Prentice Hall Hawaii Mathematics Content and Performances Standards (HCPS) II (Grades 9-12) Hawaii Content and Performance Standards II* NUMBER AND OPERATIONS STANDARD 1: Students understand numbers, ways of representing numbers, relationships among numbers, and number systems. 9-12 Recognize and use real and complex numbers and infinity. Represent real and complex numbers variously (e.g.., number line, coordinate plane, rational exponents, and logarithms). Model situations appropriately with vectors or matrices. 1. Writes solutions to problem notation which indicates recognition of type of answer, real or complex (a + bi notation). 2. Uses the concept of infinity in a number of ways (e.g., unbounded behavior of functions, sequences, as a limit for a variable). PRENTICE HALL 1-3 Exploring Real Numbers17-23, 68 5-6 Describing Number Patterns, 8-6 Geometric Sequences, Extension: Determining Limits, 268-272, 277, 424-429, 449, 495, 651 1
Prentice Hall (Continued) 3. Represents real or complex numbers in various ways (e.g., graph, rational exponents, logarithms). 4. Uses vectors or matrix operations to solve problems. (Continued) 1-2 Exponents and Order of Operations, 1-3 Exploring Real Numbers, 1-4 Adding Real Numbers, 1-5 Subtracting Real Numbers, 1-7 The Distributive Property 1-8 Properties of Real Numbers, 1-9 Graphing Data on the Coordinate Plane, 3-1 Inequalities and Their Graphs, 3-2 Solving Inequalities Using Addition and Subtraction, 3-3 Solving Inequalities Using Multiplication and Division, 3-4 Solving Multi-Step Inequalities, Extension: Interpreting Solutions, 9, 17-21, 24-25, 27, 32-34, 47-52, 54-55, 59-60, 135-139, 140-145, 147-150, 160, 161-165, 169-172, 175-178, 196, 394-423, 447-448, 450, 471, 524-528, 578-583, 620, 3-5 Compound Inequalities, 3-6 Absolute Value Equations and Inequalities, Investigation: Modeling Percents, 8-1 Zero and Negative Exponents,8-2 Scientific Notation, 8-3 Multiplication Properties of Exponents, 8-4 More Multiplication Properties of Exponents, 8-5 Division Properties of Exponents, 8-5 Multiplying Exponents, 9-3 Multiplying Binomials, 10-3 Finding and Estimating Square Roots, 11-1 Simplifying Radicals, Extension: Rational Exponent 1-4 Adding Real Numbers, 1-5 Subtracting Real Numbers, 1-6 Multiplying and Dividing Real Numbers 27, 30, 35, 43 2
Prentice Hall STANDARD 2: Students understand the meaning of operations and how they relate to each other. Add, subtract and scalar multiply vectors. Represent and operate with matrices no larger that 3x3. 1. Adds, subtracts, and scalar multiplies matrices. 2. Uses inverses of matrices to solve problems. STANDARD 3: Students use computational tools and strategies fluently and when appropriate, use estimation 1-4 Adding Real Numbers, 1-5 Subtracting Real Numbers, 1-6 Multiplying and Dividing Real Numbers 27, 30, 35, 36, 43, 45, 65, 70, 115, 329 Technology: Matrices and Solving Systems, 360-361 Recognize conditions governing use of formulas (e.g., discriminant in the quadratic formula). Identify computational limitation of calculators and computers (e.g., dividing by small numbers). Understand the effects of measurement error on computed values. Analyze effects of rounding in various situations. Use vectors or matrices to solve problems. 1. In the use of formulas, indicates conditions when a given formula can be used (e.g., when the discriminant of a quadratic formula is negative, solutions will be complex). 2. Explains or provides examples of the limitations of calculators and computers in solving problems. 3. Explains that rounding answers in certain real world situations may lead to major problems (e.g., a rocket missing the moon, a bridge collapsing). 4. Use vector or matrix operations to solve problems. 10-7 Using the Quadratic Formula, Reading Math: Using a Formula, 10-8 Using the Discriminant, 547-552, 553, 554-547 4-4 Percent of Change 205-207 1-4 Adding Real Numbers, 1-5 Subtracting Real Numbers, 1-6 Multiplying and Dividing Real Numbers, Technology: Matrices and Solving Systems 30, 35, 43, 361 3
