Prentice Hall Mathematics: Pre-Algebra 2004 Correlated to: Kentucky Core Content for Mathematics Assessment (Grades 6-8)

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1 Kentucky Core Content for Mathematics Assessment (Grades 6-8) NUMBER/COMPUTATION Concepts Students will describe properties of, define, give examples of, and/or apply to both real-world and mathematical situations: MA-M MA-M MA-M MA-M Rational numbers (integers, fractions, decimals, percents) Irrational numbers (square roots and Π only) Meaning of proportion (equivalent ratios) Place value of whole numbers and decimals SE/TE: 1-4: Integers and Absolute Value, 18-21; 2-1: Rounding and Estimating, ; 4-6: Rational Numbers, ; 5-1: Comparing and Ordering Fractions, ; 6-5: Fractions, Decimals, and Percents, SE/TE: 10-3: Area: Circles, ; 11-1: Square Roots and Irrational Numbers, ; irrational numbers: 621 SE/TE: 6-2: Proportions, SE/TE: Investigation: Exploring Decimals, 126; 3-1: Rounding and Estimating, MA-M Positive whole number exponents SE/TE: 4-2 Exponents, MA-M Representation of numbers and operations in a variety of equivalent forms using models, diagrams, and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences) SE/TE: 1-4: Integers and Absolute Value, 18-21; 1-5: 3-1: Rounding and Estimating, ; 4-2: Exponents, ; 4-4: Simplifying Fractions, ; 4-6: Rational Numbers, ; 4-9: Scientific Notation, ; 5-1: Comparing and Ordering Fractions, ; 5-2: Fractions and Decimals, ; 6-5: Fractions, Decimals, and Percents, ; 11-1: Square Roots and Irrational Numbers, Skills Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: MA-M Add, subtract, multiply, and divide rational numbers (fractions, decimals, percents, integers) to solve problems SE/TE: 1-5: Adding Integers, 24-29; 1-6: Subtracting Integers, 30-34; 1-9: Multiplying and Dividing Integers, 44-48; 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 2-9: Solving Inequalities by Adding or Subtracting,

2 MA-M Add, subtract, multiply, and divide rational numbers (fractions, decimals, percents, integers) to solve problems SE/TE: 2-10: Solving Inequalities by Multiplying or Dividing, ; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-3: Adding and Subtracting Fractions, ; 5-4: Multiplying and Dividing Fractions, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, ; 6-7: Percents and Equations, ; 6-8: Percent of Change, ; 6-9: Markup and Discount, MA-M MA-M Compute (e.g., estimate, use pencil and paper, use calculator, round, use mental math) large and small quantities and check for reasonable and appropriate computational results Apply ratios, proportional reasoning, and percents (e.g., constant rate of change, unit pricing) SE/TE: 1-5: Adding Integers, 24-29; 1-6: Subtracting Integers, 30-34; 1-9: Multiplying and Dividing Integers, 44-48; 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 2-9: Solving Inequalities by Adding or Subtracting, ; 2-10: Solving Inequalities by Multiplying or Dividing, ; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-3: Adding and Subtracting Fractions, ; 5-4: Multiplying and Dividing Fractions, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, ; 6-7: Percents and Equations, ; 6-8: Percent of Change, ; 6-9: Markup and Discount, ; Calculator: 142, 147, 221, 333, 372, 417, 447, 561, 693 SE/TE: 6-1: Ratios and Unit Rates, ; 6-2: Proportions, ; 6-3: Similar Figures and Scale Drawings, ; 6-4: Probability, ; 6-5: Fractions, Decimals, and Percents, ; 6-6: Proportions and Percents, ; 6-7: Percents and Equations, ; 6-8: Percent of Change, ; 6-9: Markup and Discount,

