High Academic Standards for Students

RFR.AF.1: Interpret parameters of a function defined by an expression in the context of the situation.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Compound Interest

Direct and Inverse Variation

Exponential Growth and Decay

Quadratics in Polynomial Form

RFR.AF.2: Sketch the graph of a function that models a relationship between two quantities, identifying key features.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Cosine Function

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Parabolas

Point-Slope Form of a Line

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 Functions

Translating and Scaling Sine and Cosine Functions

RFR.AF.3: Interpret key features of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.

Absolute Value with Linear Functions

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

Logarithmic Functions: Translating and Scaling

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Standard Form of a Line

RFR.AF.4: Use limits to describe long-range behavior, asymptotic behavior, and points of discontinuity.

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Rational Functions

RFR.AF.5: Sketch the graph of all six trigonometric functions, identifying key features.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

RFR.AF.b: Students should have opportunities to… Calculate, interpret, and use average rate of change.

Cat and Mouse (Modeling with Linear Systems)

Graphs of Derivative Functions

Slope

RFR.AF.c: Students should have opportunities to… Use multiple representations of function models appropriately.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Compound Interest

Direct and Inverse Variation

Exponential Growth and Decay

Quadratics in Polynomial Form

RFR.AF.d: Students should have opportunities to… Work with different families of functions beyond linear and quadratic functions including but not limited to exponential, logarithmic, rational, polynomial, logistic, radical, and piecewise-defined functions.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Cosine Function

Exponential Functions

Exponential Growth and Decay

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Polynomials and Linear Factors

Radical Functions

Rational Functions

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

RFR.AF.e: Students should have opportunities to… Graph rational functions including those whose graphs contain horizontal asymptotes, vertical asymptotes, oblique asymptotes, and/or holes.

General Form of a Rational Function

Rational Functions

RFR.AF.f: Students should have opportunities to… Make sense of radian measure.

RFR.AF.g: Students should have opportunities to… Use the unit circle as a tool to graph the trig functions in radians and degrees.

Cosine Function

Sine Function

Tangent Function

RFR.AF.h: Students should have opportunities to… Develop fluency with the unit circle. Include opportunities beyond the special angles, for example, explain why sin(1.1) > sin(0.3) in radians.

Cosine Function

Sine Function

Tangent Function

RFR.AF.i: Students should have opportunities to… Graph sine, cosine, tangent functions in radians and degrees and analyze/explain the characteristics of each.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

RFR.BF.1: Model relationships between quantities that require adding, subtracting, multiplying, and/or dividing functions.

Addition and Subtraction of Functions

RFR.BF.4: Determine if a function has an inverse. If so, find the inverse. If not, define a restriction on the domain that meets the requirement for invertibility and find the inverse on the restricted domain.

Logarithmic Functions

Radical Functions

RFR.BF.5: Interpret the meanings of quantities involving functions and their inverses.

RFR.BF.6: Verify by analytical methods that one function is the inverse of another.

RFR.BF.a: Students should have opportunities to… Model real-world situations with the sum, difference, product, or quotient of other function models.

Addition and Subtraction of Functions

RFR.BF.b: Students should have opportunities to… Describe relationships of quantities in functions and within a composition of those functions.

Absolute Value with Linear Functions

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Radical Functions

Rational Functions

RFR.BF.c: Students should have opportunities to… Find an inverse algebraically, for example given y = f(x) algebraically find x = f^-1(y). Work with exponential and logarithmic functions, and quadratic and square root functions at a minimum.

Logarithmic Functions

Radical Functions

RFR.BF.e: Students should have opportunities to… Describe the meaning of f^-1(20) given a function f that takes hours as an input and gives miles as an output.

RFR.IC.1: Model real-world situations which involve conic sections.

RFR.IC.2: Identify key features of conic sections (foci, directrix, radii, axes, asymptotes, center) graphically and algebraically.

Circles

Ellipses

Hyperbolas

Parabolas

RFR.IC.3: Sketch a graph of a conic section using its key features.

Circles

Ellipses

Hyperbolas

Parabolas

RFR.IC.4: Use the key features of a conic section to write its equation.

Circles

Ellipses

Hyperbolas

Parabolas

RFR.IC.5: Given a quadratic equation of the form ax² + by² + cx + dy + e = 0, determine if the equation is a circle, ellipse, parabola, or hyperbola.

RFR.IC.a: Students should have opportunities to… Explore conics as loci of points satisfying stipulated conditions.

Circles

Ellipses

Hyperbolas

Parabolas

RFR.IC.b: Students should have opportunities to… Explore conic sections with technology and manipulatives.

Circles

Ellipses

Hyperbolas

Parabolas

RFR.IC.c: Students should have opportunities to… Connect the geometric and algebraic relationships of conics.

Circles

Ellipses

Hyperbolas

Parabolas

RFR.IC.d: Students should have opportunities to… Use the method of completing the square to put the equation of the conic section into standard form.

RFR.ISS.1: Model real-world situations involving sequences or series using recursive and/or explicit definitions.

Arithmetic Sequences

Arithmetic and Geometric Sequences

RFR.ISS.2: Use covariational reasoning to describe sequences and series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

RFR.ISS.a: Students should have opportunities to… Become fluent in working with arithmetic and geometric sequences and series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

RFR.ISS.b: Students should have opportunities to… Explore several types of sequences, including but not limited to Fibonacci, telescoping, harmonic, alternating.

