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Standard III A: Patterns and Functions Benchmarks (benchmarks are math operations you must know how to do) 1. Know the numeric, graphic and symbolic properties of linear, step, absolute value and quadratic functions. Graphic properties may include rates of change, intercepts, maxima and minima. 2. Model exponential growth and decay, numerically, graphically and symbolically, using exponential functions with integer inputs. 3. Analyze the effects of coefficient changes on linear and quadratic functions and their graphs. 4. Apply basic concepts of linear, quadratic and exponential expressions or equations in real-world problems such as loans, investments and the path of a projectile. 5. Distinguish functions from other relations using graphic and symbolic methods. Standard III B: Algebra (Algebraic Thinking) Benchmarks 1. Translate among equivalent forms of expressions, such as, simplify algebraic expressions involving nested pairs of parentheses and brackets, simplify rational expressions, factor a common term from an expression and apply associative, commutative and distributive laws. 2. Understand the relationship between absolute value and distance on the number line and graph simple expressions involving absolute value such as, |x - 3| = 6 or |x + 2| < 5. 3. Find equations of a line given two points on the line, a point and the slope of the line or the slope and the y-intercept of the line. 4. Translate among equivalent forms of linear equations and inequalities. 5. Use a variety of models such as equations, inequalities, algebraic formulas, written statements, tables and graphs or spreadsheets to represent functions and patterns in real-world and mathematical problems. 6. Apply the laws of exponents to perform operations on expressions with integer exponents. 7. Solve linear equations and inequalities in one variable with numeric, graphic and symbolic methods. 8. Find real solutions to quadratic equations in one variable with numeric, graphic and symbolic methods. 9. Use appropriate terminology and mathematical notation to define and represent recursion. 10. Create and use recursive formulas to model and solve real-world and mathematical problems. 11. Solve systems of two linear equations and inequalities with two variables using numeric, graphic and symbolic methods. 12. Understand how slopes can be used to determine whether lines are parallel or perpendicular. Given a line and a point not on the line, find the equations for the lines passing through that point and parallel or perpendicular to the given line. Standard IV-A: Data Analysis and Statistics Benchmarks: 1. Construct and analyze circle graphs, bar graphs, histograms, box-and-whisker plots, scatter plots and tables, and demonstrate the strengths and weaknesses of each format by choosing appropriately among them for a given situation. 2. Use measures of central tendency and variability, such as, mean, median, maximum, minimum, range, standard deviation, quartile and percentile, to describe, compare and draw conclusions about sets of data. 3. Determine an approximate best-fit line from a given scatter plot and use the line to draw conclusions. 4. Know the influence of outliers on various measures and representations of data about real-world and mathematical problems. 5. Understand the relationship between correlation and causation. 6. Interpret data credibility in the context of measurement error and display distortion. 7. Compare outcomes of voting methods such as majority, plurality, ranked by preference, run-off and pair-wise comparison. Standard IV-B: Probability Benchmarks: 1. Select and apply appropriate counting procedures to solve real-world and mathematical problems, including probability problems. 2. Use area, trees, unions and intersections to calculate probabilities and relate the results to mutual exclusiveness, independence and conditional probabilities, in real-world and mathematical problems. 3. Use probability models, including area and binomial models, in real-world and mathematical problems. 4. For simple probability models, determine the expected values of random variables. 5. Know the effect of sample size on experimental and simulation probabilities. 6. Use a variety of experimental, simulation and theoretical methods to calculate probabilities. Standard V-A Benchmark: 1. Use models and visualization to understand and represent three-dimensional objects and their cross sections from different perspectives. Standard V-B Geometry Benchmarks: 1. Know and use theorems about triangles and parallel lines in elementary geometry to justify facts about various geometrical figures and solve real-world and mathematical problems. These theorems include criteria for two triangles to be congruent or similar and facts about parallel lines cut by a transversal. 2. Know and use theorems about circles to justify geometrical facts and solve real-world and mathematical problems. These theorems include the relationships involving tangent lines and radii, the relationship between inscribed and central angles and them relationship between the measure of a central angle and arc length. 3. Know and use properties of two- and three-dimensional figures to solve real-world and mathematical problems such as: finding area, perimeter, volume and surface area; applying direct or indirect methods of measurement; the Pythagorean theorem and its converse; and properties of 45°-45°-90° and 30°-60°-90° triangles. 4. Apply the basic concepts of right triangle trigonometry including sine, cosine and tangent to solve real-world and mathematical problems. 5. Use coordinate geometry to represent and examine geometric concepts such as the distance between two points, the midpoint of a line segment, the slope of a line and the slopes of parallel and perpendicular lines. 6. Use numeric, graphic and symbolic representations of transformations such as reflections, translations and change of scale in one, two and three dimensions to solve real-world and mathematical problems. 7. Perform basic constructions with a straightedge and compass. 8. Draw accurate representations of planar figures using a variety of tools. Standard V-C Measurement Use the interconnectedness of geometry, algebra and measurement to explore real-world and mathematical problems. 
MCA II - Standard III-A
MCA II - Standard III-B
MCA II - Standard IV-A
MCA II - Standard IV-B
MCA II - Standard V-A
MCA II - Standard V-B
MCA II - Standard V-C
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