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

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1 New York Mathematics Learning Standards (Intermediate) 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, ; Section 2C: Introduction to Algebra, ; Section 3A: Decimal Concepts, ; Section 5A: Number Theory, ; Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 1

2 make and evaluate conjectures and arguments using appropriate language make conclusions based on inductive reasoning SE/TE: Section 1C: Describing Data, 41-56; Section 5A: Number Theory, ; Section 8C: Transformation, ; Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 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, ; Section 3A: Decimal Concepts, ; Section 5A: Number Theory, ; Section 5B: Connecting Fractions and Decimals, ; Section 8C: Transformation, ; Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 2

3 justify conclusions involving simple and compound (i.e., and/or) statements SE/TE: Section 1C: Describing Data, 41-56; Section 5A: Number Theory, ; Section 8C: Transformation, ; Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 3

4 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, ; Section 3B: Adding and Subtracting with Decimals, ; Section 3C: Multiplying and Dividing with Decimals, ; Section 5B: Connecting Fractions and Decimals, ; Section 6A: Adding and Subtracting Fractions, ; Section 6B: Adding and Subtracting Mixed Numbers, ; Section 7A: Multiplying Fractions, ; Section 7B: Dividing Fractions, ; Section 10C: Percents, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 4

5 understand and apply ratios, proportions, and percents through a wide variety of hands-on explorations develop an understanding of numbered theory (primes, factors, and multiples) SE/TE: Section 10A: Ratios and Rates, ; Section 10B: Proportions, ; Section 10C: Percents, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 5A: Number Theory, ; Section 5B: Connecting Fractions and Decimals, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 5

6 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, ; Lesson 5-8: Comparing and Ordering, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 6

7 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, ; Section 3B: Adding and Subtracting with Decimals, ; Section 3C: Multiplying and Dividing with Decimals, ; Section 6A: Adding and Subtracting Fractions, ; Section 6B: Adding and Subtracting Mixed Numbers, ; Section 7A: Multiplying Fractions, ; Section 7B: Dividing Fractions, ; Section 10C: Percents, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 7

8 explore and use the operations dealing with roots and powers use grouping symbols (parentheses) to clarify the intended order of operations SE/TE: Lesson 2-4: Exponents, 78-79; Lesson 3-4: Scientific Notation, ; Section 4-8: Area of Circles, ; Extend Key Ideas: Measurement, 261, 505; Lesson 5-2: Prime Factorization, 276; ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 2B: Number Sense and Operation Sense, ; Section 2C: Introduction to Algebra, ; Lesson 11-3: Surface Area Formulas, 590 ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 8

9 apply the associative, commutative, distributive, inverse, and identity properties demonstrate an understanding of operational algorithms (procedures for adding, subtracting, etc.) SE/TE: Section 2B: Number Sense and Operation Sense, ; Section 2C: Introduction to Algebra, ; Lesson 11-3: Surface Area Formulas, 590 ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 2B: Number Sense and Operation Sense, ; Section 2C: Introduction to Algebra, ; Lesson 11-3: Surface Area Formulas, 590 ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 9

10 develop appropriate proficiency with facts and algorithms apply concepts of ratio and proportion to solve problems SE/TE: Section 2B: Number Sense and Operation Sense, ; Section 2C: Introduction to Algebra, ; Section 3B: Adding and Subtracting with Decimals, ; Section 3C: Multiplying and Dividing with Decimals, ; Section 4B: Area of Polygons, ; Section 4C: Circles; Section 6A: Adding and Subtracting Fractions, ; Section 6B: Adding and Subtracting Mixed Numbers, ; Section 7A: Multiplying Fractions, ; Section 7B: Dividing Fractions, ; Section 9B: Graphing on the Coordinate Plane, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 10A: Ratios and Rates, ; Section 10B: Proportions, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 10

11 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 use maps and scale drawings to represent real objects or places SE/TE: Section 4B: Area of Polygons, ; Section 4C: Circles; Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 8C: Transformation, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 4B: Area of Polygons, ; Section 4C: Circles; Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 9B: Graphing on the Coordinate Plane, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 11

12 use the coordinate plane to explore geometric ideas represent numerical relationships in one- and two-dimensional graphs SE/TE: Section 9A: Integers, ; Section 9B: Graphing on the Coordinate Plane, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 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, ; Section 9B: Graphing on the Coordinate Plane, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 12

13 use variables to represent relationships SE/TE: Section 2C: Introduction to Algebra, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 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, ; Section 9B: Graphing on the Coordinate Plane, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 13