Arithmetic Sequences

Arithmetic and Geometric Sequences

RFR.ETT.1: Model real-world situations involving trigonometry.

Sine, Cosine, and Tangent Ratios

Sound Beats and Sine Waves

Translating and Scaling Sine and Cosine Functions

RFR.ETT.4: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - x in terms of their values for x, where x is any real number.

Cosine Function

Sine Function

Tangent Function

RFR.ETT.5: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

RT.ETT.a: Students should have opportunities to… Go beyond using the mnemonic SohCahToa by interpreting the meaning of the trigonometric ratios as multiplicative comparisons of the appropriate sides of a right triangle. Situations should involve unknown sides and/or angles, as well as periodic functions and their inverses.

Sine, Cosine, and Tangent Ratios

RT.RTS.1: Use the structure of a trigonometric expression to identify ways to rewrite it.

Simplifying Trigonometric Expressions

RT.RTS.2: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Simplifying Trigonometric Expressions

RT.RTS.a: Students should have opportunities to… Recognize that a single identity can be manipulated into another identity.

Simplifying Trigonometric Expressions

RT.RTS.b: Students should have opportunities to… Apply the Pythagorean, sum, difference, double angle, and half angle formulas for sine and cosine to reveal and explain properties.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

RT.EPE.a: Students should have opportunities to… Convert points between polar and rectangular forms.

RT.EPE.b: Students should have opportunities to… Determine equivalent polar representations for a given point.

RV.EV.1: Recognize vector quantities as having both magnitude and direction.

RV.EV.2: Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

RV.EV.3: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

RV.EV.4: Solve problems involving velocity and other quantities that can be represented by vectors.

2D Collisions

Adding Vectors

Golf Range

Vectors

RV.EV.5: Add and subtract vectors, and multiply a vector by a scalar.

RV.EV.a: Students should have opportunities to… Distinguish vector quantities from scalar quantities. For example, distinguish the difference between velocity and speed.

2D Collisions

Adding Vectors

Vectors

RV.EV.b: Students should have opportunities to… Make sense of operations with vectors.

2D Collisions

Adding Vectors

Vectors

RM.UM.1: Use matrices to represent and manipulate data.

Dilations

Solving Linear Systems (Matrices and Special Solutions)

Translations

RM.UM.2: Use matrix operations to solve problems. Add, subtract, and multiply matrices of appropriate dimensions. Multiply matrices by scalars to produce new matrices.

Dilations

Solving Linear Systems (Matrices and Special Solutions)

Translations

RM.UM.3: Find the inverse and determinant of a matrix.

Solving Linear Systems (Matrices and Special Solutions)

RM.UM.4: Use matrices to solve systems of linear equations.

Solving Linear Systems (Matrices and Special Solutions)

RM.UM.a: Students should have opportunities to… Explore the properties of matrices and their operations.

Dilations

Solving Linear Systems (Matrices and Special Solutions)

Translations

RM.UM.b: Students should have opportunities to… Explain that the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

Solving Linear Systems (Matrices and Special Solutions)

RM.UM.c: Students should have opportunities to… Explore the roles of the zero matrix, identity matrix, inverse matrix, and the determinant of a matrix.

Solving Linear Systems (Matrices and Special Solutions)

RM.UM.d: Students should have opportunities to… Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

RM.UM.e: Students should have opportunities to… Use the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers.

RM.UM.f: Students should have opportunities to… Use matrices as a tool. Including but not limited to: producing new vectors from old vectors, creating transformations in the plane, calculating the area of geometric figures.

RM.UM.g: Students should have opportunities to… Explore matrices and solve problems with and without technology, as appropriate.

Dilations

Solving Linear Systems (Matrices and Special Solutions)

Translations

Biconditional Statements

Conditional Statements

Estimating Population Size

Pattern Flip (Patterns)

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

Fraction, Decimal, Percent (Area and Grid Models)

Improper Fractions and Mixed Numbers

Linear Inequalities in Two Variables

Modeling One-Step Equations

Multiplying with Decimals

Pattern Flip (Patterns)

Polling: City

Solving Equations on the Number Line

Using Algebraic Expressions

Conditional Statements

Estimating Population Size

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.

Biconditional Statements

Conditional Statements

Estimating Sums and Differences

5.5.1: Mathematically proficient students consider available tools when solving a mathematical problem. They choose tools that are relevant and useful to the problem at hand. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful; recognizing both the insight to be gained and their limitations. Students deepen their understanding of mathematical concepts when using tools to visualize, explore, compare, communicate, make and test predictions, and understand the thinking of others.

Biconditional Statements

Fraction, Decimal, Percent (Area and Grid Models)

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.

Arithmetic Sequences

Finding Patterns

Fraction, Decimal, Percent (Area and Grid Models)

Function Machines 2 (Functions, Tables, and Graphs)

Geometric Sequences

Pattern Flip (Patterns)

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

Finding Patterns

Function Machines 2 (Functions, Tables, and Graphs)

Geometric Sequences

Pattern Flip (Patterns)

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

Pattern Finder

Pattern Flip (Patterns)

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.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Correlation last revised: 3/25/2021

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