3 MA-M Identify and use number theory concepts [prime numbers, prime factorization, composite numbers, factors, multiples, divisibility, greatest common factor (GCF), least common multiple (LCM)] to solve problems SE/TE: 4-1: Divisibility and Factors, ; 4-3: Prime Factorization and Greatest Common Factor, ; 5-1: Comparing and Ordering Fractions, MA-M Apply order of operations SE/TE: 1-2: The Order of Operations, 8-12; 1-5: Adding Integers, 24-29; 4-2 Exponents, Relationships Students will show connections and how connections are made between concepts and skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: MA-M How whole numbers, natural numbers, integers, fractions, decimals, percents, and irrational numbers (square roots and Π only) relate to each other (e.g., convert between forms of rational numbers, compare, order) SE/TE: 1-4: Integers and Absolute Value, 18-21; 1-5: 3-1: Rounding and Estimating, ; 3-2: Estimating Decimal Products and Quotients, ; 4-2 Exponents, ; 4-4: Simplifying Fractions, ; 4-6: Rational Numbers, ; 4-9: Scientific Notation, ; 5-1: Comparing and Ordering Fractions, ; 5-2: Fractions and Decimals, ; 11-1: Square Roots and Irrational Numbers,

4 MA-M How properties such as commutative, associative, distributive, and identities show relationships among operations and may be used to justify steps in solving problems SE/TE: 2-1: Properties of Numbers, 66-70; 2-2: The Distributive Property, 71-75; 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 2-9: Solving Inequalities by Adding or Subtracting, ; 2-10: Solving Inequalities by Multiplying or Dividing, ; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, ; 7-1: Solving Two-Step Equations, ; 7-2: Solving Multi-Step Equations, ; 7-3: Multi- Step Equations with Fractions and Decimals, ; 7-5: Solving Equations with Variables on Both Sides, ; 7-6: Solving Two-Step Inequalities, ; 7-7: Transforming Formulas, ; 8-2: Equations with Two Variables, ; 8-7: Solving Systems of Linear Equations, MA-M How operations (addition and subtraction; multiplication and division; squaring and taking the square root of a number) are inversely related SE/TE: 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 2-9: Solving Inequalities by Adding or Subtracting, ; 2-10: Solving Inequalities by Multiplying or Dividing, ; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, ; 7-1: Solving Two-Step Equations, ; 7-2: Solving Multi-Step Equations, ; 7-3: Multi-Step Equations with Fractions and Decimals, ; 7-5: Solving Equations with Variables on Both Sides, ; 7-6: Solving Two-Step Inequalities, ; 7-7: Transforming Formulas, ; 8-2: Equations with Two Variables, ; 8-7: Solving Systems of Linear Equations, GEOMETRY/MEASUREMENT 4

5 Concepts Students will describe properties of, define, give examples of, and/or apply to both real-world and mathematical situations: MA-M MA-M MA-M MA-M MA-M Basic geometric elements that include points, segments, rays, lines, angles, and planes Two-dimensional shapes including circles, regular polygons, quadrilaterals (square, rectangle, rhombus, parallelogram, trapezoid), and triangles (acute, obtuse, right, equilateral, scalene, isosceles) Common three-dimensional shapes including spheres, cones, cylinders, prisms (with polygonal bases), and pyramids (with polygonal bases) Congruence, symmetry, and similarity U.S. Customary and metric units of measurement SE/TE: 9-1: Introduction to Geometry Points Lines and Planes, ; 9-2: Angle Relationships and Parallel Lines, SE/TE: 9-3: Classifying Polygons, ; 9-6: Circles, SE/TE: 10-4: Space Figures, SE/TE: 6-3: Similar Figures and Scale Drawings, ; 9-5: Congruence, SE/TE: 3-7: Using the Metric System, ; 5-5: Using Customary Units of Measurement, Skills Students will perform the following mathematical operations and/or procedures accurately and efficiently and explain how they work in real-world and mathematical situations. MA-M MA-M MA-M MA-M Identify characteristics (e.g., sides, vertices, angles, faces, edges, congruent parts) of two-dimensional and three-dimensional shapes Use appropriate tools and strategies (e.g., combining and subdividing shapes) to find measures of both regular and irregular shapes Move shapes in a coordinate plane: translate (slide), rotate (turn), reflect (flip), and dilate (magnify, reduce) Estimate measurements in standard units SE/TE: 9-3: Classifying Polygons, ; 10-4: Space Figures, SE/TE: 9-3: Classifying Polygons, ; Extension: Angles of a Polygon, 475 SE/TE: 9-8: Translations, ; 9-9: Symmetry and Reflections, ; 9-10: Rotations, SE/TE: 3-7: Using the Metric System, ; 5-5: Using Customary Units of Measurement,

