AII.NQ: Number and Quantity

1.1: Together, irrational numbers and rational numbers complete the real number system, representing all points on the number line, while there exist numbers beyond the real numbers called complex numbers.

AII.NQ.1: Students will… Identify numbers written in the form a + bi, where a and b are real numbers and i² = –1, as complex numbers.

AII.NQ.1.a: Add, subtract, and multiply complex numbers using the commutative, associative, and distributive properties.

Points in the Complex Plane

1.2: Matrices are a useful way to represent information.

AII.NQ.2: Students will… Use matrices to represent and manipulate data.

Dilations
Translations

AII.NQ.3: Students will… Multiply matrices by scalars to produce new matrices.

Dilations

AII.NQ.4: Students will… Add, subtract, and multiply matrices of appropriate dimensions.

Translations

AII.NQ.5: Students will… Describe the roles that zero and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real numbers.

AII.NQ.5.a: Students will… Find the additive and multiplicative inverses of square matrices, using technology as appropriate.

Solving Linear Systems (Matrices and Special Solutions)

AII.NQ.5.b: Students will… Explain the role of the determinant in determining if a square matrix has a multiplicative inverse.

Solving Linear Systems (Matrices and Special Solutions)

AII.NQ.1: Algebra

1.3.1: Expressions can be rewritten in equivalent forms by using algebraic properties, including properties of addition, multiplication, and exponentiation, to make different characteristics or features visible.

AII.NQ.1.6: Students will… Factor polynomials using common factoring techniques, and use the factored form of a polynomial to reveal the zeros of the function it defines.

Quadratics in Factored Form

AII.NQ.1.7: Students will… Prove polynomial identities and use them to describe numerical relationships.

Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

1.3.3: The structure of an equation or inequality (including, but not limited to, one-variable linear and quadratic equations, inequalities, and systems of linear equations in two variables) can be purposefully analyzed (with and without technology) to determine an efficient strategy to find a solution, if one exists, and then to justify the solution.

AII.NQ.1.9: Students will… For exponential models, express as a logarithm the solution to (ab)^(ct) = d, where a, c, and d are real numbers and the base b is 2 or 10; evaluate the logarithm using technology to solve an exponential equation.

Logarithmic Functions

1.3.4: Expressions, equations, and inequalities can be used to analyze and make predictions, both within mathematics and as mathematics is applied in different contexts—in particular, contexts that arise in relation to linear, quadratic, and exponential situations.

AII.NQ.1.10: Students will… Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities
Exploring Linear Inequalities in One Variable
Roots of a Quadratic
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Linear Systems (Slope-Intercept Form)

AII.NQ.1.11: Students will… Solve quadratic equations with real coefficients that have complex solutions.

Roots of a Quadratic

AII.NQ.1.12: Students will… Solve simple equations involving exponential, radical, logarithmic, and trigonometric functions using inverse functions.

Logarithmic Functions
Radical Functions

AII.NQ.1.13: Students will… Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales and use them to make predictions.

Exponential Functions
Exponential Growth and Decay
Quadratics in Polynomial Form
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

AII.NQ.2: Connecting Algebra to Functions

1.4.1: Graphs can be used to obtain exact or approximate solutions of equations, inequalities, and systems of equations and inequalities—including systems of linear equations in two variables and systems of linear and quadratic equations (given or obtained by using technology).

AII.NQ.2.14: Students will… 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).

AII.NQ.2.14.a: Find the approximate solutions of an equation graphically, using tables of values, or finding successive approximations, using technology where appropriate.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)

AII.NQ.3: Functions

1.5.1: Functions can be described by using a variety of representations: mapping diagrams, function notation (e.g., f(x) = x²), recursive definitions, tables, and graphs.

AII.NQ.3.15: Students will… Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Direct and Inverse Variation
Logarithmic Functions

1.5.2: Functions that are members of the same family have distinguishing attributes (structure) common to all functions within that family.

AII.NQ.3.16: Students will… Identify the effect on the graph of replacing f(x) by f(x) + k, k · f(x), f(k · 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.

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

1.5.3: Functions can be represented graphically, and key features of the graphs, including zeros, intercepts, and, when relevant, rate of change and maximum/minimum values, can be associated with and interpreted in terms of the equivalent symbolic representation.

AII.NQ.3.17: Students will… 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.

Cosine Function
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Sine Function
Tangent Function

AII.NQ.3.18: Students will… Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions

AII.NQ.3.19: Students will… 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)
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope

AII.NQ.3.20: Students will… Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

AII.NQ.3.20.a: Graph polynomial functions expressed symbolically, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions

AII.NQ.3.20.b: Graph sine and cosine functions expressed symbolically, showing period, midline, and amplitude.

Cosine Function
Sine Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

AII.NQ.3.20.c: Graph logarithmic functions expressed symbolically, showing intercepts and end behavior.

Logarithmic Functions
Logarithmic Functions: Translating and Scaling

AII.NQ.3.20.d: Graph reciprocal functions expressed symbolically, identifying horizontal and vertical asymptotes.

Rational Functions

AII.NQ.3.20.e: Graph square root and cube root functions expressed symbolically.

Radical Functions

AII.NQ.3.20.f: Compare the graphs of inverse functions and the relationships between their key features, including but not limited to quadratic, square root, exponential, and logarithmic functions.

Logarithmic Functions
Radical Functions

AII.NQ.3.21: Students will… Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle, building on work with non-right triangle trigonometry.

