MA 12.1: Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.1.1: Students will represent and show relationships among real numbers.

MA 12.1.1.b: Compare, contrast and apply the properties of numbers and the real number system, including rational, irrational, imaginary, and complex numbers

Points in the Complex Plane - Activity A

MA 12.1.2: Students will demonstrate the meaning and effects of arithmetic operations with real numbers.

MA 12.1.2.a: Use drawings, words, and symbols to explain the effects of such operations as multiplication and division, and computing positive powers and roots on the magnitude of quantities (e.g., if you take the square root of a number, will the result always be smaller than the original number? (e.g., square root of 1/4 = 1/2))

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Using Algebraic Equations
Using Algebraic Expressions

MA 12.1.2.b: Use drawings, words, and symbols to explain that the distance between two numbers on the number line is the absolute value of their difference

Using Algebraic Equations
Using Algebraic Expressions

MA 12.2: Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.2.1: Students will analyze characteristics, properties, and relationships among geometric shapes and objects.

MA 12.2.1.b: Analyze properties and relationships among classes of two and three dimensional geometric objects using inductive reasoning and counterexamples

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Polygon Angle Sum - Activity A
Prisms and Cylinders - Activity A
Special Quadrilaterals
Triangle Angle Sum - Activity A

MA 12.2.1.c: State and prove geometric theorems using deductive reasoning (e.g., parallel lines with transversals, congruent triangles, similar triangles)

Biconditional Statement
Conditional Statement
Simplifying Trigonometric Expressions

MA 12.2.1.d: Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions)

Classifying Quadrilaterals - Activity B
Congruence in Right Triangles
Investigating Angle Theorems - Activity A
Parallelogram Conditions
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Special Quadrilaterals

MA 12.2.1.e: Identify and apply right triangle relationships (e.g., sine, cosine, tangent, special right triangles, converse of Pythagorean Theorem)

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MA 12.2.1.g: Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems

Chords and Arcs
Classifying Triangles
Inscribing Angles
Parallelogram Conditions
Simplifying Trigonometric Expressions

MA 12.2.2: Student will use coordinate geometry to analyze and describe relationships in the coordinate plane.

MA 12.2.2.a: Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, circle equations)

Circles

MA 12.2.2.c: Apply the distance formula

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MA 12.2.2.d: Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square)

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity B
Classifying Triangles
Isosceles and Equilateral Triangles
Parallelogram Conditions
Triangle Angle Sum - Activity A

MA 12.2.3: Students will apply and analyze transformations.

MA 12.2.3.a: Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes

Dilations
Reflections
Rotations, Reflections and Translations
Translations

MA 12.2.3.b: Perform and describe multiple transformations

Dilations
Reflections
Rotations, Reflections and Translations

MA 12.2.4: Students will use visualization, spatial reasoning, and geometric modeling to solve problems.

MA 12.2.4.a: Sketch and draw appropriate representations of geometric objects using ruler, protractor, or technology

3D and Orthographic Views - Activity A
Classifying Quadrilaterals - Activity B
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

MA 12.2.4.b: Use geometric models to visualize, describe, and solve problems (e.g., find the height of a tree; find the amount of paint needed for a room; scale model)

3D and Orthographic Views - Activity A

MA 12.2.5: Students will apply the units, systems, and formulas to solve problems.

MA 12.2.5.a: Use strategies to find surface area and volume of complex objects

Surface and Lateral Area of Prisms and Cylinders

MA 12.2.5.f: Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)

Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

MA 12.2.5.g: Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively

Dilations
Similar Polygons

MA 12.3: Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.3.1: Students will generalize, represent, and analyze relationships using algebraic symbols.

MA 12.3.1.a: Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear)

Cosine Function
Cubic Function Activity
Distance-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

MA 12.3.1.b: Identify domain and range of functions represented in either symbolic or graphical form (e.g., linear, non-linear)

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

MA 12.3.1.c: Identify the slope and intercepts of a linear relationship from an equation or graph

Defining a Line with Two Points
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs

MA 12.3.1.d: Identify characteristics of linear and non-linear functions

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Using Tables, Rules and Graphs

MA 12.3.1.e: Graph linear and non-linear functions

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

MA 12.3.1.f: Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations

Distance-Time Graphs
Function Machines 2 (Functions, Tables, and Graphs)

MA 12.3.1.g: Graph and interpret linear inequalities

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA 12.3.1.h: Represent, interpret, and analyze functions and their inverses

Cosine Function
Distance-Time Graphs
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Using Tables, Rules and Graphs

MA 12.3.1.i: Determine if a relation is a function

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions

MA 12.3.2: Students will model and analyze quantitative relationships.

