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
Quadratics in Vertex Form
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