MEASUREMENT Prentice Hall STANDARD 1: Students understand attributes, units, systems of units in measurement; and develop and use techniques, tools, and formulas for measuring. 4-1 Ratio and Proportion, 6-1 Rate of 1. Expresses rates of change as a ratio of two different measures, where units are included in the ratio. Change and Slope 182-183, 186-187, 227, 282-289, 331 Explain rate of change as a quotient of two different measures (e.g., velocity = change in displacement/change in time). Use degree measures in problem situations. Determine precision, accuracy and measurement errors; identify sources and magnitudes of possible errors in a measurement setting; describe how errors can propagate within computations; and determine how much imprecision is reasonable in various measurements. Experimentally determine and use formulas for the volume of a sphere, cylinder, and cone. Apply limit concepts to develop concepts of area under a curve and instantaneous rate of change. Combine measurements using multiplication or ratios to produce measurements such as force, work, velocity, acceleration, density, pressure, or trigonometric ratios. 2. Solves problems involving degree measures. 3. Completes an error analysis for measurement data by (a) determining precision, accuracy and measurement errors; and (b) identifying sources and magnitudes of possible errors. 4. Describes how errors can compound with multiple computations in a problem. 5. Solves problems using formulas for the volume of a sphere, cylinder and cone. 2-1 Solving One-Step Equations, 2-2 Solving Two-Step Equations, 2-3 Solving Multi-Step Equations, 2-4 Equations with Variables on Both Sides, Chapter 7 Review, 11-7 Trigonometric Ratios 79, 85, 92, 98, 388, 621-627, 631, 632 1-2 Exponents and Order of Operations, 2-6 Formulas, 9-2 Multiplying and Factoring, 9-4 Multiplying Special Cases, 9-8 Factoring by Grouping, Extension: Cubic Functions, Skills Handbook: Perimeter, Area, and Volume 14, 113, 465, 478, 500, 567, 572, 731 4
Prentice Hall 6. Solves problems involving formulas used in science, business, or math applications (e.g., force, work, velocity, acceleration, density, pressure, or trigonometric ratios. 1-3 Exploring Real Numbers, 1-6 Multiplying and Dividing Real Numbers, 2-5 Equations and Problem Solving, 2-6 Formulas, Extension: Developing Geometric Formulas, Real- World Snapshots: Shifting Gears, 3-5 Compound Inequalities, 4-1 Ratio and Proportion, 4-3 Proportions and Percent Equations, 4-4 Percent of Change, 5-5 Direct Variation, 7-3 Solving Systems Using Elimination, 9-8 Factoring by Grouping,10-1 Exploring Quadratic Graphs, 10-2 Quadratic Functions, 10-3 Finding and Estimating Square Roots, 10-8 Using the Discriminant, 11-5 Solving Radical Equations, 11-7 Trigonometric Ratios, 12-1 Inverse Variation, 12-2 Graphing Rational Functions, 12-7 Solving Rational Equations, 11-2 The Pythagorean Theorem22, 43, 103-110, 111-114, 116-117, 127, 130, 164, 187, 201, 203, 206-208, 228, 266, 359, 498-501, 515, 518-519,526, 527, 532-533, 538, 549-551, 555-557, 584-589, 611, 621-627, 631, 632, 641, 642, 649, 676 5
GEOMETRY AND SPATIAL SENSE Prentice Hall STANDARD 1: Students analyze properties of objects and relationships among the properties. Make and evaluate conjectures about, and solve problems involving classes of two- and three-dimensional objects (e.g., Are all squares rectangles? (None for this course) STANDARD 2: Students use transformations and symmetry to analyze mathematical situations. 4-2 Proportions and Similar Figures, 11-2 The Pythagorean Theorem, Extension: Special Right Triangles, 9-2 Multiplying and Factoring, 9-3 Multiplying Binomials, 9-4 Multiplying Special Cases, 9-6 Factoring Trinomials of the Type ax 2 +bx+c, 9-8 Factoring by Grouping, 12-3 Simplifying Rational Expressions, 12-4 Multiplying and Dividing Rational Expressions, 12-5 Dividing Polynomials,189-195, 462, 467-471, 474, 477, 479, 488, 498-501, 584-589, 598-599, 613, 655, 660, 665 Represent transformations of objects in the plane with coordinates, vectors, or matrices; describe the effects of a given transformation. Apply transformations to threedimensional objects. (None for this course) 6-7 Graphing Absolute Value Equations, 11-6 Graphing Square Root Functions, Skills Handbook: Translations, Skills Handbook: Reflections, Skills Handbook: Rotations, 325-329, 333, 334, 345, 423, 615-617, 732, 733, 734 6
Prentice Hall.STANDARD 3: Students use visualization and spatial reasoning to solve problems both within and outside of mathematics Sketch three-dimensional objects and spaces from different perspective and (None for this course) interpret two- and three-dimensional drawings of objects. Analyze and describe cross-sections, truncations, and compositions/decompositions of threedimensional objects. STANDARD 4: Students select and use different representational systems, including coordinate geometry 10-5 Factoring to Solve Quadratic Equations, 11-5 Solving Radical Equations 537, 611, 613 Solve problems involving two- and three-dimensional figures. Analyze and apply coordinate systems on a sphere (distance and place on the earth s surface, positions of stars in heavens). PATTERNS, FUNCTIONS, AND ALGEBRA 1. Solves problems involving two- and three dimensional figures using coordinate geometry. 