### II: Number Sense, Computation, and Operations

#### II.A: Number Sense

II.A.1: Represent and compare rational and irrational numbers symbolically and on a number line.

#### II.B: Computation and Operation

II.B.3: Recognize the impact of units such as degrees and radians on calculations.

II.B.6: Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.

### III: Patterns, Functions, and Algebra

#### III.A: Patterns and Functions

III.A.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.

III.A.2: Model exponential growth and decay, numerically, graphically and symbolically, using exponential functions with integer inputs.

III.A.3: Analyze the effects of coefficient changes on linear and quadratic functions and their graphs.

III.A.5: Distinguish functions from other relations using graphic and symbolic methods.

#### III.B: Algebra (Algebraic Thinking)

III.B.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.

III.B.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.

III.B.4: Translate among equivalent forms of linear equations and inequalities.

III.B.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.

III.B.6: Apply the laws of exponents to perform operations on expressions with integer exponents.

III.B.7: Solve linear equations and inequalities in one variable with numeric, graphic and symbolic methods.

III.B.8: Find real solutions to quadratic equations in one variable with numeric, graphic and symbolic methods.

III.B.11: Solve systems of two linear equations and inequalities with two variables using numeric, graphic and symbolic methods.

III.B.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.

### IV: Data Analysis, Statistics, and Probability

#### IV.A: Data and Statistics

IV.A.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.

IV.A.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.

IV.A.3: Determine an approximate best-fit line from a given scatter plot and use the line to draw conclusions.

IV.A.5: Understand the relationship between correlation and causation.

#### IV.B: Probability

IV.B.1: Select and apply appropriate counting procedures to solve real-world and mathematical problems, including probability problems.

IV.B.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.

IV.B.3: Use probability models, including area and binomial models, in real-world and mathematical problems.

IV.B.5: Know the effect of sample size on experimental and simulation probabilities.

IV.B.6: Use a variety of experimental, simulation and theoretical methods to calculate probabilities.

### V: Spatial Sense, Geometry, and Measurement

#### V.A: Spatial Sense

V.A.1: Use models and visualization to understand and represent three-dimensional objects and their cross sections from different perspectives.

#### V.B: Geometry

V.B.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.

V.B.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 the relationship between the measure of a central angle and arc length.

V.B.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 45o-45o-90o and 30o-60o-90o triangles.

V.B.4: Apply the basic concepts of right triangle trigonometry including sine, cosine and tangent to solve real-world and mathematical problems.

V.B.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.

V.B.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.

V.B.7: Perform basic constructions with a straightedge and compass.

Correlation last revised: 10/24/2008

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.