Prentice Hall: Middle School Math, Course Correlated to: New York Mathematics Learning Standards (Intermediate)

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NEW YORK MATHEMATICS LEARNING STANDARDS

PAGE(S) WHERE TAUGHT

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Mathematical Reasoning

Key Idea:Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

Students will:

• apply a variety of reasoning strategies SE/TE: Section 1A: Reading and Interpreting Graphs, 5-22; Section 1B: Displaying Data, 23-40; Section 1C: Describing Data, 41-56; Section 2A: Making Sense of Large Numbers, 65-84; Section 2B: Number Sense and Operation Sense, 85-108; Section 2C: Introduction to Algebra, 109-128; Section 3A: Decimal Concepts, 137-158; Section 5A: Number Theory, 269-286; Section 12A: Introduction to Probability, 625-640; Section 12B: Fairness, 641-656

TR: Solutions Manual; Overhead Transparency Package; Skills Intervention Kit; Test Taking Tips on Transparencies; Reading Strategies for Problem Solving Package; SAT 9

Assessment Package; TerraNova

Assessment Package; Block Scheduling Handbook; Multilingual Handbook

TECH: Resource Pro, a Teacher’s Resource Planner CD-ROM; Interactive Math: Lessons and Tools CD-ROM; MathSURF Web Site; The Know Zone Web Site; Math Blaster Pre-Algebra CD-ROM; Wide World of

Mathematics; TestWorks: Test and Practice CD-ROM

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• make and evaluate conjectures and arguments using appropriate language

SE/TE: Section 1C: Describing Data, 41-56; Section 5A: Number Theory, 269-286; Section 8C: Transformation, 443-458; Section 12A: Introduction to Probability, 625-640; Section 12B: Fairness, 641-656

• make conclusions based on inductive reasoning

SE/TE: Section 1A: Reading and Interpreting Graphs, 5-22; Section 1B: Displaying Data, 23-40; Section 1C: Describing Data, 41-56; Section 2A: Making Sense of Large Numbers, 65-84; Section 2C: Introduction to Algebra, 109-128; Section 3A: Decimal Concepts, 137-158; Section 5A: Number Theory, 269-286; Section 5B: Connecting Fractions and Decimals, 287-314; Section 8C: Transformation, 443-458; Section 12A: Introduction to Probability, 625-640; Section 12B: Fairness, 641-656

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• justify conclusions involving simple and compound (i.e., and/or) statements

SE/TE: Section 1C: Describing Data, 41-56; Section 5A: Number Theory, 269-286; Section 8C: Transformation, 443-458; Section 12A: Introduction to Probability, 625-640; Section 12B: Fairness, 641-656

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Number Sense & Numeration

Key Idea:Students use NUMBER SENSE AND NUMERATION to develop an understanding of multiple uses of numbers in the real world, use of numbers to communicate mathematically, and use of numbers in the development of mathematical ideas.

• understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, expanded and scientific notation)

SE/TE: Section 2A: Making Sense of Large Numbers, 65-84; Section 3A: Decimal Concepts, 137-158; Section 3B: Adding and Subtracting with Decimals, 159-174; Section 3C: Multiplying and Dividing with Decimals, 175-200; Section 5B: Connecting Fractions and Decimals, 287-314; Section 6A: Adding and Subtracting Fractions, 323-340; Section 6B: Adding and Subtracting Mixed Numbers, 341-351; Section 7A: Multiplying Fractions, 365-380; Section 7B: Dividing Fractions, 381-398; Section 10C: Percents, 549-570 TR: Solutions Manual; Overhead Transparency

Package; Skills Intervention Kit; Test Taking Tips on Transparencies; Reading Strategies for Problem Solving Package; SAT 9

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• understand and apply ratios, proportions, and percents through a wide variety of hands-on explorations

SE/TE: Section 10A: Ratios and Rates, 513-528; Section 10B: Proportions, 529-548; Section 10C: Percents, 549-570

• develop an understanding of numbered theory (primes, factors, and multiples)

SE/TE: Section 5A: Number Theory, 269-286; Section 5B: Connecting Fractions and Decimals, 287-314

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• recognize order relations for decimals, integers, and rational numbers

SE/TE: Lesson 1-6: Stem-and-Leaf Diagrams, 34; Lesson 2-3: Comparing and Ordering Numbers, 74-75; Lesson 3-3: Comparing and Ordering Decimals, 148-149; Lesson 5-8: Comparing and Ordering, 308-309 TR: Solutions Manual; Overhead Transparency

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Mathematical Operations & Relationships

Key Idea:Students use MATHEMATICAL OPERATIONS and RELATIONSHIPS among them to understand mathematics.