6 MA-M Use formulas to find area and perimeter of triangles and quadrilaterals, area and circumference of circles, and surface area and volume of rectangular prisms SE/TE: 10-1: Area: Parallelograms, ; 10-2: Area: Triangles and Trapezoids, ; 10-3: Area: Circles, ; 10-5: Surface Area: Prisms and Cylinders, ; 10-6: Surface Area: Pyramids, Cones, and Spheres, ; 10-7: Volume: Prisms and Cylinders, ; 10-9: Volume: Pyramids, Cones, and Spheres, MA-M MA-M Estimate and determine measurement of angles Use Pythagorean theorem to find hypotenuse SE/TE: 9-1: Introduction to Geometry Points Lines and Planes, ; 9-2: Angle Relationships and Parallel Lines, ; 9-5: Congruence, l 9-7: Constructions, ; 11-7: Angles of Elevation and Depression, SE/TE: 11-2: The Pythagorean Theorem, Relationships Students show connections and how connections are made between concepts and skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: MA-M How measurements and measurement formulas are related or different (perimeter and area; rate, time, and distance; circumference and area of a circle) SE/TE: 10-1: Area: Parallelograms, ; 10-2: Area: Triangles and Trapezoids, ; 10-3: Area: Circles, ; 10-5: Surface Area: Prisms and Cylinders, ; 10-6: Surface Area: Pyramids, Cones, and Spheres, MA-M MA-M MA-M How measurements and measurement formulas are related or different (perimeter and area; rate, time, and distance; circumference and area of a circle) How two-dimensional and threedimensional figures are related as seen in different orientations (e.g., top view, side view, threedimensional shapes drawn on isometric dot paper) How proportional figures are related (scale drawings, similar figures) SE/TE: 10-7: Volume: Prisms and Cylinders, ; 10-9: Volume: Pyramids, Cones, and Spheres, ; 11-3: Distance and Midpoint Formulas, SE/TE: 9-3: Classifying Polygons, ; 10-4: Space Figures, SE/TE: 6-3: Similar Figures and Scale Drawings, PROBABILITY/STATISTICS 6

7 Concepts Students will describe properties of, define, give examples of, and/or apply to both real-world and mathematical situations: MA-M MA-M MA-M Meaning of central tendency (mean, median, mode) Meaning of dispersion (range, cluster, gaps, outliers) Characteristics and appropriateness of graphs (e.g., bar, line, circle), and plots (e.g., line, stem-and-leaf, boxand-whiskers, scatter) SE/TE: 3-3: Mean, Median, and Mode, ; Technology: Mean and Median on a Graphing Calculator SE/TE: 3-3: Mean, Median, and Mode, ; 8-1: Relations and Functions, ; 12-1: Frequency Tables and Line Plots, ; range: 449, 679 SE/TE: 12-1: Frequency Tables and Line Plots, ; 12-2: Box-and-Whisker Plots, ; 12-3: Using Graphs to Persuade, Skills Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: MA-M Organize, represent, analyze, and interpret sets of data SE/TE: 12-1: Frequency Tables and Line Plots, ; 12-2: Box-and-Whisker Plots, ; 12-3: Using Graphs to Persuade, ; Problem-Solving Strategies: Make a Table, , 341 MA-M MA-M MA-M Construct and interpret displays of data (e.g., table, circle graph, line plot, stem-and-leaf plot, box-andwhiskers plot) Find mean, median, mode, and range; recognize outliers, gaps, and clusters of data Calculate theoretical probabilities and tabulate experimental results from simulations SE/TE: 12-1: Frequency Tables and Line Plots, ; 12-2: Box-and-Whisker Plots, ; 12-3: Using Graphs to Persuade, ; Problem-Solving Strategies: Make a Table, , 341 SE/TE: 3-3: Mean, Median, and Mode, ; 8-1: Relations and Functions, ; 12-1: Frequency Tables and Line Plots, ; range: 449, 679; 12-2: Box-and-Whisker Plots, ; 12-3: Using Graphs to Persuade, SE/TE: 12-4: Counting Outcomes and Theoretical Probability, ; 12-5: Independent and Dependent Events, ; 12-7: Experimental Probability,

