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

Rational Numbers, Opposites, and Absolute Values

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))

Fractions with Unlike Denominators
Square Roots

MA 12.1.3: Students will compute fluently and accurately using appropriate strategies and tools.

MA 12.1.3.c: Multiply and divide numbers using scientific notation

Unit Conversions

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.a: Identify and explain the necessity of and give examples of definitions and theorems

Biconditional Statements

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

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Parallel, Intersecting, and Skew Lines
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

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

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

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
Circles
Inscribed Angles

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.b: Apply the midpoint formula

Circles

MA 12.2.2.c: Apply the distance formula

Circles
Distance Formula

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

Isosceles and Equilateral Triangles
Parallelogram Conditions
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Special Parallelograms
Triangle Angle Sum
Triangle Inequalities

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

Rotations, Reflections, and Translations
Translations

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

MA 12.2.5.c: Convert between various units of area and volume, such as square feet to square yards

Unit Conversions

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

Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

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)

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Geometric Sequences
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

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

Exponential Functions
Introduction to Functions
Logarithmic Functions
Radical Functions

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

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

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

Absolute Value with Linear Functions
Graphs of Polynomial Functions
Linear Functions
Slope-Intercept Form of a Line

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

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Vertex Form
Slope-Intercept Form of a Line

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

Exponential Functions
Translating and Scaling Functions

MA 12.3.1.g: Graph and interpret linear inequalities

Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

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

Logarithmic Functions

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

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)

Quadratics in Polynomial Form
Slope-Intercept Form of a Line
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)
Using Algebraic Expressions

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

Linear Functions

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

Linear Functions

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

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

Dividing Exponential Expressions
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

MA 12.3.3.c: Add and subtract polynomials

Addition and Subtraction of Functions
Addition of Polynomials

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
Modeling the Factorization of x²+bx+c

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.g: Solve linear equations and inequalities including absolute value

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form)

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

Solving Algebraic Equations II

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

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

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

Arithmetic 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 Functions

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

Solving Formulas for any Variable

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

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

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.a: Interpret data represented by the normal distribution and formulate conclusions

Polling: City

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

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

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

Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)

MA 12.4.1.d: Describe the shape and determine spread (variance, standard deviation) and outliers of a data set

Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode
Polling: City
Real-Time Histogram
Sight vs. Sound Reactions

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

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

MA 12.4.1.g: Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection and the conclusions that can rightfully be made

Polling: City
Polling: Neighborhood

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

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)

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

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

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

Polling: City
Probability Simulations
Theoretical and Experimental Probability

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

Independent and Dependent Events
Theoretical and Experimental Probability

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

Binomial Probabilities
Permutations and Combinations