6-5 Parallel and Perpendicular Lines, 11-3 The Distance and Midpoint Formulas 316, 591-596 STANDARD 1: Students understand various types of patterns and functional relationships. Describe and use relations and functions (e.g., absolute value, piecewise defined, step, trigonometric, logarithmic, exponential, polynomial). Analyze and use linear relations among three variables. Analyze and use quadratic relations between two variables. 1. Performs operations on functions (e.g., addition, subtraction, multiplication, division, composition, inverse). 7
Prentice Hall 2. Determines properties of relations and functions that may include some or all of the following: domain, range, symmetry, asymptotes, points of discontinuity, relative maximum/minimum values, zeroes, intercepts, concavity, points of inflection). 3. Graphs relations and functions using their properties. 5-2 Relations and Functions, 6-2 Slope- Intercept Form, 6-3 Standard Form, 6-4 Point-Slope Form and Writing Linear Equations, 6-5 Parallel Lines and Perpendicular Lines, 10-1 Exploring Quadratic Graphs, 10-2 Quadratic Functions, 10-4 Solving Quadratic Equations, Technology: Finding Roots, 10-5 Factoring to Solve Quadratic Equations, 10-6 Completing the Square, 10-7 Using the Quadratic Formula, Extension: Cubic Functions, 12-2 Graphing Rational Functions, 241-246, 275-278, 290-296, 298-302, 304-309, 311-316, 510-523, 529-553, 567, 569-572, 644-650 6-1 Rate of Change and Slope, 6-2 Slope- Intercept Form, 6-3 Standard Form, 6-4 Point-Slope Form and Writing Linear Equations, 12-2 Graphing Rational Functions, 275-278, 282-289, 290-296, 298-302, 304-309, 644-650 8
Prentice Hall 4. Uses relations and functions to solve problems. 5-5 Direct Variation, 7-1 Solving Systems by Graphing, 7-2 Solving Systems by Using Substitution, Solving Systems Using Elimination, 10-6 Completing the Square, 10-7 Using the Quadratic Formula, Extension: Cubic Functions, 11-5 Solving Radical Equations; 12-1 Inverse Variation, 12-2 Graphing Rational Equations, 260-265, 275-278, 340-345, 347-359, 362-368, 370-385, 387-390, 423, 430-435, 437-444, 449, 450, 529-553, 567, 569-572, 607-611, 637-642, 644-650, 5. Represents and uses arithmetic, geometric and other sequences and series. 6. Analyzes quadratic relations between two variables 7. Uses quadratic relations with two variables to solve problems. 5-6 Describing Number Patterns, 8-6 Geometric Sequences, 268-272, 275-278, 424-429, 449, 450 7-2 Solving Systems Using Substitution, 351 10-1 Exploring Quadratic Graphs, 10-2 Quadratic Functions, 510-523, 569-572 9
Prentice Hall.STANDARD 2: Students use symbolic forms to represent, model, and analyze mathematical situations Represent relations and functions with graphs, tables, and symbolic rules and 1. Represents relations and functions with translate among these representations. graph, tables of values, and symbolic Model phenomena with a variety of rules and translates among these functions and explain how and why a representations. particular function can model many different situations. Approximate and interpret accumulation and rates of change for functions representing a variety of situations (e.g., compound interest). 1. Determines which function best fits a given situation and justifies that choice of function. 2. Describes several different situations that can be represented by the same type of function and justifies the function used. 1-1 Using Variables, 5-3 Function Rules, Tables, and Graphs, Technology: Function Rules, Tables, and Graphs, 5-4 Writing a Function Rule, 5-5 Direct Variation, Technology: Investigating y=mx+b, 6-4 Point-Slope Form and Writing Equations, 6-5 Parallel and Perpendicular Lines, 6-7 Graphing Absolute Value Equations, 11-6 Graphing Square Root Functions, 12-1 Inverse Variation, Technology: Graphing Rational Functions, 4-8, 23, 247-258, 260-265, 267, 276-278, 290, 304-309, 315-316, 325-329, 332-334, 614-618, 639-641, 643 5-1 Relating Graphs to Events, 8-8 Exponential Growth and Decay, 236-240, 442 10
