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).

 Comparing and Ordering Decimals
 Rational Numbers, Opposites, and Absolute Values

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

 Unit Conversions 2 - Scientific Notation and Significant Digits

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.

 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

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).

 Estimating Population Size

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

 Translations

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

 Biconditional Statements

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).

 Beam to Moon (Ratios and Proportions)
 Estimating Population Size
 Part-to-part and Part-to-whole Ratios

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

 Compound Interest
 Percent of Change
 Real-Time Histogram

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

 Determining a Spring Constant
 Direct and Inverse Variation

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).

 Perimeter and Area of Rectangles

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

 Perimeters and Areas 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).

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c
 Simplifying Algebraic Expressions II

8.11.02: Represent mathematical relationships using symbolic algebra.

 Square Roots
 Using Algebraic Expressions

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.

 Addition and Subtraction of Functions
 Exponential Functions
 Linear Functions
 Logarithmic Functions
 Translating and Scaling Functions

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

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

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

 Cat and Mouse (Modeling with Linear Systems)
 Direct and Inverse Variation
 Slope-Intercept Form of a Line

8.11.06: Evaluate variable expressions and functions.

 Solving Equations by Graphing Each Side
 Solving Equations on the Number Line

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).

 Absolute Value Equations and Inequalities
 Point-Slope Form of a Line
 Slope-Intercept Form of a Line
 Solving Equations on the Number Line
 Standard Form of a Line

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).

 Absolute Value with Linear Functions
 Addition and Subtraction of Functions
 Exponential Functions
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Zap It! Game

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

 Cat and Mouse (Modeling with Linear Systems)
 Point-Slope Form of a Line
 Slope
 Slope-Intercept Form of a Line

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

 Zap It! Game

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

 Exponential Functions
 Point-Slope Form of a Line
 Radical Functions
 Slope

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

 Arithmetic Sequences
 Linear Functions
 Slope-Intercept Form of a Line

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

 Linear Programming
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)
 Systems of Linear Inequalities (Slope-intercept form)

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

 Area of Triangles

8.11.17: Solve systems of equations and inequalities.

 Linear Programming
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Standard Form)
 Systems of Linear Inequalities (Slope-intercept form)

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

 Roots of a Quadratic

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

 Absolute Value with Linear Functions
 Area of Triangles
 Compound Interest
 Cosine Function
 Exponential Functions
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Tangent Function
 Translating and Scaling Functions

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

 Addition and Subtraction of Functions
 Circles
 Ellipses
 Hyperbolas
 Parabolas

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

 Investigating Angle Theorems

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

9.11.01: Apply the Pythagorean theorem.

 Circles
 Cosine Function
 Distance Formula
 Sine Function
 Tangent Function

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.

 Dilations
 Rotations, Reflections, and Translations
 Translations

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

 Dilations

9.11.04: Classify plane figures according to their properties.

 Classifying Quadrilaterals
 Classifying Triangles
 Parallelogram Conditions
 Special Parallelograms

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).

 Classifying Quadrilaterals
 Concurrent Lines, Medians, and Altitudes
 Parallelogram Conditions
 Triangle Angle Sum
 Triangle Inequalities

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

 Surface and Lateral Areas of Prisms and Cylinders

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

 Classifying Quadrilaterals

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

 Circles
 Distance Formula

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).

 Chords and Arcs
 Inscribed Angles

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

 Points in the Coordinate Plane

9.11.12: Solve problems involving similar figures.

 Perimeters and Areas of Similar Figures
 Similar Figures
 Similarity in Right Triangles

9.11.13: Solve problems using triangle congruence.

 Congruence in Right Triangles
 Constructing Congruent Segments and Angles
 Proving Triangles Congruent

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

 Parallel, Intersecting, and Skew Lines

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

 Circumference and Area of Circles
 Inscribed Angles

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

 Conditional Statements

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

 Similarity in Right Triangles
 Sine, Cosine, and Tangent Ratios

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

 Cosine Function
 Sine Function
 Tangent Function

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

 Translating and Scaling Functions

9.11.22: Define, identify, and evaluate trigonometric ratios.

 Cosine Function
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Tangent Function

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

 Simplifying Trigonometric Expressions
 Sine, Cosine, and Tangent Ratios
 Sum and Difference Identities for Sine and Cosine

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.

 Polling: City
 Real-Time Histogram

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

 Stem-and-Leaf Plots

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Real-Time Histogram
 Stem-and-Leaf Plots

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Real-Time Histogram
 Stem-and-Leaf Plots

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Real-Time Histogram

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

 Binomial Probabilities
 Geometric Probability
 Independent and Dependent Events
 Theoretical and Experimental Probability

10.11.08: Compute probabilities for compound events.

 Independent and Dependent Events

10.11.09: Determine geometric probability based on area.

 Geometric Probability

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

 Binomial Probabilities
 Permutations and Combinations

Correlation last revised: 1/20/2017

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