Cosine Function
Sine Function
Tangent Function

1.5.4: Functions model a wide variety of real situations and can help students understand the processes of making and changing assumptions, assigning variables, and finding solutions to contextual problems.

AII.NQ.3.22: Students will… Use the mathematical modeling cycle to solve real-world problems involving polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions, from the simplification of the problem through the solving of the simplified problem, the interpretation of its solution, and the checking of the solution’s feasibility.

Absolute Value Equations and Inequalities
Distance-Time Graphs - Metric
Distance-Time and Velocity-Time Graphs
Logarithmic Functions: Translating and Scaling
Quadratics in Polynomial Form
Roots of a Quadratic
Sine Function

AII.DSP: Data Analysis, Statistics, and Probability

AII.DSP.1: Quantitative Literacy

2.1.1: Mathematical and statistical reasoning about data can be used to evaluate conclusions and assess risks.

AII.DSP.1.23: Students will… Use mathematical and statistical reasoning about normal distributions to draw conclusions and assess risk; limit to informal arguments.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

2.1.2: Making and defending informed data-based decisions is a characteristic of a quantitatively literate person.

AII.DSP.1.24: Students will… Design and carry out an experiment or survey to answer a question of interest, and write an informal persuasive argument based on the results.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Histograms
Polling: Neighborhood
Sight vs. Sound Reactions
Stem-and-Leaf Plots

AII.DSP.2: Visualizing and Summarizing Data

2.2.1: Distributions of quantitative data (continuous or discrete) in one variable should be described in the context of the data with respect to what is typical (the shape, with appropriate measures of center and variability, including standard deviation) and what is not (outliers), and these characteristics can be used to compare two or more subgroups with respect to a variable.

AII.DSP.2.25: Students will… From a normal distribution, use technology to find the mean and standard deviation and estimate population percentages by applying the empirical rule.

AII.DSP.2.25.a: Use technology to determine if a given set of data is normal by applying the empirical rule.

Sight vs. Sound Reactions

AII.DSP.3: Statistical Inference

2.3.1: Study designs are of three main types: sample survey, experiment, and observational study.

AII.DSP.3.26: Students will… Describe the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City
Sight vs. Sound Reactions
Time Estimation

2.3.2: The role of randomization is different in randomly selecting samples and in randomly assigning subjects to experimental treatment groups.

AII.DSP.3.27: Students will… Distinguish between a statistic and a parameter and use statistical processes to make inferences about population parameters based on statistics from random samples from that population.

Populations and Samples

2.3.4: Bias, such as sampling, response, or nonresponse bias, may occur in surveys, yielding results that are not representative of the population of interest.

AII.DSP.3.30: Students will… Evaluate where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are representative of the population of interest.

Polling: City

2.3.5: The larger the sample size, the less the expected variability in the sampling distribution of a sample statistic.

AII.DSP.3.31: Students will… Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic.

AII.DSP.3.31.a: Simulate a sampling distribution of sample means from a population with a known distribution, observing the effect of the sample size on the variability.

Populations and Samples

AII.DSP.3.31.b: Demonstrate that the standard deviation of each simulated sampling distribution is the known standard deviation of the population divided by the square root of the sample size.

Real-Time Histogram
Sight vs. Sound Reactions
Time Estimation

2.3.6: The sampling distribution of a sample statistic formed from repeated samples for a given sample size drawn from a population can be used to identify typical behavior for that statistic. Examining several such sampling distributions leads to estimating a set of plausible values for the population parameter, using the margin of error as a measure that describes the sampling variability.

AII.DSP.3.32: Students will… Produce a sampling distribution by repeatedly selecting samples of the same size from a given population or from a population simulated by bootstrapping (resampling with replacement from an observed sample). Do initial examples by hand, then use technology to generate a large number of samples.

AII.DSP.3.32.a: Verify that a sampling distribution is centered at the population mean and approximately normal if the sample size is large enough.

Populations and Samples
Sight vs. Sound Reactions

AII.DSP.3.32.b: Verify that 95% of sample means are within two standard deviations of the sampling distribution from the population mean.

Polling: City
Real-Time Histogram

AII.DSP.3.32.c: Create and interpret a 95% confidence interval based on an observed mean from a sampling distribution.

Polling: City
Real-Time Histogram

AII.GM: Geometry and Measurement

AII.GM.1: Measurement

3.1.1: When an object is the image of a known object under a similarity transformation, a length, area, or volume on the image can be computed by using proportional relationships.

AII.GM.1.34: Students will… Define the radian measure of an angle as the constant of proportionality of the length of an arc it intercepts to the radius of the circle; in particular, it is the length of the arc intercepted on the unit circle.

Radians

AII.GM.4: Solving Applied Problems and Modeling in Geometry

3.4.1: Recognizing congruence, similarity, symmetry, measurement opportunities, and other geometric ideas, including right triangle trigonometry in real-world contexts, provides a means of building understanding of these concepts and is a powerful tool for solving problems related to the physical world in which we live.

AII.GM.4.35: Students will… Choose trigonometric functions (sine and cosine) to model periodic phenomena with specified amplitude, frequency, and midline.

Sine Function
Sound Beats and Sine Waves
Translating and Scaling Sine and Cosine Functions

AII.GM.4.36: Students will… Prove the Pythagorean identity sin² (theta) + cos² (theta) = 1 and use it to calculate trigonometric ratios.

Cosine Function
Sine Function

Correlation last revised: 3/2/2020

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