Academic Standards

A2.N-CN.A: Perform arithmetic operations with complex numbers.

A2.N-CN.A.1: Apply the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Write complex numbers in the form (a + bi) with a and b real.

Points in the Complex Plane

Roots of a Quadratic

A2.N-CN.C: Use complex numbers in polynomial identities and equations.

A2.N-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.

Points in the Complex Plane

Roots of a Quadratic

A2.A-SSE.A: Interpret the structure of expressions.

A2.A-SSE.A.2: Use structure to identify ways to rewrite polynomial and rational expressions. Focus on polynomial operations and factoring patterns.

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

A2.A-APR.B: Understand the relationship between zeros and factors of polynomials.

A2.A-APR.B.2: Know and apply the Remainder and Factor Theorem: For a polynomial p(x) and a number a, the remainder on division by (x - a) is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

Dividing Polynomials Using Synthetic Division

A2.A-APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Focus on quadratic, cubic, and quartic polynomials including polynomials for which factors are not provided.

Graphs of Polynomial Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

A2.A-APR.C: Use polynomial identities to solve problems.

A2.A-APR.C.4: Prove polynomial identities and use them to describe numerical relationships.

A2.A-CED.A: Create equations that describe numbers or relationships.

A2.A-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include problem-solving opportunities utilizing real-world context. Focus on equations and inequalities arising from linear, quadratic, rational, and exponential functions.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Exploring Linear Inequalities in One Variable

Geometric Sequences

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

A2.A-REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

A2.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. Extend from quadratic equations to rational and radical equations.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

A2.A-REI.A.2: Solve rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

A2-A-REI.B: Solve equations and inequalities in one variable.

A2.A-REI.B.4: Fluently solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, 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.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Points in the Complex Plane

Roots of a Quadratic

A2-A-REI.D: Represent and solve equations and inequalities graphically.

A2.A-REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Include problems in real-world context. Extend from linear, quadratic, and exponential functions to cases where f(x) and/or g(x) are polynomial, rational, exponential, and logarithmic functions.

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Standard Form of a Line

A2.F-IF.B: Interpret functions that arise in applications in terms of the context.

A2.F-IF.B.4: 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. Include problem-solving opportunities utilizing a real-world context. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Functions include linear, quadratic, exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root and piecewise-defined functions.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Cosine Function

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Roots of a Quadratic

Sine Function

Slope-Intercept Form of a Line

Tangent Function

Translating and Scaling Sine and Cosine Functions

A2.F-IF.B.6: Calculate and interpret the average rate of change of a continuous function (presented symbolically or as a table) on a closed interval. Estimate the rate of change from a graph. Include problem-solving opportunities utilizing real-world context. Functions include linear, quadratic, exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root and piecewise-defined functions.

Cat and Mouse (Modeling with Linear Systems)

Compound Interest

Point-Slope Form of a Line

Slope

Slope-Intercept Form of a Line

Translating and Scaling Functions

A2.F-IF.C: Analyze functions using different representations.

A2.F-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions include linear, quadratic, exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root and piecewise-defined functions.

Absolute Value with Linear Functions

Addition and Subtraction of Functions

Arithmetic Sequences

Compound Interest

Cosine Function

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Point-Slope Form of a Line

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Roots of a Quadratic

Sine Function

Slope-Intercept Form of a Line

Standard Form of a Line

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Zap It! Game

A2.F-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

A2.F-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions and classify those functions as exponential growth or decay.

Compound Interest

Exponential Functions

A2.F-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions.). Functions include linear, quadratic, exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root and piecewise-defined functions.

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Slope-Intercept Form of a Line

Translating and Scaling Functions

A2.F-BF.A: Build a function that models a relationship between two quantities.

A2.F-BF.A.1: Write a function that describes a relationship between two quantities. Functions include linear, quadratic, exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root and piecewise-defined functions. Include problem-solving opportunities utilizing real-world context.

A2.F-BF.A.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

A2.F-BF.A.1b: Combine function types using arithmetic operations and function composition.

Addition and Subtraction of Functions

A2.F-BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

A2.F-BF.B: Build new functions from existing functions.

A2.F-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Functions include linear, quadratic, exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root and piecewise-defined functions.

Absolute Value with Linear Functions

Exponential Functions

General Form of a Rational Function

Introduction to Exponential Functions

Quadratics in Vertex Form

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

A2.F-BF.B.4: Find inverse functions.

