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  • Arkansas Standards
  • Mathematics: Algebra III

Arkansas - Mathematics: Algebra III

Curriculum Framework | Adopted: 2016

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

MO: : Matrix Operations


MO.1.AIII: : Students will perform operations with matrices and use them to solve systems of equations.

MO.1.AIII.2: : Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).

Screenshot of Dilations

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form. 5 Minute Preview


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MO.1.AIII.7: : Work with 2 𝑋 2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area.

Screenshot of Dilations

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form. 5 Minute Preview


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Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


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MO.1.AIII.8: : Represent a system of linear equations as a single matrix equation in a vector variable.

Screenshot of Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Matrices and Special Solutions)

Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview


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MO.1.AIII.9: : Find the inverse of a matrix if it exists; use the inverse to solve systems of linear equations using technology for matrices of dimension 3 𝑋 3 or greater.

Screenshot of Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Matrices and Special Solutions)

Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview


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CS: : Conic Sections


CS.2.AIII: : Students will identify, analyze, and sketch the graphs of the conic sections and relate the equations and graphs.

CS.2.AIII.1: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Screenshot of Points in the Complex Plane

Points in the Complex Plane

Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview


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CS.2.AIII.2: : Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; find the equations for the asymptotes of a hyperbola.

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Ellipses

Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview


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Screenshot of Hyperbolas

Hyperbolas

Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response. 5 Minute Preview


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Screenshot of Rational Functions

Rational Functions

Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview


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CS.2.AIII.3: : Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section.

Screenshot of Circles

Circles

Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview


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CS.2.AIII.4: : Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate.

Screenshot of Addition and Subtraction of Functions

Addition and Subtraction of Functions

Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview


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Screenshot of Circles

Circles

Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview


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Screenshot of Ellipses

Ellipses

Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview


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Screenshot of Hyperbolas

Hyperbolas

Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response. 5 Minute Preview


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Screenshot of Parabolas

Parabolas

Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview


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Screenshot of Rational Functions

Rational Functions

Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview


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CS.2.AIII.5: : Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology.

Screenshot of Linear Programming

Linear Programming

Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview


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Screenshot of Solving Equations by Graphing Each Side

Solving Equations by Graphing Each Side

Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview


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Screenshot of Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Matrices and Special Solutions)

Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Solving Linear Systems (Standard Form)

Solving Linear Systems (Standard Form)

Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview


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Screenshot of Systems of Linear Inequalities (Slope-intercept form)

Systems of Linear Inequalities (Slope-intercept form)

Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview


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FOP: : Function Operations and Properties


FOP.3.AIII: : Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses.

FOP.3.AIII.1: : Compose functions (e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).

Screenshot of Function Machines 1 (Functions and Tables)

Function Machines 1 (Functions and Tables)

Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview


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FOP.3.AIII.2: : Verify, by composition, that one function is the inverse of another.

Screenshot of Logarithmic Functions

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview


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FOP.3.AIII.3: : Read values of an inverse function from a graph or a table, given that the function has an inverse.

Screenshot of Logarithmic Functions

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview


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FOP.3.AIII.5: : Combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential and relate these functions to the model).

Screenshot of Addition and Subtraction of Functions

Addition and Subtraction of Functions

Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview


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FOP.3.AIII.6: : Understand the inverse relationship between exponents and logarithms; use this relationship to solve problems involving logarithms and exponents.

Screenshot of Logarithmic Functions

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview


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FOP.3.AIII.7: : Graph transformations of functions including quadratic, absolute value, square root, cube root, cubic, and step functions; graph piece-wise defined functions including these transformations.

Screenshot of Absolute Value with Linear Functions

Absolute Value with Linear Functions

Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview


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Screenshot of Exponential Functions

Exponential Functions

Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview


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Screenshot of Quadratics in Vertex Form

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview


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Screenshot of Translating and Scaling Functions

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview


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Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


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Screenshot of Zap It! Game

Zap It! Game

Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview


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IF: : Interpreting Functions


IF.4.AIII: : Students will be able to interpret different types of functions and key characteristics including polynomial, exponential, logarithmic, and rational functions.

IF.4.AIII.1: : Graph rational functions identifying zeros and asymptotes when suitable factorizations are available; show end behavior.

Screenshot of General Form of a Rational Function

General Form of a Rational Function

Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Rational Functions

Rational Functions

Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview


Lesson Info
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IF.4.AIII.2: : Analyze and interpret polynomial functions numerically, graphically, and algebraically, identifying key characteristics such as intercepts, end behavior, domain and range, relative and absolute maximum and minimum, as well as intervals over which the function increases and decreases.

Screenshot of Graphs of Polynomial Functions

Graphs of Polynomial Functions

Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview


Lesson Info
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Screenshot of Polynomials and Linear Factors

Polynomials and Linear Factors

Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview


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Screenshot of Quadratics in Factored Form

Quadratics in Factored Form

Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview


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Screenshot of Quadratics in Vertex Form

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview


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IF.4.AIII.3: : Analyze and interpret rational functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes (vertical, horizontal, and slant), end behavior, point discontinuities, intercepts, and domain and range.

Screenshot of General Form of a Rational Function

General Form of a Rational Function

Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Rational Functions

Rational Functions

Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview


Lesson Info
Launch Gizmo

IF.4.AIII.4: : Analyze and interpret exponential functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.

Screenshot of Exponential Functions

Exponential Functions

Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview


Lesson Info
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Screenshot of Introduction to Exponential Functions

Introduction to Exponential Functions

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview


Lesson Info
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Screenshot of Logarithmic Functions

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview


Lesson Info
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IF.4.AIII.5: : Analyze and interpret logarithmic functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.

Screenshot of Logarithmic Functions

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview


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SS: : Sequences and Series


SS.5.AIII: : Students will use sequences and series to represent and analyze mathematical situations.

SS.5.AIII.1: : Write arithmetic and geometric sequences both recursively and with an explicit formula; translate between the two forms.

Screenshot of Arithmetic Sequences

Arithmetic Sequences

Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview


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Screenshot of Arithmetic and Geometric Sequences

Arithmetic and Geometric Sequences

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview


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Screenshot of Geometric Sequences

Geometric Sequences

Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview


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SS.5.AIII.2: : Use arithmetic and geometric sequences both recursively and with an explicit formula to model situations.

Screenshot of Arithmetic Sequences

Arithmetic Sequences

Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview


Lesson Info
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Screenshot of Arithmetic and Geometric Sequences

Arithmetic and Geometric Sequences

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Geometric Sequences

Geometric Sequences

Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview


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Correlation last revised: 9/16/2020

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