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. Ability to find square roots and cube roots Ability to use rules of exponents to simplify expressions Computation 1.12.6 E/S A1 Section 3.8 Section 8.3-8.5 Solve mathematical problems involving exponents and roots. Ability to evaluate powers of variables, make conjectures about powers of 10, and find counterexamples. Ability to simplify exponents Ability to read and write 1.12.7 E/S A1, D2 Section 8.3-8.5 Section 8.3-8.5 Section 8.2 June 2008 Page 1 of 13 Douglas County School District
numbers in scientific notation, and in decimal notation Ability to solve exponential equations for doubling and halving Ability to solve rational equations Ability to simplify square roots, and solve equations with square roots Section 8.7-8.8 Section 12.6 Section 11.1-11.3 Perform addition, subtraction, and scalar multiplication on matrices. Section 2.1-2.3 Solving Problems and Number Theory Identify and apply real number properties to solve problems. Ability to add, subtract, multiply, and divide integers (without the use of a calculator) Ability to evaluate variable expressions, and to identify and extend patterns Ability to evaluate expressions using order of operations Ability to model distributive property, and to combine like terms Ability to evaluate expressions with negative numbers, and using absolute value 1.12.8 I/S A1, A3, E2 Section 2.1-2.3 Section 1.4 Section 1.2 Section 2.4 Section 1.3 June 2008 Page 2 of 13 Douglas County School District
Content Standard 2: Patterns, Functions, and Algebra Patterns Use algebraic expressions to identify and describe the n th term of a sequence. Model and write equations 2.12.1 E/S E1, E5 Section 5.4, 5.7 Variables and Unknowns Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations. Ability to collect like terms with two variables Ability to solve equations by balancing Ability to identify opposites Ability to solve and model inequalities Ability to rewrite equations and formulas Ability to simplify ratios, find unit rates, and to solve problems using ratios Ability to write proportions, and to solve proportions Ability to write equations for inverse variation 2.12.2 E/S A1, A2, B2, E2, E6 Section 2.4 Section 3.1 Section 3.2 Section 4.1-4.3 Section 3.6 Section 3.4 Section 3.4-3.5 Section 5.6 Number Sentences, Expressions, and Polynomials Add, subtract, multiply, and factor 1 st and 2 nd degree polynomials connecting the arithmetic and algebraic processes. Ability to solve multi-step equations Ability to solve equations with 2.12.3 I/S A1, B2, E2, E3 Section 3.2 Section 3.3 June 2008 Page 3 of 13 Douglas County School District
variables on both sides Ability to solve equations using reciprocals Ability to factor and expand algebraic expressions, find x- intercepts of parabolas by factoring Ability to expand binomials, and find the line of symmetry of a parabola Ability to factor trinomials and sketch the graph of a parabola Ability to identify polynomials and to model real-world situations with equations Section 3.1 Section 9.5, 10.3-10.5 Section 10.2 Section 10.3 Section 9.1-9.8 Simplify algebraic expressions, including exponents and radicals. Ability to simplify expressions involving negative exponents and zero as an exponent Ability to evaluate using rules of exponents Section 8.1 Section 8.1-8.4 Relations and Functions Determine the domain and range of functions, including linear, quadratic, and absolute value, algebraically and graphically. Ability to describe graphs of functions 2.12.4. E/S Section 5.2-5.4 Solve absolute value equations and inequalities both algebraically and graphically. Ability to recognize functions and draw graphs of functions Ability to write equations of functions, graph equations of functions, and identify shapes of graphs Section 5.2 Section 5.3 June 2008 Page 4 of 13 Douglas County School District
Linear Equations and Inequalities Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology). Ability to write an inequality, graph an inequality on a number line Ability to solve and model inequalities Ability to solve systems of equations Ability to graph linear inequalities Ability to solve systems of linear inequalities Ability to solve systems of linear equations by graphing, and graph systems of linear inequalities Ability to solve systems of equations by substitution Ability to solve systems of equations by elimination 2.12.5 I/S Algebraic Representations and Applications Section 4.1 Section 4.2-4.3 Sections 7.1-7.4 Section 7.5 Section 7.6 Section 7.1 Section 7.2 Section 7.3 Solve mathematical and practical problems involving linear and quadratic equations with a variety of methods, including discrete methods (with and without technology). Ability to model problems with a table, graph or equation Ability to transform parabolas Ability to graph a parabola and find factors of a parabola Ability to solve equations with quadratic formula Ability to sketch from a quadratic equation: direction, vertex, line of symmetry, y- 2.12.6 E/S E6 Section 5.1 Section 10.1 Section 10.2-10.3 Section 10.6 Section 10.2 June 2008 Page 5 of 13 Douglas County School District
intercept Ability to solve equations using square roots Ability to solve quadratic equations by factoring Ability to use the quadratic formula to solve equations Section 10.3 Section 10.4 Section 10.6 Content Standard 3: Measurement Comparison, Estimation, and Conversion Estimate and convert between customary and metric systems. Ability to convert using dimensional analysis 3.12.1 I/L B3, F5 Section 3.4 Precision in Measurements Justify, communicate, and differentiate between precision, error, and tolerance in practical problems. Formulas 3.12.2 I/S Addressed in Geometry Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations. Money 3.12.3 E/S B2, D1 Addressed in Geometry Interpret and apply consumer data presented in charts, tables, and graphs to make informed financial decisions related to practical applications. Ability to use and interpret data from matrices, spreadsheets and graphs 3.12.4 E/S C4 Section 3.1 June 2008 Page 6 of 13 Douglas County School District
