# Honors Integrated Algebra/Geometry 3 Critical Content Mastery Objectives Students will:

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1 Content Standard 1: Numbers, Number Sense, and Computation Place Value Fractions Comparing and Ordering Counting Facts Estimating and Estimation Strategies Determine an approximate value of radical and exponential expressions using a variety of methods. Computation Solve mathematical problems involving exponents and roots. Ability to use exponential E/S A E/S A1, D2 Addressed in Int. 1, Int. 2 Section 5.1 November 15, 2007 Page 1 of 13 Douglas County School District

2 growth and decay functions to model situations Ability to model situations with base e Ability to solve problems with negative exponents Ability to solve problems with fractional exponents and radicals Ability to graph inverse functions Ability to evaluate logarithmic functions Ability to use properties of logarithms to solve problems Ability to solve real-life problems with exponential and logarithmic equations Ability to solve rational equations Ability to calculate with rational exponents Ability to add, subtract, graph and analyze rational expressions Ability to multiply and divide with exponents Ability to multiply and simplify radical expressions Ability to add, subtract, multiply, divide, and rationalize denominators of radical expressions Perform addition, subtraction, and scalar multiplication on matrices. Section 5.2 Section 5.3 Section 5.4 Section 5.5 Section 5.6 Section 5.7 Section 5.8 Algebra 2, Section 8.6 Section 5.3 Algebra 2, Sections 8.4, 8.5 Algebra 2, Section 5.1 Algebra 2, Section 6.2 Algebra 2, Section 6.2 Addressed in Int. 2 Solving Problems and Number Theory Identify and apply real number properties to solve problems I/S A1, A3, E2 Addressed in Int. 1, Int. 2 November 15, 2007 Page 2 of 13 Douglas County School District

3 Content Standard 2: Patterns Functions, and Algebra Patterns Use algebraic expressions to identify and describe the n th term of a sequence E/S E1, E5 Ability to describe patterns, continue patterns graph sequences, and find apparent limits Ability to identify arithmetic and geometric sequences Ability to find sum of finite arithmetic series Ability to find sum of finite geometric series Ability to find sum of infinite geometric series Variables and Unknowns Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations E/S A1, B2, E2, E3 Section 4.1 Section 4.4 Section 4.5 Section 4.6 Section 4.7 Addressed in Int. 1, Int. 2 Number Sentences, Expressions, and Polynomials Add, subtract, multiply, and factor 1 st and 2 nd degree polynomials connecting the arithmetic and algebraic processes I/S Ability to recognize, evaluate and graph polynomial functions Ability to multiply polynomials Ability to factor trinomials and the difference of two squares by grouping a polynomial of four or more Section 2.5 Algebra 2, section 5.3 Algebra 2, sections 4.3, 4.4, 5.4 November 15, 2007 Page 3 of 13 Douglas County School District

4 terms. Ability to solve equations using factoring Algebra 2, section 5.4 Simplify algebraic expressions, including exponents and radicals. Ability to simplify rational expressions, multiply rational expressions, and divide rational expressions Ability to simplify complex rational expressions Ability to simplify expressions with integer exponents Algebra 2, Section 8.4 Algebra 2, Section 8.5 Algebra 2, Section 5.1 Relations and Functions Determine the domain and range of functions, including linear, quadratic, and absolute value, algebraically and graphically E/S Ability to recognize and use functions Ability to use linear functions to describe situations and ability to find domain and range of linear functions Ability to associate functions with graphs. Ability to relate periodic functions to the real world Ability to apply the characteristics of sine and cosine functions and graphs Ability to transform sine and cosine graphs Ability to use sine and cosine functions to model realworld data Section 2.1 Section 2.2 Section 10.1 Section 10.2 Section 10.3 Section 10.4 Section 10.5 November 15, 2007 Page 4 of 13 Douglas County School District