14 develop and explore models that do and do not rely on chance investigate both two- and three-dimensional transformations SE/TE: Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 8C: Transformation, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 14

15 use appropriate tools to construct and verify geometric relationships develop procedures for basic geometric constructions SE/TE: Section 4A: Units of Measurement, ; Section 4B: Area of Polygons, ; Section 4C: Circles; Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 8C: Transformation, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Key Ideas: Geometry, 459 ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 15

16 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 realworld situations select appropriate standard and nonstandard measurement units and tools to measure to a desired degree of accuracy SE/TE: Section 4A: Units of Measurement, ; Section 4B: Area of Polygons, ; Section 4C: Circles; Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 8C: Transformation, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 4A: Units of Measurement, ; Section 4B: Area of Polygons, ; Section 4C: Circles; Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 8C: Transformation, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 16

17 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 4A: Units of Measurement, ; Section 4B: Area of Polygons, ; Section 4C: Circles; Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 8C: Transformation, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 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 ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 17

18 explore and produce graphic representations of data using calculators/ computers develop critical judgment for the reasonableness of measurement SE/TE: Technology: 242, 440, 568 ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 4A: Units of Measurement, ; Section 4B: Area of Polygons, ; Section 4C: Circles; Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 8C: Transformation, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 18

19 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, ; Section 3C: Multiplying and Dividing with Decimals, ; Section 6A: Adding and Subtracting Fractions, ; Section 6B: Adding and Subtracting Mixed Numbers, ; Section 7A: Multiplying Fractions, ; Section 7B: Dividing Fractions, ; Section 10C: Percents, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 19

20 use estimation to solve problems for which exact answers are inappropriate SE/TE: Section 3B: Adding and Subtracting with Decimals, ; Section 3C: Multiplying and Dividing with Decimals, ; Section 6A: Adding and Subtracting Fractions, ; Section 6B: Adding and Subtracting Mixed Numbers, ; Section 7A: Multiplying Fractions, ; Section 7B: Dividing Fractions, ; Section 10C: Percents, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The estimate the probability of events SE/TE: Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 20

21 use simulation techniques to estimate probabilities determine probabilities of independent and mutually exclusive events SE/TE: Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 12A: Introduction to Probability, ; Section 12B: Fairness, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 21

22 Patterns and Functions 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 describe and represent patterns and functional relationships using tables, charts and graphs, algebraic expressions, rules, and verbal descriptions SE/TE: Lesson 2-5: Mental Math, 87; Lesson 2-9: Numerical Patterns, ; Extend Key Ideas: Patterns and Relationships, 129, 201; Lesson 4-5: Area of Parallelograms, 236; Chapter 5: Patterns and Number Theory, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Lesson 2-5: Mental Math, 87; Lesson 2-9: Numerical Patterns, ; Extend Key Ideas: Patterns and Relationships, 129, 201; Lesson 4-5: Area of Parallelograms, 236; Chapter 5: Patterns and Number Theory, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 22

23 develop methods to solve basic linear and quadratic equations 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, ; Section 2C: Introduction to Algebra, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 2B: Number Sense and Operation Sense, ; Section 2C: Introduction to Algebra, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 23

24 verify results of substituting variables SE/TE: Section 2B: Number Sense and Operation Sense, ; Section 2C: Introduction to Algebra, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The apply the concept of similarity in relevant situations SE/TE: Lesson 10-7: Similar Figures, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 24

25 use properties of polygons to classify them SE/TE: Section 8B: Polygons, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The explore relationships involving points, lines, angles, and planes SE/TE: Section 8A: Lines and Angles, ; Section 8B: Polygons, ; Section 8C: Transformation, ; Section 9B: Graphing on the Coordinate Plane, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 25

26 develop and apply the Pythagorean principle in the solution of problems explore and develop basic concepts of right triangle trigonometry SE/TE: Section 8B: Polygons, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The SE/TE: Section 8B: Polygons, ; Section 11A: Solids and Surface Area, ; Section 11B: Volume, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 26

27 use patterns and functions to represent and solve problems SE/TE: Lesson 2-5: Mental Math, 87; Lesson 2-9: Numerical Patterns, ; Extend Key Ideas: Patterns and Relationships, 129, 201; Lesson 4-5: Area of Parallelograms, 236; Chapter 5: Patterns and Number Theory, ; Interactive Math: Lessons and Tools ; MathSURF Web Site; The 27

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