8 MA-M Make predictions and draw conclusions from statistical data and probability experiments SE/TE: 12-4: Counting Outcomes and Theoretical Probability, ; 12-5: Independent and Dependent Events, ; 12-7: Experimental Probability, ; 12-8: Random Samples and Surveys, MA-M MA-M Use counting techniques, tree diagrams, area models, and tables to solve probability problems Represent probabilities in multiple ways such as fractions, decimals, percents, and area models SE/TE: 12-4: Counting Outcomes and Theoretical Probability, ; 12-5: Independent and Dependent Events, ; 12-6: Permutations and Combinations, SE/TE: 12-4: Counting Outcomes and Theoretical Probability, ; 12-5: Independent and Dependent Events, ; 12-7: Experimental Probability, Relationships Students will show connections and how connections are made between concepts and skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: MA-M MA-M How different representations of data (e.g. tables, graphs, diagrams, plots) are related How theoretical probability and experimental probability are related SE/TE: 12-1: Frequency Tables and Line Plots, ; 12-2: Box-and-Whisker Plots, ; 12-3: Using Graphs to Persuade, ; Problem-Solving Strategies: Make a Table, , 341 SE/TE: 12-4: Counting Outcomes and Theoretical Probability, ; 12-7: Experimental Probability, MA-M MA-M How data gathering, bias issues, faulty data analysis, and misleading representations affect interpretations and conclusions about data (e.g., changing the scale on a graph, polling only a specific group of people, using limited or extremely small sample size) How probability and statistics are used to make predictions and/or draw conclusions SE/TE: 12-1: Frequency Tables and Line Plots, ; 12-2: Box-and-Whisker Plots, ; 12-3: Using Graphs to Persuade, ; 12-8: Random Samples and Surveys, ; Problem-Solving Strategies: Make a Table, , 341 SE/TE: 12-4: Counting Outcomes and Theoretical Probability, ; 12-5: Independent and Dependent Events, ; 12-7: Experimental Probability, ; 12-8: Random Samples and Surveys, ALGEBRAIC IDEAS 8

9 Concepts Students will describe properties of, define, give examples of, and/or apply to both real-world and mathematical situations: MA-M Variables, equations, inequalities, and algebraic expressions SE/TE: 1-1: Variables and Expressions, 4-7; 1-3: Evaluating Expressions, 14-17; 2-3: Simplifying Variable Expressions, 76-78; 2-4: Variables and Equations, 80-83; 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 2-8: Inequalities and Their Graphs, ; 2-9: Solving Inequalities by Adding or Subtracting, ; 2-10: Solving Inequalities by Multiplying or Dividing, ; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, ; 7-1: Solving Two-Step Equations, ; 7-2: Solving Multi-Step Equations, ; 7-3: Multi- Step Equations with Fractions and Decimals, ; 7-5: Solving Equations with Variables on Both Sides, ; 7-6: Solving Two-Step Inequalities, ; 8-7: Solving Systems of Linear Equations, ; 8-8: Graphing linear Inequalities, MA-M MA-M Functions (e.g., the relationship between time and cost of some long distance phone calls, y = 2x + 1) through tables, graphs, verbal rules, and algebraic notations Rectangular (Cartesian) coordinate system/grid and ordered pairs SE/TE: 8-1: Relations and Functions, ; 8-4: Writing Rules for Linear Functions, ; 13-1: 13-2: Graphing Nonlinear Functions, ; 13-3: Exponential Growth and Decay, SE/TE: 1-10: The Coordinate Plane, 50-54; 2-8: Inequalities and Their Graphs, ; 8-3: Slope and y-intercept, ; 8-8: Graphing linear Inequalities, ; 13-2: Graphing Nonlinear Functions, Skills Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: 9

