Prentice Hall Pre-Algebra 2004 Correlated to: Hawaii Mathematics Content and Performance Standards (HCPS) II (Grades 9-12)

Transcription

1 Hawaii Mathematics Content and Performance Standards (HCPS) II (Grades 9-12) NUMBER AND OPERATIONS STANDARD 1: Students understand numbers, ways of representing numbers, relationships among numbers, and number systems. 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. Uses the concept of infinity in a number of ways (e.g., unbounded behavior of functions, sequences, as a limit for a variable). 2. Represents real or complex numbers in various ways (e.g., graph, rational exponents, logarithms). STANDARD 2: Students understand the meaning of operations and how they relate to each other. 2. Add, subtract and scalar multiply vectors. 1. Adds, subtracts, and scalar 3. Represent and operate with matrices no multiplies matrices. larger that 3x3. SE/TE: 1.4 Integers and Absolute Value, Investigation: Modeling Integers, 1-5 Adding Integers, 1-6 Subtracting Integers, 2-2 The Distributive Property, 2-3 Simplifying Variable Expression, Investigation: Using Models with Equations, Review: Writing and Comparing Decimals, 4-2 Exponents, 4-6 Rational Numbers, 4-7 Exponents and Multiplication, 4-8 Exponents and Division, 4-9 Scientific Notation, Technology: Scientific Notation with Calculators, 5-1 Comparing and Ordering Fractions, 5-2 Fractions and Decimals, 5-3 Adding and Subtracting Fractions, 5-9 Powers of Products and Quotients, 11-1 Square Roots and Irrational Numbers SE/TE: Extension: Matrices and Translations 1

2 STANDARD 3: Students use computational tools and strategies fluently and when appropriate, use estimation. SE/TE: Calculator hint on page 9, page Explains or provides examples of the limitations of calculators and computers in solving problems. 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. 2. Explains how measurement error affects computations (e.g., inappropriate units, inaccurate measure, imprecise tools). 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). SE/TE: Extension: Precision and Significant Digits, Extension: Greatest Possible Error SE/TE: Technology: Rounding Error MEASUREMENT STANDARD 1: Students understand attributes, units, systems of units in measurement; and develop and use techniques, tools, and formulas for measuring. 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 1. Expresses rates of change as a ratio of two different measures, where units are included in the ratio. situations. 2. Solves problems involving degree measures. SE/TE: 6-1 Ratios and Unit Ratios SE/TE: Review: Drawing and Measuring Angles; 9-2 Angle Relationships and Parallel Lines; 11-6 Sine, Cosine, and Tangent Ratios; Technology: Finding Angle Measures; 11-7 Angles of Elevation and Depression 2

3 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, 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. Determines how much imprecision is reasonable 6. Experimentally determines formulas for the volume of sphere, cylinder, and cone. 7. Solves problems using formulas for the volume of a sphere, cylinder and cone. or trigonometric ratios. 8. Solves problems involving formulas used in science, business, or math applications (e.g., force, work, velocity, acceleration, density, pressure, or trigonometric ratios. GEOMETRY AND SPATIAL SENSE STANDARD 1: Students analyze properties of objects and relationships among the properties. Make and evaluate conjectures about, and solve problems involving classes of 1. Makes and evaluates conjectures about two- and three-dimensional objects classes of two- and three-dimensional (e.g., Are all squares rectangles? SE/TE: Technology: Rounding Error SE/TE: Technology: Rounding Error SE/TE: Extension: Precision and Significant Digits SE/TE: 10-7 Volumes: Prisms and Cylinders: 10-9 Volumes: Pyramids, Cones, and Spheres SE/TE: 3-4 Using Formulas; 7-8 Simple and Compound Interest; 10-5 Surface Area: Prisms and Cylinders: 10-6 Surface Area: Pyramids, Cones, and Spheres; 11-2 The Pythagorean Theorem; 11-3 Distance and Midpoint Formulas; 11-6 Sine, Cosine, and Tangent Ratios SE/TE: 9-3 Classifying Polygons, Extension: Angles of a Polygon 3

4 2. Solves problems involving classes of two- and three-dimensional STANDARD 2: Students use transformations and symmetry to analyze mathematical situations Represent transformations of objects in the plane with coordinates, vectors, or 1. Represents transformations of objects matrices; describe the effects of a given in the plane (e.g., translation, rotation, transformation. reflection and dilation) by using Apply transformations to threedimensional sketches with coordinates, vectors, functional notations, or matrices. 2. Draws or finds the location of the image under a given transformation or describes the position of the image in relationship to the pre-image. SE/TE: 6-3 Similar Figures and Scale Drawings, 9-5 Congruence, 9-6 Circles, 10-1 Area: Parallelograms, 10-2 Area: Triangles and Trapezoids, 10-3 Area: Circles, 11-5 Special Right Triangles SE/TE: Technology: Dilations, 9-8 Translations, Extension: Matrices and Translations, 9-9 Symmetry and Reflections, 9-10 Rotations, Extension: Tessellations SE/TE: Technology: Dilations, 9-8 Translations, Extension: Matrices and Translations, 9-9 Symmetry and Reflections, 9-10 Rotations 3. Names a three-dimensional shape formed by the transformation on a twoor three-dimensional object. 4. Applies transformations to threedimensional 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 interpret two- and three-dimensional drawings of 1. Sketches three-dimensional objects from different perspectives/views. 2. Given the different views of an object, sketches the isometric drawing. SE/TE: Extension: Three Views of an Object SE/TE: Extension: Three Views of an Object 4