Prentice Hall DATA ANALYSIS, STATISTICS, AND PROBABILITY STANDARD 1: Students pose questions and collect, organize, and represent data to answer those questions. Design and carry out investigations or experiments with two variables. Select appropriate methods for collecting, recording, organizing, and representing data; and describe how a change in representation affects the likely interpretation of the information. 1. Identifies purpose of investigation of experiment by stating hypothesis or posing questions. 2. Identifies two variables in an investigation or experiment. 3. Creates a survey instrument, if applicable, where: a. The sample population is identified. b. The sampling method is described. 4. Outlines a plan for organizing and representing data. 5. Collects and organizes data (e.g., makes tables, graphs). 6. Describes potentially misleading interpretations that may by due to different types of representation. Skills Handbook: Conducting a Survey, 745 2-7 Using Measures of Central Tendency, Extension: Sampling, Skills Handbook: Line Plots, Skills Handbook: Bar Graphs, Skills Handbook: Histograms, Skills Handbook: Line Graphs, Skills Handbook: Circle Graphs, Skills Handbook: Box-and-Whisker Plots, Skills Handbook: Choosing an Appropriate Graph, 120-123, 225, 735, 736, 737, 738, 739, 740, 741 Skills Handbook: Misleading Graphs 742 11
Prentice Hall.STANDARD 2: Students interpret data using methods of exploratory data analysis Compute, identify and interpret measures of center and spread (including standard deviation) Look for patterns in data and understand their use in interpretation of the data. Explain how sample size or transformations of data affect shape, center, and spread. Explain trends and use technology to determine how well different models fit data (e.g., line of best fit). 1. Computes and identifies measures of center and spread (including standard deviation). 2. Describes the population using measures of central tendency and spread. 3. Describes trends in data and uses them to interpret data (e.g., positive or negative correlation). 4. Explains how sample size or transformations of data affect shape, center and spread. 5. Uses technology to find the line or curve of best fit for data collected. STANDARD 3: Students develop and evaluate inferences, predictions, and arguments that are based on data. Identify good models for phenomena (e.g., exponential model for population growth). Apply models to predict unobserved outcomes. Evaluate conclusions based on data and support inferences with valid 1. Identifies what best fits the data provided (e.g., linear (amount of sales tax), quadratic (height of bouncing ball), exponential (growth of certificates of deposit), sinusoidal (tides, number of daylight hours throughout the year)). arguments. 2. Identifies functions and interpolates or extrapolates data to predict unobserved outcomes. 2-7 Using Measures of Central Tendency, 8-123, 127, 128, 139 1-9 Graphing Data on the Coordinate Plane, -64, 69, 70 2-7 Using Measures of Central Tendency 122 6-6 Scatter Plots and Equations of Lines, Technology: Fitting Exponential Curves to Data, 18-324, 329, 333, 334, 399, 436, 495 Algebra 1 2004 10-9 Choosing a Linear, Quadratic, or Exponential Model 559-565, 571-572 8-7 Exponential Functions, 8-8 Exponential Growth and Decay, 10-9 Choosing a Linear, Quadratic, or Exponential Model, 0-435, 437-444, 564 12
Prentice Hall (Continued) 3. Identifies predictions, inferences, or conclusions..standard 4: Students understand and apply basic notions of chance and probability Identify relationships among events (e.g., inclusion, disjoint, complementary, independent, and dependent). Compute probabilities of two events under different relationships unions and intersections. Use fundamental counting principle, permutations, and combinations as counting techniques to solve problems. Compute the theoretical probabilities of repeated experiments with replacement and repeated experiments without replacement. Recognize random variables in real situations (e.g., insurance, life expectancy) and estimate and compute expectations. 1. Identifies relationships among events (e.g., inclusion, disjoint, complementary, independent, and dependent). 2. Calculates probabilities of two events under union and intersection 3. Applies permutations, combinations, and the fundamental counting principle to calculate probabilities of events. 4. Calculates theoretical probabilities of repeated experiments with and without replacement. 5. Examines real life situations and determines if any random variable plays a major role. 6. Estimates and calculates expected values. 4-5 Applying Ratios to Probability, 4-6 Probability of Compound Events, 212-215, 220-223, 229, 230 4-6 Probability of Compound Events, 219-223 12-8 Counting Methods and Permutations, 12-9 Combinations, 679-685, 686-691 Investigation: Understanding Probability, 4-5 Applying Ratios to Probability, 4-6 Probability of Compound Events, 210, 212-216, 220-223, 229, 230 13