Prentice Hall Algebra Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009

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1 Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level numbers are abstract symbols that represent real-world quantities 1. The complex number system includes real numbers and imaginary numbers a. Show that between any two rational numbers there are an infinite number of rational numbers, and that between any two irrational numbers there are also an infinite number of irrational numbers (DOK 1-2) b. Express the square root of a negative number using imaginary numbers (DOK 1) SE/TE: 11-17, 41-47, , , , SE/TE: , 265 Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency 2. Formulate, represent, and use algorithms with real numbers flexibly, accurately, and efficiently a. Use appropriate computation methods that encompass estimation and calculation (DOK 2-3) b. Use technology to perform operations (addition, subtraction, multiplication, and division) on numbers written in scientific notation (DOK 1-2) c. Describe factors affecting take-home pay and calculate the impact (PFL) (DOK 2-3) d. Design and use a budget, including income (net take-home pay) and expenses (mortgage, car loans, and living expenses) to demonstrate how living within your means is essential for a secure financial future (PFL) (DOK 2-4) SE/TE: 11-17, , , , Students perform computations with numbers in scientific notation in Prentice Hall Algebra 1. SE/TE: 18, 23, 576, 716 SE/TE: 18-19, 23, 53, 187, 576, 579, 599 1

2 Recognize and make sense of the many ways that variability, chance, and randomness appear in a variety of contexts 3. Systematic counting techniques are used to describe and solve problems a. Use combinatorics (Fundamental Counting Principle, permutations and combinations) to solve problems in real-world contexts (DOK 1-2) SE/TE: Content Area: Mathematics Grade Level Expectations: High School Standard: Patterns, Functions, and Algebraic Structures Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data 1. Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables a. Determine* when a relation is a function using a table, a graph, or an equation (DOK 1-2) b. Demonstrate the relationship between all representations of linear functions using point-slope, slope-intercept, and standard form of a line (DOK 1-2) c. Represent* linear, quadratic, absolute value, power, exponential, logarithmic, rational, trigonometric (sine and cosine), and step functions in a table, graph, and equation and convert from one representation to another (DOK 1-3) d. Determine the inverse (expressed graphically or in tabular form) of a function from a graph or table (DOK 1-2) e. Categorize sequences as arithmetic, geometric, or neither and develop formulas for the general terms related to arithmetic and geometric sequences (DOK 1-3) SE/TE: 60-67, 68-73, 74-80, 81-88, 92-98, , , , , , , , , , SE/TE: 68-73, 74-80, 81-88, 92-98, , SE/TE: 60-67, 68-73, 74-80, 81-88, 92-98, , , , , , , , , , SE/TE: , 413, , 508, , 922 SE/TE: , 578, , , 594,

3 Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data 2. Graphs and tables are used to describe the qualitative behavior of common types of functions a. Evaluate* a function at a given point in its domain given an equation (including function notation), a table, and a graph (DOK 1-2) b. Identify* the domain and range of a function given an equation (including function notation), a table, and a graph (DOK 1-2) c. Identify* intercepts, zeros (or roots), maxima, minima, and intervals of increase and decrease, and asymptotes of a function given an equation (including function notation), a table, and a graph (DOK 1-2) d. Make qualitative statements about the rate of change of a function, based on its graph or table (DOK 1-3) SE/TE: 63-65, 70, 84, 94-95, , 210, 342, 431, 434, 437, , , 520, 565, 844 SE/TE: 61-67, 334, 398, 399, 408, 414, 434, 435, , 527 SE/TE: 76-80, 158, 195, 199, 202, 205, 207, 211, 241, 243, , , 435, , SE/TE: 68-73, 74-80, 81-88, 92-98, 437 Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data 3. Parameters influence the shape of the graphs of functions a. Apply* transformations (translation, reflection, dilation) to a parent function, f(x) (DOK 1-3) b. Interpret the results of these transformations verbally, graphically, and symbolically (DOK 1-3) SE/TE: , , , , 455, , , , , 881 SE/TE: , , , , 455, , , , , 881 3

4 Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations 4. Expressions, equations, and inequalities can be expressed in multiple, equivalent forms a. Perform and justify steps in generating equivalent expressions by identifying properties used including the commutative, associative, inverse, identity, and distributive properties (DOK 1-3) b. Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions including those involving nth roots (DOK 1-2) c. Solve equations for one variable in terms of the others (DOK 1-2) SE/TE: 13-15, 21, 24, 26-29, , 765, 768, SE/TE: SE/TE: 29, 31 Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency 5. Solutions to equations, inequalities and systems of equations are found using a variety of tools a. Find* solutions to quadratic and cubic equations and inequalities by using appropriate algebraic methods such as factoring, completing the square, graphing or using the quadratic formula (DOK 1-3) b. Find* solutions to equations involving power, exponential, rational and radical functions (DOK 1-3) c. Solve* systems of linear equations and inequalities with two variables (DOK 1-2) SE/TE: , , , , 277 SE/TE: , 416, 418, , , SE/TE: , , , 163, , , 182,