A2.F-BF.B.4a: Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, recognizing that functions f and g are inverse functions if and only if f(x) = y and g(y) = x for all values of x in the domain of f and all values of y in the domain of g.

A2.F-BF.B.4b: Understand that if a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a).

A2.F-LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.

A2.F-LE.A.4: For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithms that are not readily found by hand or observation using technology.

A2.F-LE.B: Interpret expressions for functions in terms of the situation they model.

A2.F-LE.B.5: Interpret the parameters in an exponential function with rational exponents utilizing real-world context.

Arithmetic Sequences

Compound Interest

Introduction to Exponential Functions

A2.F-TF.A: Extend the domain of trigonometric functions using the unit circle.

A2.F-TF.A.2: Explain how the unit circle in the coordinate plane enables the extension of sine and cosine functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function

Sine Function

Tangent Function

A2.F-TF.B: Model periodic phenomena with trigonometric functions.

A2.F-TF.B.5: Create and interpret sine, cosine and tangent functions that model periodic phenomena with specified amplitude, frequency, and midline.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

A2.F-TF.C: Apply trigonometric identities.

A2.F-TF.C.8: Use the Pythagorean identity sin²(theta) + cos²(theta) = 1 and the quadrant of the angle theta to find sin(theta), cos(theta), or tan(theta) given sin(theta) or cos(theta).

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

A2.S-ID.A: Summarize, represent, and interpret data on a single count or measurement variable.

A2.S-ID.A.4: Use the mean and standard deviation of a data set to fit it to a normal curve, and use properties of the normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, or tables to estimate areas under the normal curve.

Polling: City

Populations and Samples

Real-Time Histogram

A2.S-ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.

A2.S-ID.B.6: Represent data of two quantitative variables on a scatter plot, and describe how the quantities are related. Extend to polynomial and exponential models.

A2.S-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

Zap It! Game

A2.S-IC.A: Understand and evaluate random processes underlying statistical experiments.

A2.S-IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Polling: City

Polling: Neighborhood

Populations and Samples

A2.S-IC.A.2: Explain whether a specified model is consistent with results from a given data-generating process.

Polling: City

Polling: Neighborhood

Populations and Samples

A2.S-IC.B: Make inferences and justify conclusions from experiments, and observational studies.

A2.S-IC.B.3: Recognize the purposes of and differences between designed experiments, sample surveys and observational studies.

A2.S-IC.B.4: Use data from a sample survey to estimate a population mean or proportion; recognize that estimates are unlikely to be correct and the estimates will be more precise with larger sample sizes.

A2.S-CP.A: Understand independence and conditional probability and use them to interpret data.

A2.S-CP.A.3: 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

A2.S-CP.A.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

A2.S-CP.A.5: Recognize and explain the concepts of conditional probability and independence utilizing real-world context.

Independent and Dependent Events

A2.S-CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

A2.S-CP.B.6: Use Bayes Rule to 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

A2.S-CP.B.8: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

Independent and Dependent Events

5.1.1: Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. While engaging in productive struggle to solve a problem, they continually ask themselves, “Does this make sense?' to monitor and evaluate their progress and change course if necessary. Once they have a solution, they look back at the problem to determine if the solution is reasonable and accurate. Mathematically proficient students check their solutions to problems using different methods, approaches, or representations. They also compare and understand different representations of problems and different solution pathways, both their own and those of others.

Biconditional Statements

Conditional Statements

Estimating Population Size

5.2.1: Mathematically proficient students make sense of quantities and their relationships in problem situations. Students can contextualize and decontextualize problems involving quantitative relationships. They contextualize quantities, operations, and expressions by describing a corresponding situation. They decontextualize a situation by representing it symbolically. As they manipulate the symbols, they can pause as needed to access the meaning of the numbers, the units, and the operations that the symbols represent. Mathematically proficient students know and flexibly use different properties of operations, numbers, and geometric objects and when appropriate they interpret their solution in terms of the context.

Estimating Population Size

Using Algebraic Expressions

5.3.1: Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

5.4.1: Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Estimating Population Size

Using Algebraic Expressions

5.6.1: Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

Biconditional Statements

Using Algebraic Expressions

5.7.1: Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

5.8.1: Mathematically proficient students look for and describe regularities as they solve multiple related problems. They formulate conjectures about what they notice and communicate observations with precision. While solving problems, students maintain oversight of the process and continually evaluate the reasonableness of their results. This informs and strengthens their understanding of the structure of mathematics which leads to fluency.

Correlation last revised: 4/4/2018

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