5 Solve absolute value equations and inequalities both algebraically and graphically. Ability to use piecewise functions and absolute value functions Section 2.3 Linear Equations and Inequalities Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology) I/S Ability to use graphs and equations to model situations and to find break-even point using graph and algebra Ability to solve problems using systems of equations Ability to solve real-life problems by maximizing and minimizing Ability to use systems of inequalities to model and solve real-world linear programming problems Section 1.4 Section 1.5 Section 1.7 Section 1.8 Algebraic Representations and Applications Solve mathematical and practical problems involving linear and quadratic equations with a variety of methods, including discrete methods (with and without technology) E/S E6 Ability to use quadratic functions to describe situations Ability to solve radical equations, and graph and Section 2.4 Section 2.6, Algebra 2, section, 6.6 November 15, 2007 Page 5 of 13 Douglas County School District

6 interpret radical functions, with and without technology Ability to solve rational equations, and graph and interpret rational functions, with and without technology Ability to combine functions Section 2.7, Algebra 2, section 8.6 Section 2.8 Content Standard 3: Measurement Comparison, Estimation, and Conversion Estimate and convert between customary and metric systems. Precision in Measurements I/L B3, F5 Addressed in Int. 1 Justify, communicate, and differentiate between precision, error, and tolerance in practical problems I/S Addressed in Int. 1, 1C Formulas Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations E/S B2, D1 Ability to use explicit formulas for sequences Ability to use recursive formulas for sequences Section 4.2 Section 4.3 Money Interpret and apply consumer data presented in charts, tables, and graphs to make informed financial decisions related to practical applications E/S C4 Addressed in Int. 1, Consumer Math November 15, 2007 Page 6 of 13 Douglas County School District

7 Ratios and Proportions Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems I/S D1 Addressed in Int. 1, 2 Time Content Standard 4: Spatial Relationships, Geometry, and Logic Two Dimensional Shapes Identify and use the parts of a circle to solve mathematical and practical problems E/S D1, D3 Ability to examine relationships between inscribed polygons and circles Ability to examine relationships between inscribed angles and arcs of circles Ability to examine properties of tangents to circles Ability to examine relationships between circumscribed polygons and circles Section 3.5 Section 3.6 Section 3.7 Section 3.8 Identify and apply properties of interior and exterior angles of polygons to solve mathematical and practical problems. Ability to use formulas to find sum of interior angles of polygons, and sum of Section 3.4 November 15, 2007 Page 7 of 13 Douglas County School District

8 exterior angles of polygons Congruence, Similarity, and Transformations Apply properties of similarity through right triangle trigonometry to find missing angles and sides E/S D1, E2, E6 Addressed in Int. 1, Int. 2 Coordinate Geometry and Lines of Symmetry Three Dimensional Figures Algebraic Connections Determine the slope of lines using coordinate geometry and algebraic techniques. Identify parallel, perpendicular, and intersecting lines by slope. Graph linear equations and find possible solutions to those equations using coordinate geometry. Find possible solution sets of systems of equations whose slopes indicate parallel, perpendicular, or intersecting lines. Lines, Angles, and their Properties E/S E1, E4, E5, E6 Addressed in Int. 1, Int. 2 Solve problems using complementary and supplementary angles, congruent angles, vertical angles, angles formed when parallel lines are cut by a transversal and angles in polygons I/S A4, B1, D1 Addressed in 8 th grade Pre- Integrated Math, Consumer Math, Int. 2 November 15, 2007 Page 8 of 13 Douglas County School District

9 Triangles Apply the Pythagorean Theorem and its converse in mathematical and practical situations I/S D1, D2, E2, E6 Addressed in Int. 1 Constructions Solve problems by drawing and/or constructing geometric figures to demonstrate geometric relationships. Logic Ability to use polar coordinates to indicate points Ability to convert from polar to rectangular coordinates Ability to use vectors to solve problems Ability to translate graphs Ability to stretch graphs Ability to reflect graphs Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations. Ability to find relationships between implications and their converses, inverses, and contrapositives Ability to write coordinate proof Ability to write clear definitions Content Standard 5: Data Analysis Data Collection and Organization W/L A4, B2, D1, E I/S D2 Section 8.1 Section 8.2 Sections 8.3, 8.4 Section 9.2 Section 9.4 Section 9.7 Section 3.1 Section 3.2 Section 3.3 November 15, 2007 Page 9 of 13 Douglas County School District

