Content Standard 1: Numbers, Number Sense, and Computation

Transcription

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 E/S A1 Solve mathematical problems involving exponents and roots. Ability to solve equations with direct variation of powers Perform addition, subtraction, and scalar multiplication on matrices. Solving Problems and Number Theory E/S A1, D2 Section , Alg2 Identify and apply real number properties to solve problems. Ability to demonstrate mastery in prerequisite skills found in Skills Handbook in the Geometry textbook including solving equations, order of operations, and graphing lines I/S A1, A3, E2 Skills Handbook 754, June 2008 Page 1 of 12 Douglas County School District

2 Content Standard 2: Patterns Functions, and Algebra Patterns Use algebraic expressions to identify and describe the n th term of a sequence. Variables and Unknowns E/S E1, E5 Section 1.1 Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations. Ability to demonstrate mastery in prerequisite skills found in Skills Handbook of Geometry textbook including solving equations, order of operations, and graphing lines E/S A1, A2, B2, E2, E6 Number Sentences, Expressions, and Polynomials Skills Handbook Add, subtract, multiply, and factor 1 st and 2 nd degree polynomials connecting the arithmetic and algebraic processes I/S A1, B2, E2, E3, Alg2 Simplify algebraic expressions, including exponents and radicals. Ability to simplify an expression for the measure of a figure Relations and Functions Section 1.6, 3.5 Determine the domain and range of functions, including linear, quadratic, and absolute value, algebraically and graphically. Solve absolute value equations and inequalities both algebraically and graphically E/S, Alg2 June 2008 Page 2 of 12 Douglas County School District

3 Linear Equations and Inequalities Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology) I/S, Alg2 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 Content Standard 3: Measurement Comparison, Estimation, and Conversion Estimate and convert between customary and metric systems. Ability to estimate by comparing, and to estimate probabilities. Precision in Measurements I/L B3, F5 Section 10.8 Justify, communicate, and differentiate between precision, error, and tolerance in practical problems. Formulas I/S Skills Handbook Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations. Ability to use distance formula to show relationships in quadrilaterals Ability to find midpoint of a segment Ability to find area using E/S B2, D1 Section 6.4, 6.6 Section 6.7 Section June 2008 Page 3 of 12 Douglas County School District

4 formulas Ability to find surface area of prisms, cylinders, pyramids Ability to find volume of cylinders, prisms, pyramids and cones Money Section 11.2 Section Interpret and apply consumer data presented in charts, tables, and graphs to make informed financial decisions related to practical applications. Ability to make statements about information presented in tables and graphs, and concept maps Ratios and Proportions E/S C4 Skills Handbook Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems. Ability to find surface area of spheres and volume of spheres Ability to draw dilations Ability to find area and volume of similar figures I/S D1 Section Section 9.5 Section 10.4 Time June 2008 Page 4 of 12 Douglas County School District

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. Ability to find circumference of a circle, and find arc length Ability to find area of a circle, and area of a sector 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 E/S D1, D3 Section Section 10.7 Section 12.3 Section 12.2 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 exterior angles of polygons Ability to classify quadrilaterals Ability to use coordinate geometry to verify properties of polygons Ability to identify congruent polygons, name polygons, and identify transformation Ability to classify angles, estimate angle measures, and find unknown angle measures Section 12.4 Section 3.5 Section 6.1 Section 6.6 Section 6.1, 6.4, Section 1.6, June 2008 Page 5 of 12 Douglas County School District

6 Congruence, Similarity, and Transformations Apply properties of similarity through right triangle trigonometry to find missing angles and sides. Ability to apply converses of D1, E2, E6 parallel line theorems Ability to apply the Triangle Sum theorem to numerical problems and to proofs Ability to prove that triangles are similar Ability to identify congruent triangles using ASA and AAS Ability to identify congruent triangles using SAS and SSS Ability to apply properties of isosceles triangles, equilateral triangles, and perpendicular bisectors Ability to identify similar right triangles and to find geometric mean Ability to learn relationships of and triangles, and find sine, cosine, and tangent of an angle Ability to find values for sine and for cosine of an angle Ability to find values for tangent of an angle Coordinate Geometry and Lines of Symmetry Section Section 3.4 Section 7.3 Section Section 4.3 Section 4.5, 5.2 Section Section 8.2 Section 8.3 Section 8.4 Three Dimensional Figures Algebraic Connections Determine the slope of lines using coordinate geometry and algebraic techniques E/S E1, E4, E5, E6 Identify parallel, perpendicular, and intersecting lines by slope. June 2008 Page 6 of 12 Douglas County School District

7 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 Section 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. Ability to write proofs about angles Ability to write proofs using properties of parallel lines Triangles I/S A4, B1, D1 Section 2.5 Section Apply the Pythagorean Theorem and its converse in mathematical and practical situations. Ability to write if-then statements and to write converses Constructions I/S D1, D2, E2, E6 Section 8.1 Section Solve problems by drawing and/or constructing geometric figures to demonstrate geometric relationships. Ability to transform geometric figures Ability to represent figures on a coordinate plane using standard positions Ability to estimate distances on a map and recognize symbols representing geometric terms Ability to identify geometric W/L A4, B2, D1, E1 Section Section Section 1.5, 1.8, 7.1 June 2008 Page 7 of 12 Douglas County School District

8 shapes on a coordinate plane, find area of triangles and polygons drawn on a coordinate plane Ability to translate figures on a coordinate plane and recognize translational symmetry Ability to recognize rotational symmetry and rotate figures on polar graph paper Ability to draw reflections Logic Section Section 9.1, 9.4 Section Section 9.2 Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations. Ability to use and, or, and not with Venn Diagrams, number line graphs, and coordinate plane graphs Ability to translate among various forms of implications Ability to use Rules of Logic to distinguish between valid and invalid arguments Ability to write biconditionals and good definitions Ability to identify elements of paragraph proofs, flow proofs, and two-column proofs Ability to use postulates of algebra to write proofs Ability to know difference between inductive and deductive reasoning I/S D2 Section Section Section Section Throughout Ch 2 Section 2.4 Section June 2008 Page 8 of 12 Douglas County School District

9 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 use diagrams and tables to count possibilities E/S C4, C5 Skills Handbook Central Tendency and Data Distribution Select and apply appropriate statistical measures in mathematical and practical situations. Interpretation of Data I/S C1, C2 Distinguish between a sample and a census (population) E/S C2, C4, C5 Samples and surveys addressed in Pre-Algebra Identify sources of bias and their effect on data representations and statistical conclusions. Use the shape of a normal distribution to compare and analyze data from a sample. 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. Ability to use multiplication counting principle and to find number of permutations I/S Skills Handbook 762 June 2008 Page 9 of 12 Douglas County School District

10 Experimental and Theoretical Probability Determine the probability of an event with and without replacement using sample spaces I/S C3 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 I/L C4 Formulate and justify inferences based on a valid data sample. June 2008 Page 10 of 12 Douglas County School District

11 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 11 of 12 Douglas County School District

12 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 12 of 12 Douglas County School District