5 Analyze and describe cross-sections, truncations, and compositions/decompositions of threedimensional 3. Draws or describes cross-sections, truncations and compositions/ decompositions of two- and threedimensional STANDARD 4: Students select and use different representational systems, including coordinate geometry. Solve problems involving two- and three-dimensional figures. 1. Solves problems involving two- and Analyze and apply coordinate systems on three dimensional figures using a sphere (distance and place on the coordinate geometry. earth s surface, positions of stars in heavens). PATTERNS, FUNCTIONS, AND ALGEBRA 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). (None for this course) Analyze and use linear relations among three variables. Analyze and use quadratic relations between two variables. STANDARD 2: Students use symbolic forms to represent, model, and analyze mathematical situations. 1. Represent relations and functions with graphs, tables, and symbolic rules and translate among these representations. 1. Represents relations and functions with graph, tables of values, and symbolic rules and translates among these representations. SE/TE: 10-4 Space Figures, Extension: Cross Sections of Space Figures SE/TE: 1-10 The Coordinate Plane, 11-3 Distance and Midpoint Formulas SE/TE: 13-3 Exponential Growth and Decay SE/TE: 1-10 The Coordinate Plane, Technology: Graphing Ordered Pairs, Technology: Making a Table, 6-10 Make a Table, Extension: Compound Inequalities, 13-2 Graphing Non-linear Functions, 13-3 Exponential Growth and Decay 5

6 2. Model phenomena with a variety of functions and explain how and why a particular function can model many different situations. 3. Approximate and interpret accumulation and rates of change for functions representing a variety of situations (e.g., compound interest). 2. Determines which function best fits a given situation and justifies that choice of function. 3. Describes several different situations that can be represented by the same type of function and justifies the function used. 4. Uses the function to predict intermediate values (interpolation), given a situation involving accumulation (or change). SE/TE: Investigation: Modeling: Relating Graphs to Events SE/TE: 8-1 Relations and Functions DATA ANALYSIS AND PROBABILITY STANDARD 1: Students pose questions and collect, organize, and represent data to answer those questions. SE/TE: Chapter 12 Project 1. Identifies purpose of investigation of experiment by stating hypothesis or posing questions. 5. Design and carry out investigations or experiments with two variables. 6. Select appropriate methods for collecting, recording, organizing, and representing data; and describe how a change in representation affects the likely interpretation of the information. 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). SE/TE: Chapter 12 Project SE/TE: Chapter 12 Project SE/TE: Chapter 12 Project SE/TE: Technology: Data and Graphs, 8-5 Scatter Plots, Technology: Making Histograms, 12-2 Box-and-Whisker Plots, Extension: Stem-and-Leaf Plots, Chapter 12 Project 6

7 6. Describes potentially misleading interpretations that may by due to different types of representation. STANDARD 2: Students interpret data using methods of exploratory data analysis. 7. Compute, identify and interpret measures of center and spread (including standard deviation) 8. Look for patterns in data and understand their use in interpretation of the data. 9. Explain how sample size or transformations of data affect shape, center, and spread. 10. 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. SE/TE: 12-3 Using Graphs to Persuade SE/TE: 3-3 Mean, Median, and Mode; Technology: Mean and Median on a Graphing Calculator SE/TE: 12-2 Box-and-Whisker Plots SE/TE: 8-5 Scatter Plots, 8-6 Solve by Graphing SE/TE: 3-3 Mean, Median, and Mode STANDARD 3: Students develop and evaluate inferences, predictions, and arguments that are based on data. 11. Identify good models for phenomena (e.g., exponential model for population 1. Identifies what best fits the data provided growth). (e.g., linear (amount of sales tax), 12. Apply models to predict unobserved quadratic (height of bouncing ball), outcomes. exponential (growth of certificates of 13. Evaluate conclusions based on data and deposit), sinusoidal (tides, number of support inferences with valid daylight hours throughout the year)). arguments. 2. Identifies functions and interpolates or extrapolates data to predict unobserved outcomes. SE/TE: 13-2 Graphing Non-linear Functions 7

8 3. Justifies predictions, inferences, or conclusions. STANDARD 4: Students understand and apply basic notions of chance and probability. 1. Identifies relationships among events (e.g., inclusion, disjoint, complementary, independent, and dependent). 14. Identify relationships among events (e.g., inclusion, disjoint, complementary, independent, and dependent). 15. Compute probabilities of two events under different relationships unions and intersections. 16. Use fundamental counting principle, permutations, and combinations as counting techniques to solve problems. 17. Compute the theoretical probabilities of repeated experiments with replacement and repeated experiments without replacement. 18. Recognize random variables in real situations (e.g., insurance, life expectancy) and estimate and compute expectations. 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. SE/TE: Extension: Venn Diagrams, 12-5 Independent and Dependent Events SE/TE: 6-4 Probability SE/TE: 4-5 Account for All Possibilities, 12-4 Counting Outcomes and Theoretical Probability, 12-6 Permutations and Combinations SE/TE: 12-4 Counting Outcomes and Theoretical Probability, 12-7 Experimental Probability SE/TE: 12-7 Random Samples and Surveys 6. Estimates and calculates expected values. Reference: 8