• add, subtract, multiply, and divide fractions, decimals, and integers

SE/TE: Section 2B: Number Sense and Operation Sense, 85-108; Section 3B: Adding and Subtracting with Decimals, 159-174; Section 3C: Multiplying and Dividing with Decimals, 175-200; Section 6A: Adding and Subtracting Fractions, 323-340; Section 6B: Adding and Subtracting Mixed Numbers, 341-351; Section 7A: Multiplying Fractions, 365-380; Section 7B: Dividing Fractions, 381-398; Section 10C: Percents, 549-570

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• explore and use the operations dealing with roots and powers

SE/TE: Lesson 2-4: Exponents, 78-79; Lesson 3-4: Scientific Notation, 153-155; Section 4-8: Area of Circles, 250-253; Extend Key Ideas: Measurement, 261, 505; Lesson 5-2: Prime Factorization, 276;

• use grouping symbols (parentheses) to clarify the intended order of operations

SE/TE: Section 2B: Number Sense and Operation Sense, 85-108; Section 2C: Introduction to Algebra, 109-128; Lesson 11-3: Surface Area Formulas, 590

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• apply the associative, commutative, distributive, inverse, and identity properties

• demonstrate an understanding of operational algorithms (procedures for adding, subtracting, etc.)

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• develop appropriate proficiency with facts and algorithms

SE/TE: Section 2B: Number Sense and Operation Sense, 85-108; Section 2C: Introduction to Algebra, 109-128; Section 3B: Adding and Subtracting with Decimals, 159-174; Section 3C: Multiplying and Dividing with Decimals, 175-200; Section 4B: Area of Polygons, 227-244; Section 4C: Circles; Section 6A: Adding and Subtracting Fractions, 323-340; Section 6B: Adding and Subtracting Mixed Numbers, 341-351; Section 7A: Multiplying Fractions, 365-380; Section 7B: Dividing Fractions, 381-398; Section 9B: Graphing on the Coordinate Plane, 487-504

• apply concepts of ratio and proportion to solve problems

SE/TE: Section 10A: Ratios and Rates, 513-528; Section 10B: Proportions, 529-548 TR: Solutions Manual; Overhead Transparency

TECH: Resource Pro, a Teacher’s Resource Planner CD-ROM; Interactive Math: Lessons and

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Mathematical Modeling/ Multiple Representation

Key Idea:Students use MATHEMATICAL MODELING/MULTIPLE REPRESENTATION to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

• visualize, represent, and transform two- and three-dimensional shapes

SE/TE: Section 4B: Area of Polygons, 227-244; Section 4C: Circles; Section 8A: Lines and Angles, 407-422; Section 8B: Polygons, 423-442; Section 8C: Transformation, 443-458; Section 11A: Solids and Surface Area, 579-600; Section 11B: Volume, 601-616 TR: Solutions Manual; Overhead Transparency

• use maps and scale drawings to represent real objects or places

SE/TE: Section 4B: Area of Polygons, 227-244; Section 4C: Circles; Section 8A: Lines and Angles, 407-422; Section 8B: Polygons, 423-442; Section 9B: Graphing on the Coordinate Plane, 487-504; Section 11A: Solids and Surface Area, 579-600; Section 11B: Volume, 601-616

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• use the coordinate plane to explore geometric ideas

SE/TE: Section 9A: Integers, 467-486; Section 9B: Graphing on the Coordinate Plane, 487-504 TR: Solutions Manual; Overhead Transparency

• represent numerical relationships in one- and two-dimensional graphs

SE/TE: Section 1A: Reading and Interpreting Graphs, 5-22; Section 1B: Displaying Data, 23-40; Section 1C: Describing Data, 41-56; Section 9A: Integers, 467-486; Section 9B: Graphing on the Coordinate Plane, 487-504

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• use variables to represent relationships SE/TE: Section 2C: Introduction to Algebra, 109-128 TR: Solutions Manual; Overhead Transparency

• use concrete materials and diagrams to describe the operation of real world processes and systems

SE/TE: Section 1A: Reading and Interpreting Graphs, 5-22; Section 1B: Displaying Data, 23-40; Section 1C: Describing Data, 41-56; Section 9A: Integers, 467-486; Section 9B: Graphing on the Coordinate Plane, 487-504

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• develop and explore models that do and do not rely on chance

SE/TE: Section 12A: Introduction to Probability, 625-640; Section 12B: Fairness, 641-656

• investigate both two- and three-dimensional transformations

SE/TE: Section 8C: Transformation, 443-458 TR: Solutions Manual; Overhead Transparency

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• use appropriate tools to construct and verify geometric relationships

SE/TE: Section 4A: Units of Measurement, 209-226; Section 4B: Area of Polygons, 227-244; Section 4C: Circles; Section 8A: Lines and Angles, 407-422; Section 8B: Polygons, 423-442; Section 8C: Transformation, 443-458; Section 11A: Solids and Surface Area, 579-600; Section 11B: Volume, 601-616 TR: Solutions Manual; Overhead Transparency

• develop procedures for basic geometric constructions

SE/TE: Key Ideas: Geometry, 459

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Measurement

Key Idea:Students use MEASUREMENT in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.

