4
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-56, 101; Chapter 2: FT-126; Chapter 5: MC-23, 39.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    Explaining Mathematical Reasoning
The learner will be able to use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
Strand Scope Source
Mathematical Reasoning Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.5.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 2-8, 4-8, 8-1, 10-5.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-56, 95; Chapter 2: FT-18, 120, 127; Chapter 3: MD-71, 76, 134; Chapter 4: GC-18, 21, 27, 35, 40, 42, 43, 49, 111, 121, 122, 129, 137, 144; Chapter 5: MC-2, 10, 18, 20, 35-38, 40, 50, 64, 79, 121.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta21 Expressions (course).
  
    Expressing Solutions Clearly
The learner will be able to express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
Strand Scope Source
Mathematical Reasoning Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.6.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 2-4, 4-2, 6-2, 8-7.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-14, 56, 95; Chapter 2: FT-9, 120, 127; Chapter 3: MD-35, 36, 47, 71, 76, 134; Chapter 4: GC-69, 144; Chapter 5: MC-121.
- PLATO Learning Inc., 2000, Modules: [Software].  }ta21 Expressions (course).
  
    Exact & Approximate Solutions
The learner will be able to indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
Strand Scope Source
Mathematical Reasoning Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.7.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 5-2, 6-2, 6-6, 6-6B, 8-5, 9-8, 9-10, 12-2, 12-5, 12-6, 12-7, 12-8, 13-1, 13-3, 13-4, 13-5, 13-6A, 13-6, 13-7.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 6: RS-50, 54-56.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  
    Checking Validity by Context
The learner will be able to make precise calculations and check the validity of the results from the context of the problem.
Strand Scope Source
Mathematical Reasoning Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 2.8.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 3-6, 7-3, 9-6.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-18-20, 37-39, 50, 65, 67, 79, 80, 86, 93, 94, 105, 106; Chapter 2: FT-18, 53, 73, 115; Chapter 3: MD-24, 81, 84, 123; Chapter 5: MC-2.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO requires precise calculations to master a lesson objective.
  

Mathematical Reasoning 3.0
Students determine a solution is complete and move beyond a particular problem by generalizing to other situations.

    Reasonableness of a Solution
The learner will be able to evaluate the reasonableness of the solution in the context of the original situation.
Strand Scope Source
Mathematical Reasoning Master CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 3.1; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-6, 1-8, 2-4, 2-5A, 2-5, 2-7A, 2-7, 2-8, 3-4, 3-6, 3-7, 3-8, 5-3, 5-4, 5-6, 5-8, 6-3, 6-4, 6-5, 6-7, 7-2A, 7-2, 7-5A, 7-5, 7-6, 8-3, 8-5, 8-7, 9-4, 9-4B, 9-9.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-43; Chapter 3: MD-133.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO provides instructional feedback to assist student with this standard.
Assessment Resources
- Skills Connection, EdVision.com, Version 2.1.0, 2001, Template: All Skills; Area: Mathematics [Software].   Unit: Problem Solving; Skill: Evaluating Solutions-B Grade 8.
  
    Methods of Deriving Solutions
The learner will be able to note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
Strand Scope Source
Mathematical Reasoning Introduce CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 3.2.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  2-6, 4-3, 7-1, 10-8.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-107; Chapter 2: FT-127; Chapter 3: MD-18, 19; Chapter 5: GC-20, 53-56, 58, 59.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO provides worksheets for Math Fundamentals and Towards Algebra for students to demonstrate this standard.
  
    Generalizing Results
The learner will be able to develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
Strand Scope Source
Mathematical Reasoning Master CA: Mathematics Content Standards, December 1997, Grade 7, Mathematical Reasoning 3.3; CA HSEE Math Blueprint, December 2000, 1 Test Item.
Instructional Resources
- GLENCOE Pre-Algebra, Glencoe/McGraw-Hill, California Edition, 2001., Lesson References, Chapter-Section: [Textbook].  1-1, 1-4, 1-6, 9-2.
- CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Problems: [Textbook].  Chapter 1: GO-107; Chapter 2: FT-127; Chapter 3: MD-18; Chapter 4: GC-20, 53-56, 58, 59.
- PLATO Learning Inc., 2000, Modules: [Software].  PLATO Lesson Not Available.
  

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