Grade Level Articulations

1.1.1: Solve problems and equations that require the number system to be extended from real to complex numbers.

1.1.2: Convert between radical and exponential forms of numerical expressions.

Operations with Radical Expressions

Simplifying Radical Expressions

2.1.2: Compare data sets using graphs and summary statistics, including variance and standard deviation, with or without technology.

Polling: City

Real-Time Histogram

2.1.3: Compute and explain summary statistics for distributions of data including measures of center and spread, including variance and standard deviation.

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Polling: City

Populations and Samples

Real-Time Histogram

Sight vs. Sound Reactions

Stem-and-Leaf Plots

2.1.7: Determine when arguments based on data mistake correlation for causation.

2.1.8: Draw a line of best fit for a scatterplot with or without technology, describe how the correlation coefficient relates to fit, and explain when it is appropriate to use the regression equation to make predictions.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

2.2.1: Apply probability concepts to calculate the probability of events and to make informed decisions in practical situations.

Binomial Probabilities

Independent and Dependent Events

Theoretical and Experimental Probability

2.2.2: Use the principal characteristics of the normal distribution to estimate probabilities.

2.2.3: Estimate probabilities and predict outcomes using one- and two-variable data.

2.3.1: Use the binomial theorem and Pascal's Triangle to solve problems.

2.3.2: Demonstrate the connections between the binomial coefficients, entries of Pascal's triangle, and combinations.

3.1.1: Analyze sequences and series and use them in modeling, including

3.1.1.a: explicit formulas for nth terms,

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

3.1.2: Apply recursive formulas for arithmetic and geometric sequences to solve problems.

Arithmetic Sequences

Geometric Sequences

3.1.4: Solve problems involving recursion.

Arithmetic Sequences

Geometric Sequences

3.2.1: Express and solve problems that can be modeled using linear, quadratic, logarithmic, exponential, cubic, reciprocal, absolute value, and step and other piecewise-defined functions; interpret their solutions in terms of the context.

Arithmetic Sequences

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Quadratics in Polynomial Form

Slope-Intercept Form of a Line

3.2.3: Graph absolute value, and step and other piecewise-defined functions identifying their key characteristics.

Absolute Value with Linear Functions

Translating and Scaling Functions

3.2.4: Graph exponential functions identifying their key characteristics.

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

3.2.6: Graph polynomial functions identifying their key characteristics.

Graphs of Polynomial Functions

Polynomials and Linear Factors

Quadratics in Factored Form

3.2.7: Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions.

Exponential Functions

General Form of a Rational Function

Hyperbolas

Introduction to Exponential Functions

Logarithmic Functions

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

Polynomials and Linear Factors

Radical Functions

Rational Functions

Roots of a Quadratic

3.2.8: Find the major and minor axes, intercepts and asymptotes of conic sections.

3.2.9: Find domain, range, intercepts, period, amplitude, and asymptotes of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

3.2.10: Given a function

3.2.10.a: find the inverse of the function,

3.2.12: Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes Rule of Signs, the Conjugate Root Theorem) to find the zeros of a polynomial function.

Graphs of Polynomial Functions

3.2.14: Combine functions by composition, as well as by addition, subtraction, multiplication, and division including any necessary restrictions on the domain.

Addition and Subtraction of Functions

3.2.16: Identify the degree of a given polynomial function and write a polynomial function of a given degree.

Graphs of Polynomial Functions

Polynomials and Linear Factors

3.3.1: Rewrite and describe the need for equivalent forms of algebraic expressions.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

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

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

3.3.2: Apply the laws of exponents including rational and negative exponents to rewrite expressions in alternative forms.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

3.3.4: Use matrices to represent everyday problems that involve systems of linear equations.

Solving Linear Systems (Matrices and Special Solutions)

3.3.5: Simplify radical expressions by performing operations on them.

Operations with Radical Expressions

Simplifying Radical Expressions

3.3.6: Divide a polynomial by a lower degree polynomial.

Dividing Polynomials Using Synthetic Division

3.3.7: Find complex solutions for quadratic equations.

3.3.8: Describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression with and without technology.

Logarithmic Functions

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

Polynomials and Linear Factors

Roots of a Quadratic

3.3.11: Add, subtract, and compute the dot product of two-dimensional vectors; multiply a two-dimensional vector by a scalar.

3.4.5: Solve problems involving compound interest.

3.4.6: Demonstrate the relationship between

3.4.6.a: simple interest and linear growth

3.4.6.b: compound interest and exponential growth.

4.1.1: Perform basic geometric constructions using a variety of methods, including

4.1.1.a: perpendicular bisector of a line segment,

Concurrent Lines, Medians, and Altitudes

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

4.1.1.b: bisector of an angle

Concurrent Lines, Medians, and Altitudes

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

4.1.1.c: perpendicular or parallel lines.

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Parallel, Intersecting, and Skew Lines

4.2.1: Describe how changing the parameters of a quadratic function affects the shape and position of its graph (f(x) = a(x-h)²+k).

Graphs of Polynomial Functions

Zap It! Game

4.2.2: Describe how changing the parameters of an exponential function affects the shape and position of its graph (f(x) = ab to the x power).

Introduction to Exponential Functions

4.3.2: Determine an equation of a circle given its center and radius; given an equation of a circle, find its center and radius.

4.3.3: Graph equations of conic sections explaining the relationship between their algebraic form and key characteristics of the graph.

Circles

Ellipses

Hyperbolas

Parabolas

4.3.4: Graph all six trigonometric functions identifying their key characteristics.

Translating and Scaling Functions

4.3.5: Evaluate all six trigonometric functions at angles between (0 degrees and 360 degrees, 0 and 2π radians) using the unit circle in the coordinate plane.

Cosine Function

Sine Function

Tangent Function

4.4.1: Explain, use, and convert between degree and radian measures for angles.

Cosine Function

Sine Function

Tangent Function

Correlation last revised: 1/20/2017

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