Gizmos for South Dakota - Mathematics: Algebra 2 (Content Standards adopted 2018)

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

A.SSE: : Seeing Structure in Expressions

1.1: : Interpret the structure of expressions.

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

A.SSE.1.a: : Interpret parts of an expression, such as terms, factors, and coefficients.

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

A.SSE.2: : Recognize and use the structure of an expression to identify ways to rewrite it.

A.APR: : Arithmetic with Polynomials and Rational Expressions

2.1: : Understand the relationship between zeros and factors of polynomials.

A.APR.2: : Know and apply the Remainder Theorem.

A.APR.3: : Identify zeros of polynomials by factoring.

A.APR.3.a: : When suitable factorizations are available, use the zeros to construct a rough graph of the related function.

A.APR.3.b: : When given a graph, use the zeros to construct a possible factorization of a polynomial.

A.CED: : Creating Equations

3.1: : Create equations that describe numbers or relationships.

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

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

A.CED.3: : Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

A.CED.4: : Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.REI: : Reasoning with Equations and Inequalities

4.1: : Understand solving equations as a process of reason and explain the reasoning.

A.REI.2: : Solve rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Rational functions are limited to those whose numerators are of degree at most 1 and denominators of degree at most 2. Radical functions are limited to square roots or cube roots of at most quadratic polynomials.

4.2: : Solve equations and inequalities in one variable.

A.REI.4: : Select, justify and apply appropriate methods to solve quadratic equations in one variable. Recognize complex solutions and write them as a +/- bi for real numbers a and b.

4.3: : Represent and solve equations and inequalities graphically.

A.REI.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, including but not limited to using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

F.IF: : Interpreting Functions

5.1: : Interpret functions that arise in applications in terms of the context.

F.IF.4: : For functions that model 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries (including even, odd, or neither); end behavior; and periodicity.

F.IF.5: : Relate the domain of a function to its graph and find an appropriate domain in the context of the problem.

5.2: : Analyze functions using different representations.

F.IF.7: : Graph parent functions and their transformations expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7.b: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.7.c: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.IF.7.e: : Graph logarithmic functions, showing intercepts and end behavior.

F.IF.7.f: : Graph trigonometric functions (sine and cosine), showing period, midline, and amplitude.

F.IF.9: : Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

F.BF: : Building Functions

6.1: : Build new functions from existing functions.

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

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

F.BF.1.b: : Determine an explicit expression from a graph.

F.BF.1.c: : Combine standard function types using arithmetic operations.

F.BF.3: : Identify the effect on the graph of f(x) replaced with 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 contrasting cases and illustrate an explanation of the effects on the graph using technology.

F.BF.4: : Find inverse functions.

F.BF.4.c: : Read values of an inverse function from a graph or a table, given that the function has an inverse.

F.BF.5: : Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

F.LE: : Linear, Quadratic and Exponential Models

7.1: : Construct and compare linear and exponential models and solve.

F.LE.4: : For exponential models, express as a logarithm the solution to ab to the ct power = dwhere a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

F.TF: : Trigonometric Functions

8.1: : Extend the domain of trigonometric functions using the unit circle.

F.TF.1: : Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

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

8.2: : Model periodic phenomena with trigonometric functions.

F.TF.5: : Choose trigonometric functions (sine and cosine) to model periodic phenomena with specified amplitude, frequency, and midline.

8.3: : Prove and apply trigonometric identities.

F.TF.8: : Prove the Pythagorean identity sin²(A) + cos²(A) = 1 and use it to calculate trigonometric ratios.

N.CN: : The Complex Number System

9.1: : Perform arithmetic operations with complex numbers.

N.CN.1: : Know there is a complex number i such that i² = -1, and every complex number has the form a + bi where a and b are real numbers.

N.CN.2: : Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

9.2: : Use complex numbers in polynomials identities and equations.

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

S.ID: : Interpreting Categorical and Quantitative Data

10.1: : Summarize, represent and interpret data on a single count or measurement variable.

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

S.IC: : Making Inferences and Justifying Conclusions

11.1: : Understand and evaluate random processes underlying statistical experiments.

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

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

11.2: : Make interferences and justify conclusions from sample surveys, experiments and observational studies.

S.IC.3: : Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

S.IC.4: : Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S.IC.5: : Use data from a randomized experiment to compare two treatment groups; use simulations to decide if differences between parameters are significant.

S.IC.6: : Evaluate reports based on data.

Correlation last revised: 9/16/2020

South Dakota - Mathematics: Algebra 2

Content Standards | Adopted: 2018