MA 12.3.2.a: Model contextualized problems using various representations (e.g., graphs, tables, one variable equalities, one variable inequalities, linear equations in slope intercept form, inequalities in slope intercept form, system of linear equations with two variables)

Linear Inequalities in Two Variables - Activity A
Modeling Linear Systems - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

MA 12.3.2.b: Represent a variety of quantitative relationships using linear equations and one variable inequalities

Linear Functions
Slope-Intercept Form of a Line - Activity A

MA 12.3.2.c: Analyze situations to determine the type of algebraic relationship (e.g., linear, nonlinear)

Linear Functions
Slope-Intercept Form of a Line - Activity A

MA 12.3.2.d: Model contextualized problems using various representations for non-linear functions (e.g., quadratic, exponential, square root, and absolute value)

Exponential Functions - Activity A

MA 12.3.3: Students will represent and solve equations and inequalities.

MA 12.3.3.a: Explain/apply the reflexive, symmetric, and transitive properties of equality

Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

MA 12.3.3.b: Simplify algebraic expressions involving exponents (e.g., (3x to the 4th power)²)

Dividing Exponential Expressions
Multiplying Exponential Expressions

MA 12.3.3.c: Add and subtract polynomials

Addition of Polynomials - Activity A

MA 12.3.3.d: Multiply and divide polynomials (e.g., divide x³ ? 8 by x ? 2, divide x to the 4th power ? 5x³ ? 2x by x²)

Dividing Polynomials Using Synthetic Division

MA 12.3.3.e: Factor polynomials

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA 12.3.3.f: Identify and generate equivalent forms of linear equations

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs

MA 12.3.3.g: Solve linear equations and inequalities including absolute value

Inequalities Involving Absolute Values
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

MA 12.3.3.h: Identify and explain the properties used in solving equations and inequalities

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

MA 12.3.3.i: Solve quadratic equations (e.g., factoring, graphing, quadratic formula)

Factoring Special Products
Roots of a Quadratic

MA 12.3.3.k: Multiply, divide, and simplify rational expressions

Dividing Exponential Expressions

MA 12.3.3.l: Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables

Dividing Exponential Expressions

MA 12.3.3.m: Derive and use the formulas for the general term and summation of finite arithmetic and geometric series

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MA 12.3.3.n: Combine functions by composition, as well as by addition, subtraction, multiplication, and division

Addition and Subtraction of Polynomials
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

MA 12.3.3.o: Solve an equation involving several variables for one variable in terms of the others

Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

MA 12.3.3.p: Analyze and solve systems of two linear equations in two variables algebraically and graphically

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

MA 12.4: Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.4.1: Students will formulate a question and design a survey or an experiment in which data is collected and displayed in a variety of formats, then select and use appropriate statistical methods to analyze the data.

MA 12.4.1.b: Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set

Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Populations and Samples

MA 12.4.1.c: Explain how sample size and transformations of data affect measures of central tendency

Line Plots
Mean, Median and Mode
Populations and Samples

MA 12.4.1.f: Create scatter plots, analyze patterns, and describe relationships in paired data

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

MA 12.4.2: Students will develop and evaluate inferences to make predictions.

MA 12.4.2.a: Compare data sets and evaluate conclusions using graphs and summary statistics

Line Plots
Mean, Median and Mode
Populations and Samples

MA 12.4.2.c: Develop linear equations for linear models to predict unobserved outcomes using regression line and correlation coefficient

Correlation

MA 12.4.2.d: Recognize when arguments based on data confuse correlation with causation

Correlation

MA 12.4.3: Students will apply and analyze concepts of probability.

MA 12.4.3.a: Construct a sample space and a probability distribution

Binomial Probabilities

MA 12.4.3.b: Identify dependent and independent events and calculate their probabilities

Compound Independent Events
Compound Independent and Dependent Events

MA 12.4.3.c: Use the appropriate counting techniques to determine the probability of an event (e.g., combinations, permutations)

Binomial Probabilities
Permutations
Permutations and Combinations

MA 12.4.3.e: Determine the relative frequency of a specified outcome of an event to estimate the probability of the outcome

Geometric Probability - Activity A