5 Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions 6. Quantitative relationships in the real world can be modeled and solved using functions a. Represent, solve*, and interpret problems in various contexts using linear, quadratic, and exponential functions (DOK 2-3) b. Represent, solve*, and interpret problems involving direct and inverse variations and a combination of direct and inverse variation (DOK 2-3) c. Analyze* the impact of interest rates on a personal financial plan (PFL) (DOK 2-4) d. Evaluate* the costs and benefits of credit (PFL) (DOK 2-4) e. Analyze various lending sources, services, and financial institutions (PFL) (DOK 2-4) Content Area: Mathematics Grade Level Expectations: High School Standard: Data Analysis, Statistics, and Probability SE/TE: 61, 70, 81, 84, 92-98, 100, 105, 112, , 201, 205, 207, , 445, SE/TE: 68-73, , 508 SE/TE: 19, 23, 53, 187, 448, 461, 491, 576, 579, 599 Students solve problems involving credit cards and loan payments in Prentice Hall Algebra 1. Students solve problems involving lending sources and services and financial institutions in Algebra. SE/TE: 19, 53, 585 Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data 1. Statistical methods take variability into account, supporting informed decision-making through quantitative studies designed to answer specific questions a. Formulate appropriate research questions that can be answered with statistical analysis (DOK 1-3) b. Determine appropriate data collection methods to answer a research question (DOK 1-3) c. Explain how data might be analyzed to provide answers to a research question (DOK 1-3) SE/TE: SE/TE: SE/TE:

6 Communicate effective logical arguments using mathematical justification and proof. Mathematical argumentation involves making and testing conjectures, drawing valid conclusions, and justifying thinking 2. The design of an experiment or sample survey is of critical importance to analyzing the data and drawing conclusions a. Identify the characteristics of a welldesigned and well-conducted survey (DOK 1-2) b. Identify the characteristics of a welldesigned and well-conducted experiment (DOK 1-2) c. Differentiate between the inferences that can be drawn in experiments versus observational studies (DOK 1-3) SE/TE: SE/TE: , 725, 728 SE/TE: 719 Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data 3. Visual displays and summary statistics condense the information in data sets into usable knowledge a. Identify and choose appropriate ways to summarize numerical or categorical data using tables, graphical displays, and numerical summary statistics (describing shape, center and spread) and accounting for outliers when appropriate (DOK 1-3) b. Define and explain how sampling distributions (developed through simulation) are used to describe the sample-to-sample variability of sample statistics (DOK 1-2) c. Describe the relationship between two categorical variables using percents (DOK 1-2) d. When the relationship between two numerical variables is reasonably linear, apply* the least-squares criterion for line fitting, use Pearson's correlation coefficient as a measure of strength, and interpret the slope and y-intercept in the context of the problem (DOK 1-3) SE/TE: , , , 724, , , SE/TE: , 724 SE/TE: 692, SE/TE:

7 Recognize and make sense of the many ways that variability, chance, and randomness appear in a variety of contexts 4. Randomness is the foundation for using statistics to draw conclusions when testing a claim or estimating plausible values for a population characteristic a. Define and explain the meaning of significance (both practical and statistical) (DOK 1-2) b. Explain the role of p-values in determining statistical significance (DOK 1-2) c. Determine the margin of error associated with an estimate of a population characteristic (DOK 1-2) In Prentice Hall Prentice Hall Algebra 2, students use z-scores to transform normal distributions into standard normal distributions and approximate binomial distributions. SE/TE: In Prentice Hall Prentice Hall Algebra 2, students use z-scores to transform normal distributions into standard normal distributions and approximate binomial distributions. SE/TE: SE/TE: Recognize and make sense of the many ways that variability, chance, and randomness appear in a variety of contexts 5. Probability models outcomes for situations in which there is inherent randomness, quantifying the degree of certainty in terms of relative frequency of occurrence a. Develop* simulations that demonstrate probability as a long-run relative frequency (DOK 2-3) b. Apply and solve problems using the concepts of independence and conditional probability (DOK 1-3) c. Apply and solve problems using the concept of mutually exclusive properties when combining probabilities (DOK 1-3) d. Evaluate* and interpret probabilities using a normal distribution (DOK 1-3) e. Find* and interpret the expected value and standard deviation of a discrete random variable X (DOK 1-3) SE/TE: 682, 685, SE/TE: , SE/TE: SE/TE: , SE/TE: , 724 7

