M2.N: Number and Quantity

M2.N.RN: The Real Number System

M2.N.RN.A: Extend the properties of exponents to rational exponents.

M2.N.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Exponents and Power Rules

M2.N.CN: The Complex Number System

M2.N.CN.A: Perform arithmetic operations with complex numbers.

M2.N.CN.A.1: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

Points in the Complex Plane
Roots of a Quadratic

M2.N.CN.A.2: Know and use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

M2.N.CN.B: Use complex numbers in polynomial identities and equations.

M2.N.CN.B.3: Solve quadratic equations with real coefficients that have complex solutions.

Points in the Complex Plane
Roots of a Quadratic

M2.A: Algebra

M2.A.SSE: Seeing Structure in Expressions

M2.A.SSE.A: Interpret the structure of expressions.

M2.A.SSE.A.1: Interpret expressions that represent a quantity in terms of its context.

M2.A.SSE.A.1.a: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Translating and Scaling Functions
Using Algebraic Expressions

M2.A.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Trigonometric Expressions
Solving Algebraic Equations II
Using Algebraic Expressions

M2.A.SSE.B: Write expressions in equivalent forms to solve problems.

M2.A.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

M2.A.SSE.B.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

M2.A.SSE.B.3.b: Complete the square in a quadratic expression in the form Ax² + Bx + C to reveal the maximum or minimum value of the function it defines.

Quadratics in Vertex Form

M2.A.APR: Arithmetic with Polynomials and Rational Expressions

M2.A.APR.A: Perform arithmetic operations on polynomials.

M2.A.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

M2.A.CED: Creating Equations

M2.A.CED.A: Create equations that describe numbers or relationships.

M2.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

M2.A.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales.

Absolute Value Equations and Inequalities
Circles
Compound Interest
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

M2.A.CED.A.3: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

M2.A.REI: Reasoning with Equations and Inequalities

M2.A.REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

M2.A.REI.A.1: Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Two-Step Equations

M2.A.REI.B: Solve equations and inequalities in one variable.

M2.A.REI.B.2: Solve quadratic equations and inequalities in one variable.

M2.A.REI.B.2.a: Use the method of completing the square to rewrite any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

Roots of a Quadratic

M2.A.REI.B.2.b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

M2.A.REI.C: Solve systems of equations.

M2.A.REI.C.3: Write and solve a system of linear equations in context.

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

M2.F: Functions

M2.F.IF: Interpreting Functions

M2.F.IF.A: Interpret functions that arise in applications in terms of the context.

M2.F.IF.A.1: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

M2.F.IF.A.2: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Logarithmic Functions
Radical Functions
Rational Functions

M2.F.IF.A.3: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Cat and Mouse (Modeling with Linear Systems)
Slope

M2.F.IF.B: Analyze functions using different representation.

M2.F.IF.B.4: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.

M2.F.IF.B.4.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Graphs of Polynomial Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Zap It! Game

M2.F.IF.B.4.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

M2.F.IF.B.4.c: Graph exponential and logarithmic functions, showing intercepts and end behavior.

Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

M2.F.IF.B.5: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

M2.F.IF.B.5.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

M2.F.IF.B.5.b: Know and use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Functions

M2.F.IF.B.6: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function
Graphs of Polynomial Functions
Linear Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form

M2.F.BF: Building Functions

M2.F.BF.A: Build a function that models a relationship between two quantities.

M2.F.BF.A.1: Write a function that describes a relationship between two quantities.

M2.F.BF.A.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

M2.F.BF.A.1.b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

M2.F.BF.B: Build new functions from existing functions.

M2.F.BF.B.2: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

M2.G: Geometry

M2.G.SRT: Similarity, Right Triangles, and Trigonometry

M2.G.SRT.A: Understand similarity in terms of similarity transformations.

M2.G.SRT.A.1: Verify informally the properties of dilations given by a center and a scale factor.

Dilations
Similar Figures

M2.G.SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Circles
Dilations
Similar Figures
Similarity in Right Triangles

M2.G.SRT.A.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Similar Figures

M2.G.SRT.B: Prove theorems involving similarity.

M2.G.SRT.B.4: Prove theorems about similar triangles.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures

M2.G.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.

Chords and Arcs
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Dilations
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

M2.G.SRT.C: Define trigonometric ratios and solve problems involving triangles.

M2.G.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Sine, Cosine, and Tangent Ratios

M2.G.SRT.C.8: Solve triangles.

M2.G.SRT.C.8.a: Know and use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

M2.G.GMD: Geometric Measurement and Dimension

M2.G.GMD.A: Explain volume and surface area formulas and use them to solve problems.

M2.G.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid.

Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones

M2.G.GMD.A.2: Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems.

Prisms and Cylinders
Pyramids and Cones

M2.S: Statistics and Probability

M2.S.ID: Interpreting Categorical and Quantitative Data

M2.S.ID.A: Summarize, represent, and interpret data on two categorical and quantitative variables.

M2.S.ID.A.1: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

M2.S.ID.A.1.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

M2.S.CP: Conditional Probability and the Rules of Probability

M2.S.CP.A: Understand independence and conditional probability and use them to interpret data.

M2.S.CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

M2.S.CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Independent and Dependent Events

M2.S.CP.A.3: Know and understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Independent and Dependent Events

M2.S.CP.A.4: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

M2.S.CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

M2.S.CP.B.5: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A and interpret the answer in terms of the model.

Independent and Dependent Events