### 6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.

6.11.01: Recognize, represent, order, compare real numbers, and locate real numbers on a number line (e.g., pi, square root of 2, square root of 5, 2/3, -1.6).

6.11.02: Represent numbers in equivalent forms (e.g., fraction/decimal/percent, exponential/logarithmic, radical/rational exponents, absolute value, scientific notation).

6.11.05: Simplify or test expressions by applying field properties (commutative, associative, distributive), order properties (transitive, reflexive, symmetric), and properties of equality for the set of real numbers.

6.11.09: Solve problems involving estimates or data (e.g., use averages to estimate the cost of a job that includes labor and materials).

6.11.12: Solve problems using simple matrix operations (addition, subtraction, multiplication, scalar multiplication).

6.11.15: Judge the reasonableness of solutions, and find mistakes in calculation, logic, and formula application.

6.11.17: Set up, evaluate, or solve number sentences or word problems involving ratios and proportions with rational numbers (e.g., scale drawing, unit rate, scale factor, rate of change).

6.11.18: Set up, evaluate, or solve common problems involving percent (e.g., sales tax, tip, interest, discount, markup, commission, compound interest).

6.11.19: Set up, evaluate, or solve problems stated in terms of direct and inverse variation of simple quantities.

### 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.

7.11.04: Describe the general trends of how the change in one measure affects other measures in the same figure (e.g., length, area, volume).

7.11.05: Determine the linear measure, perimeter, area, surface area, and volume of similar figures.

### 8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

8.11.01: Simplify or identify equivalent algebraic expressions (e.g., exponential, rational, logarithmic, factored, polynomial).

8.11.02: Represent mathematical relationships using symbolic algebra.

8.11.03: Identify essential quantitative relationships in a situation, and determine the class or classes of functions (e.g., linear, quadratic, exponential) that model the relationships.

8.11.04: Determine a specific term, a finite sum, or a rule that generates terms of a pattern.

8.11.05: Model and describe slope as a constant rate of change.

8.11.06: Evaluate variable expressions and functions.

8.11.07: Identify an equation of a line or an equation of a line of best fit from given information (e.g., from a set of ordered pairs, graphs, tables).

8.11.08: Recognize and describe the general shape and properties of functions from graphs, tables, or equations (e.g., linear, absolute value, quadratic, exponential, logarithmic).

8.11.09: Identify slope from an equation, table of values, or graph.

8.11.10: Interpret the role of the coefficients and constants on the graphs of linear and quadratic functions, given a set of equations.

8.11.11: Analyze functions by investigating domain, range, rates of change, intercepts, and zeros.

8.11.14: Model problems using mathematical functions and relations (e.g., linear, non-linear).

8.11.15: Interpret the graph of a system of equations and inequalities, including cases where there are no solutions.

8.11.16: Solve linear equations and inequalities, including selecting and evaluating formulas.

8.11.17: Solve systems of equations and inequalities.

8.11.18: Solve quadratic equations over the complex number system, including selecting and evaluating formulas.

8.11.19: Solve problems that include nonlinear functions, including selecting and evaluating formulas (i.e., absolute value, trigonometric, logarithmic, exponential).

8.11.20: Identify, interpret, and write equations for circles and other conic sections.

8.11.21: Recognize and apply mathematical and algebraic axioms, theorems of algebra, and deductive reasoning.

### 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

9.11.01: Apply the Pythagorean theorem.

9.11.02: Identify and represent transformations (rotations, reflections, translations, dilations) of an object in the plane, and describe the effects of transformations on points in words or coordinates.

9.11.03: Determine how changing the scale factor affects the size and position of a figure in the plane.

9.11.04: Classify plane figures according to their properties.

9.11.05: Identify, apply, or solve problems that require knowledge of geometric properties of plane figures (e.g., triangles, quadrilaterals, parallel lines cut by a transversal, angles, diagonals, triangle inequality).

9.11.07: Identify the relationship between two-dimensional patterns (e.g., nets) and related three-dimensional objects (e.g., cylinders, prisms, cones).

9.11.08: Identify two- and three-dimensional figures that would match a set of given conditions.

9.11.09: Solve problems that involve calculating distance, midpoint, and slope using coordinate geometry.

9.11.10: Identify, apply, and solve problems that require knowledge of geometric relationships of circles (e.g. arcs, chords, tangents, secants, central angles, inscribed angles).

9.11.11: Graph, locate, and identify points on a coordinate system.

9.11.12: Solve problems involving similar figures.

9.11.13: Solve problems using triangle congruence.

9.11.14: Describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).

9.11.15: Identify relationships between circles and other objects in the plane (e.g., inscribed circles, concentric circles, internal/external tangency).

9.11.17: Recognize and apply mathematical and geometric axioms, fundamental theorems of geometry, and deductive reasoning.

9.11.19: Determine distances and angle measures using indirect measurement (e.g., properties of right triangles, Law of Sines, Law of Cosines).

9.11.20: Solve problems using 45°-45°-90° and 30°-60°-90° triangles.

9.11.21: Identify graphs of a given trigonometric function (sin x, cos x) using its characteristics (e.g., period, amplitude).

9.11.22: Define, identify, and evaluate trigonometric ratios.

9.11.23: Use trigonometric identities (e.g., sin²x + cos²x = 1)

### 10: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.

10.11.01: Read, interpret, predict, interpolate, extrapolate, and use information from a variety of graphs, charts, and tables.

10.11.02: Translate from one representation of data to another (e.g., a bar graph to a circle graph).

10.11.04: Find an unknown value in a dataset given information about descriptive statistics.

10.11.05: Calculate, interpret, and use measures of central tendency and dispersion.

10.11.06: Compare two or more data sets on measures of central tendency and dispersion.

10.11.07: Compute the probability of an event composed of single or repeated trials with or without replacement.

10.11.08: Compute probabilities for compound events.

10.11.09: Determine geometric probability based on area.

10.11.10: Apply counting techniques (e.g., permutations, combinations, Fundamental Counting Principle).

Correlation last revised: 5/10/2018

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