8 f. Analyze* the cost of insurance as a method to offset the risk of a situation (PFL) (DOK 2-4) Content Area: Mathematics Grade Level Expectations: High School Standard: Shape, Dimension, and Geometric Relationships In Prentice Hall Algebra 2, students apply mathematics to a wide variety of real-life situations, including depreciation, financial planning, and income. SE/TE: 19, 23, 53, 187, 448, 461, 4491, 576, 579, 599, 716 Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics 1. Attributes of two- and three-dimensional objects are measurable and can be quantified a. Calculate (or estimate when appropriate) the perimeter and area of a two-dimensional irregular shape (DOK 2-3) b. Justify, interpret, and apply the use of formulas for the surface area, and volume of cones, pyramids, and spheres including realworld situations (DOK 2-3) c. Solve for unknown quantities in relationships involving perimeter, area, surface area, and volume (DOK 1-3) d. Apply the effect of dimensional change, utilizing appropriate units and scales in problemsolving situations involving perimeter, area, and volume (DOK 2-3) SE/TE: 17, 30, 52, 73, 238, 246, 294, 310, 407, 414, , 781, 791, 917, 925 SE/TE: 66, 222, 294, 301, 308, 309, 329, 410, 426, 449, 577 SE/TE: 17, 30, 52, 66, 73, 238, 246, 294, 310, 407, 414, 449, 577, , 781 SE/TE: 73, 238, 246, 301, 366, 410, 426, 577 Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics 2. Objects in the plane and their parts, attributes, and measurements can be analyzed deductively a. Classify polygons according to their similarities and differences (DOK 1-2) b. Solve for unknown attributes of geometric shapes based on their congruence, similarity, or symmetry (DOK 1-3) Students classify polygons in Prentice Hall Geometry. SE/TE: Students apply concepts of congruence, similarity, and symmetry in Prentice Hall Geometry. SE/TE: 379, 866 8

9 c. Know and apply properties of angles including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve problems. Justify the results using two-column proofs, paragraph proofs, flow charts, or illustrations (DOK 1-3) d. Develop conjectures and solve problems about geometric figures including definitions and properties (congruence, similarity, and symmetry). Justify these conjectures using twocolumn proofs, paragraph proofs, flow charts, or illustrations (DOK 2-3) Students demonstrate their knowledge and understanding of properties of angles in Prentice Hall Geometry. SE/TE: 31 In Prentice Hall Algebra 2, students make conjectures about algebraic properties of functions, patterns, and graphs. Students develop and justify conjectures about geometric figures in Prentice Hall Geometry. SE/TE: 295, 317, 420, 578, 594, 651, 882 Apply transformation to numbers, shapes, functional representations, and data 3. Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically a. Make conjectures involving twodimensional objects represented with Cartesian coordinates. Justify these conjectures using twocolumn proofs, paragraph proofs, flow charts, and/or illustrations (DOK 2-3) b. Represent transformations (reflection, translation, rotation, and dilation) using Cartesian coordinates (DOK 2-3) c. Develop arguments to establish what remains invariant and what changes after a transformation (reflection, translation, rotation, and dilations). Justify these conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations (DOK 2-3) In Prentice Hall Algebra 2, students study properties of graphs of functions and relations in the coordinate plane. Students make conjectures about geometric figures represented with Cartesian coordinates in Prentice Hall Geometry. SE/TE: 74-80, 81-88, , 154, , 163, 238, , 621, , , 661, 781, 791, In Prentice Hall Algebra 2, students represent transformations of graphs of relations and functions using Cartesian coordinates. Students transform geometric figures in the Cartesian coordinate plane in Prentice Hall Geometry. SE/TE: , , , , 455, , , , , 881 In Prentice Hall Algebra 2, students transform graphs of relations and functions. Students develop and justify conjectures about transformations of geometric figures in Prentice Hall Geometry. SE/TE: , , , , 455, , , , , 881 9

10 d. Using construction tools, including technology, make conjectures about relationships among properties of shapes in the plane including those formed through transformation. Justify these conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations (DOK 2-3) Students use construction tools, including compass and straightedge, paper folding, and computer technology, in Prentice Hall Geometry. Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions 4. Right triangles are central to geometry and its applications a. Apply right triangle trigonometry (sine, cosine, and tangent) to find indirect measures of lengths and angles (DOK 1-2) b. Apply the Pythagorean theorem and its converse to solve real-world problems (DOK 1-2) c. Determine the midpoint of a line segment and the distance between two points in the Cartesian coordinate plane (DOK 1-2) Right triangle trigonometry is applied extensively in Prentice Hall Geometry. SE/TE: 879, The Pythagorean Theorem is applied extensively in Prentice Hall Geometry. SE/TE: 379, 411, 640, 801, 827, 898 The midpoint and distance formulas are used more extensively in Prentice Hall Algebra 1 and Prentice Hall Geometry. SE/TE:

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