10 Organize statistical data through the use of tables, graphs, and matrices (with and without technology) E/S C4, C5 Addressed in Int. 1, Int. 2 Central Tendency and Data Distribution Select and apply appropriate statistical measures in mathematical and practical situations I/S C1, C2 Ability to recognize the effect of adding a constant to data values Ability to recognize the effect of multiplying data values by a constant Ability to recognize the effects of multiple transformations on data sets and graphs Section 9.1 Section 9.3 Section 9.5 Interpretation of Data Distinguish between a sample and a census (population) E/S C2, C4, C5 Addressed in 8 th grade Pre- Integrated Math Identify sources of bias and their effect on data representations and statistical conclusions. Addressed in Int. 1 Use the shape of a normal distribution to compare and analyze data from a sample. Ability to standardize data Section 9.6 Permutations and Combinations Apply permutations and combinations to mathematical and I/S Addressed in Int. 2 November 15, 2007 Page 10 of 13 Douglas County School District

11 practical situations, including the Fundamental Counting Principle. Experimental and Theoretical Probability Determine the probability of an event with and without replacement using sample spaces I/S C3 Addressed in Consumer Math Prep Section, Int. 2 Design, conduct, analyze, and effectively communicate the results of multi-stage probability experiments. Statistical Inferences Design, construct, analyze, and select an appropriate type of graphical representation to communicate the results of a statistical experiment. Formulate and justify inferences based on a valid data sample I/L C4 Addressed in Int. 1 Process Standard: Problem Solving 9-12 Formulate their own problems Find solutions to problems from everyday situations Develop and apply strategies to solve a variety of problems Integrate mathematical reasoning, communication and connections Generalize solutions and apply previous knowledge to new problem solving situations. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem. Apply problem solving strategies until a solution is found it is clear that no solution exists. Interpret and solve a variety of mathematical problems by paraphrasing. Identify necessary and extraneous information. Check the reasonableness of a solution. Apply technology as a tool in problem solving situations. Apply combinations of proven strategies and previous knowledge to solve non-routine problems. November 15, 2007 Page 11 of 13 Douglas County School District

12 Process Standard: Mathematical Communication 9-12 Translate information into mathematical language and symbols Process information mathematically Present results in written, oral, and visual formats Discuss and exchange ideas about mathematics as a part of learning Read a variety of fiction and nonfiction texts to learn about mathematics Use mathematical notation to communicate and explain problems Use a variety of techniques to solve mathematical problems. Evaluate written and oral presentations in mathematics. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods. Communicate and evaluate mathematical thinking based on the use of definitions, properties, rules, and symbols in problem solving. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems. Process Standard: Mathematical Reasoning 9-12 Reinforce and extend their logical reasoning abilities Reflect on, clarify, and justify their thinking Ask questions to extend their thinking Use patterns and relationships to analyze mathematical situations Determine relevant, irrelevant, and /or sufficient information to solve mathematical problems. Recognize and apply deductive and inductive reasoning. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments. Make and test conjectures about algebraic and geometric properties based on mathematical principles. Justify the validity of an argument. Construct a valid argument. Process Standard: Mathematical Connections 9-12 Link new concepts to prior knowledge Identify relationships between content strands Integrate mathematics with other disciplines. Allow the flexibility to approach problems in a variety of ways within and beyond the field of mathematics. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics. Explain the relationships between concepts and procedures. November 15, 2007 Page 12 of 13 Douglas County School District

13 Use the connections among mathematical topics to develop multiple approaches to problems. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science. Identify, explain, and apply mathematics in everyday life. November 15, 2007 Page 13 of 13 Douglas County School District

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