10 MA-M Simplify numerical and algebraic expressions SE/TE: 1-1: Variables and Expressions, 4-7; 1-3: Evaluating Expressions, 14-17; 2-3: Simplifying Variable Expressions, 76-78; 4-8: Exponents and Division, ; Technology: Evaluating Expressions with Graphing Calculators, 209 MA-M MA-M Solve simple equations and inequalities Model equations and inequalities concretely (e.g., algebra tiles or blocks), pictorially (e.g., graphs, tables), and abstractly (e.g., equations) SE/TE: 12-4: Variables and Equations, 80-83; 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 2-8: Inequalities and Their Graphs, ; 2-9: Solving Inequalities by Adding or Subtracting, ; 2-10: Solving Inequalities by Multiplying or Dividing, ; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, SE/TE: 12-4: Variables and Equations, 80-83; 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 2-8: Inequalities and Their Graphs, ; 2-9: Solving Inequalities by Adding or Subtracting, ; 2-10: Solving Inequalities by Multiplying or Dividing, ; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, MA-M MA-M Model equations and inequalities concretely (e.g., algebra tiles or blocks), pictorially (e.g., graphs, tables), and abstractly (e.g., equations) Use variables to describe numerical patterns SE/TE: 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, SE/TE: 13-1: Patterns and Sequences, ; Technology: Displaying Sequences, 693; 13-2: Graphing Nonlinear Functions, ; 13-3: Exponential Growth and Decay,

11 MA-M Represent and use functions through tables, graphs, verbal rules, and equations SE/TE: 8-1: Relations and Functions, ; 8-4: Writing Rules for Linear Functions, ; 13-2: Graphing Nonlinear Functions, ; 13-3: Exponential Growth and Decay, MA-M Write and solve equations that represent everyday situations SE/TE: 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, ; Problem-Solving Strategies: Write an Equation, 80, 81, 87, 88, 92, 103, 107, 111, 149, 152, 158, 264, 321, 353, , 368, 374, 390, 418, 442, 620 Relationships Students will show connections and how connections are made between concepts and skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: MA-M MA-M How everyday situations, tables, graphs, patterns, verbal rules, and equations relate to each other How everyday situations, tables, graphs, patterns, verbal rules, and equations relate to each other SE/TE: 2-5: Solving Equations by Adding or Subtracting, 86-90; 2-6: Solving Equations by Multiplying or Dividing, 92-95; 3-5: Solving Equations by Adding or Subtracting Decimals, ; 3-6: Solving Equations by Multiplying or Dividing Decimals, ; 5-7: Solving Equations by Adding or Subtracting Fractions, ; 5-8: Solving Equations by Multiplying Fractions, ; 8-1: Relations and Functions, ; 8-4: Writing Rules for Linear Functions, ; 12-1: Frequency Tables and Line Plots, ; 12-2: Box-and-Whisker Plots, SE/TE: 12-3: Using Graphs to Persuade, ; 13-2: Graphing Nonlinear Functions,

12 MA-M How the change in one variable affects the change in another variable (e.g., if rate remains constant, an increase in time results in an increase in distance SE/TE: 6-1: Ratios and Unit Rates, ; 6-8: Percent of Change, ; 8-1: Relations and Functions, ; 8-4: Writing Rules for Linear Functions, ; 13-2: Graphing Nonlinear Functions,

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