• estimate, make, and use measurements in real-world situations

• select appropriate standard and nonstandard measurement units and tools to measure to a desired degree of accuracy

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• develop measurement skills and informally derive and apply formula in direct measurement activities

• use statistical methods and measures of central tendencies to display, describe, and compare data

SE/TE: Section 1A: Reading and Interpreting Graphs, 5-22; Section 1B: Displaying Data, 23-40; Section 1C: Describing Data, 41-56; Lesson 3-10: Dividing by a Whole Number, 186 TR: Solutions Manual; Overhead Transparency

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• explore and produce graphic representations of data using calculators/ computers

SE/TE: Technology: 242, 440, 568

• develop critical judgment for the reasonableness of measurement

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Ideas of Uncertainty

Key Idea:Students use IDEAS of UNCERTAINTY to illustrate that mathematics involves more than exactness when dealing with everyday situations.

• use estimation to check the reasonableness of results obtained by computation, algorithms, or the use of technology

SE/TE: Section 3B: Adding and Subtracting with Decimals, 159-174; Section 3C: Multiplying and Dividing with Decimals, 175-200; Section 6A: Adding and Subtracting Fractions, 323-340; Section 6B: Adding and Subtracting Mixed Numbers, 341-351; Section 7A: Multiplying Fractions, 365-380; Section 7B: Dividing Fractions, 381-398; Section 10C: Percents, 549-570

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• use estimation to solve problems for which exact answers are inappropriate

SE/TE: Section 3B: Adding and Subtracting with Decimals, 159-174; Section 3C: Multiplying and Dividing with Decimals, 175-200; Section 6A: Adding and Subtracting Fractions, 323-340; Section 6B: Adding and Subtracting Mixed Numbers, 341-351; Section 7A: Multiplying Fractions, 365-380; Section 7B: Dividing Fractions, 381-398; Section 10C: Percents, 549-570

• estimate the probability of events SE/TE: Section 12A: Introduction to Probability, 625-640; Section 12B: Fairness, 641-656

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• use simulation techniques to estimate probabilities

• determine probabilities of independent and mutually exclusive events

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Patterns andFunctions

Key Idea:Students use PATTERNS and FUNCTIONS to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

• recognize, describe, and generalize a wide variety of patterns and functions

SE/TE: Lesson 2-5: Mental Math, 87; Lesson 2-9: Numerical Patterns, 102-106; Extend Key Ideas: Patterns and Relationships, 129, 201; Lesson 4-5: Area of Parallelograms, 236; Chapter 5: Patterns and Number Theory, 266-319

• describe and represent patterns and functional relationships using tables, charts and graphs, algebraic expressions, rules, and verbal descriptions

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• develop methods to solve basic linear and quadratic equations

SE/TE: Section 2B: Number Sense and Operation Sense, 85-108; Section 2C: Introduction to Algebra, 109-128

• develop an understanding of functions and functional relationships: that a change in one quantity (variable) results in change in another

SE/TE: Section 2B: Number Sense and Operation Sense, 85-108; Section 2C: Introduction to Algebra, 109-128

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• verify results of substituting variables SE/TE: Section 2B: Number Sense and Operation Sense, 85-108; Section 2C: Introduction to Algebra, 109-128

• apply the concept of similarity in relevant situations

SE/TE: Lesson 10-7: Similar Figures, 543-546 TR: Solutions Manual; Overhead Transparency

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• use properties of polygons to classify them SE/TE: Section 8B: Polygons, 423-442

• explore relationships involving points, lines, angles, and planes

SE/TE: Section 8A: Lines and Angles, 407-422; Section 8B: Polygons, 423-442; Section 8C: Transformation, 443-458; Section 9B: Graphing on the Coordinate Plane, 487-504 TR: Solutions Manual; Overhead Transparency

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• develop and apply the Pythagorean principle in the solution of problems

SE/TE: Section 8B: Polygons, 423-442; Section 11A: Solids and Surface Area, 579-600; Section 11B: Volume, 601-616

• explore and develop basic concepts of right triangle trigonometry

SE/TE: Section 8B: Polygons, 423-442; Section 11A: Solids and Surface Area, 579-600; Section 11B: Volume, 601-616

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• use patterns and functions to represent and solve problems