Ratios and Proportions Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems. Ability to use proportions to find sides of similar polygons, to prove congruence, and to read scale drawings Time 3.12.5 I/S D1 Section 3.5 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. 4.12.1 E/S D1, D3 Addressed in Geometry Identify and apply properties of interior and exterior angles of polygons to solve mathematical and practical problems. Congruence, Similarity, and Transformations Apply properties of similarity through right triangle trigonometry to find missing angles and sides. 4.12.2 E/S D1, E2, E6 Coordinate Geometry and Lines of Symmetry Three Dimensional Figures Algebraic Connections Addressed in Geometry Determine the slope of lines using coordinate geometry and algebraic 4.12.5 E/S E1, E4, E5, E6 June 2008 Page 7 of 13 Douglas County School District
techniques. Ability to find slope of a line and the equation of a line Section 6.1 Identify parallel, perpendicular, and intersecting lines by slope. Ability to find slopes of parallel lines and perpendicular lines Section 6.6 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. Ability to find direct variation and slope of a line Ability to write a direct variation equation from a table, graph direct variation equations, and find slope given two coordinates Ability to write a direct variation equation from a graph, graph direct variation equations, and find slope (rise/run) Ability to graph equations, find slope and y-intercept from an equation, and find slope and y- intercept from a graph Ability to change equation from slope-intercept form to standard form, and graph equations using intercepts Ability to write equations for horizontal and vertical lines Ability to write equations given two points, or slope and one point Section 5.5 Section 6.1 Section 6.1 Section 6.2 Section 6.4 Section 6.1 Section 6.5 June 2008 Page 8 of 13 Douglas County School District
Lines, Angles, and their Properties 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. 4.12.6 I/S A4, B1, D1 Addressed in Pre-Algebra, Geometry Triangles Apply the Pythagorean Theorem and its converse in mathematical and practical situations. Ability to use the Pythagorean Theorem to find lengths of sides and of sides of right triangles Constructions 4.12.7 I/S D1, D2, E2, E6 Section 3.9 Solve problems by drawing and/or constructing geometric figures to demonstrate geometric relationships. Ability to identify coordinates on a coordinate plane 4.12.8 W/L A4, B2, D1, E1 Section 1.4 Logic Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations. 4.12.9 I/S D2 Addressed in Geometry June 2008 Page 9 of 13 Douglas County School District
Content Standard 5: Data Analysis Data Collection and Organization Organize statistical data through the use of tables, graphs, and matrices (with and without technology). Ability to choose a data display to show a data set 5.12.1 E/S C4, C5 Section 1.5, Skills Handbook Central Tendency and Data Distribution Select and apply appropriate statistical measures in mathematical and practical situations. Ability to find mean, median, and mode, to identify outliers in a data set, and to calculate range Interpretation of Data 5.12.2 I/S C1, C2 Section 1.6 Distinguish between a sample and a census (population). 5.12.3 E/S C2, C4, C5 Census and Surveys addressed in Pre-Algebra Identify sources of bias and their effect on data representations and statistical conclusions. Ability to analyze misleading graphs Use the shape of a normal distribution to compare and analyze data from a sample. Skills Handbook Check item specifications and performance indicators when they are revised (summer 2007?)? Permutations and Combinations Apply permutations and combinations to mathematical and practical situations, including the Fundamental Counting Principle. 5.12.4 I/S Section 12.7-12.8 June 2008 Page 10 of 13 Douglas County School District
Experimental and Theoretical Probability Determine the probability of an event with and without replacement using sample spaces. Ability to find experimental and theoretical probability, and to identify complementary events Ability to find probability of mutually exclusive events, find probability of complementary events, and calculate odds 5.12.5 I/S C3 Section 2.6 Section 2.6 Design, conduct, analyze, and effectively communicate the results of multi-stage probability experiments. Ability to find probability of independent events and of dependent events Statistical Inferences Section 2.7 Design, construct, analyze, and select an appropriate type of graphical representation to communicate the results of a statistical experiment. Ability to use histograms, frequency tables, and stemand-leaf plots to display data Ability to draw a box-andwhisker plot, and use it to compare data sets 5.12.6 I/L C4 Skills Handbook Formulate and justify inferences based on a valid data sample. Ability to make and interpret scatter plots of data, and to use scatter plots to make predictions by creating a fitted line Section 1.5, 6.7 June 2008 Page 11 of 13 Douglas County School District
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. 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. June 2008 Page 12 of 13 Douglas County School District
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. 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. June 2008 Page 13 of 13 Douglas County School District