Algebra 2 (2006)
1. Real Numbers, Algebra, and Problem Solving
1.1. Real Numbers and Operations
![Screenshot of Adding on the Number Line](/Assets/img/blank.gif)
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
1.2. Multiplication and Division of Real Numbers
![Screenshot of Dividing Fractions](/Assets/img/blank.gif)
Dividing Fractions
Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview
1.3. Algebraic Expressions and Properties of Numbers
![Screenshot of Using Algebraic Expressions](/Assets/img/blank.gif)
Using Algebraic Expressions
Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview
1.5. Solving Equations
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
1.6. Writing Equations
![Screenshot of Using Algebraic Equations](/Assets/img/blank.gif)
Using Algebraic Equations
Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview
1.8. Properties of Exponents
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
2. Equations and Inequalities
2.2. Using Equations
![Screenshot of Using Algebraic Equations](/Assets/img/blank.gif)
Using Algebraic Equations
Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview
2.3. Solving Formulas
![Screenshot of Solving Formulas for any Variable](/Assets/img/blank.gif)
Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview
2.4. Solving Inequalities
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
2.6. Compound Inequalities
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
2.7. Absolute Value
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
2.8. Proofs in Solving Equations
![Screenshot of Conditional Statements](/Assets/img/blank.gif)
Conditional Statements
Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
3. Relations, Functions, and Graphs
3.2. Graphs
![Screenshot of Points in the Coordinate Plane](/Assets/img/blank.gif)
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
3.3. Functions
![Screenshot of Introduction to Functions](/Assets/img/blank.gif)
Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview
3.4. Graphs of Linear Equations
![Screenshot of Linear Functions](/Assets/img/blank.gif)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
3.5. Slope
![Screenshot of Slope](/Assets/img/blank.gif)
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
3.6. More Equations of Lines
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
4. Systems of Equations and Problem Solving
4.1. Systems of Equations in Two Variables
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
4.3. Using a System of Two Equations
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
4.6. Consistent and Dependent Systems
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
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
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
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
4.7. Systems of Inequalities
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
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
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
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
4.8. Using Linear Programming
![Screenshot of Linear Programming](/Assets/img/blank.gif)
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
5. Polynomials and Polynomial Equations
5.2. Addition and Subtraction of Polynomials
![Screenshot of Addition of Polynomials](/Assets/img/blank.gif)
Addition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
5.4. Factoring
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
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
5.5. More Factoring
![Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
![Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
5.7. Solving Equations by Factoring
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
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
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
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
5.8. Using Equations
6. Rational Expressions and Equations
6.5. Synthetic Division
![Screenshot of Dividing Polynomials Using Synthetic Division](/Assets/img/blank.gif)
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
6.7. Using Rational Equations
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.8. Formulas
![Screenshot of Solving Formulas for any Variable](/Assets/img/blank.gif)
Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.9. Variation and Problem Solving
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
6.10. Reasoning Strategies
![Screenshot of Finding Patterns](/Assets/img/blank.gif)
Finding Patterns
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview
7. Powers, Roots, and Complex Numbers
7.1. Radical Expressions
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
7.2. Multiplying and Simplifying
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
7.3. Operations with Radical Expressions
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
7.4. More Operations with Radical Expressions
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
7.8. Complex Numbers and Graphing
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
8. Quadratic Equations
8.3. The Quadratic Formula
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
8.4. Solutions to Quadratic Equations
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
9. Quadratic Functions and Transformations
9.2. Transformations
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
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
9.3. Stretching and Shrinking
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
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
9.4. Graphs of Quadratic Functions
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
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
9.5. Graphs of f(x)=a(x-h)
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
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
9.6. Standard Form for Quadratic Functions
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
9.7. Graphs and x-intercepts
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
10. Equations of Second Degree
10.1. Coordinate Geometry
![Screenshot of Distance Formula](/Assets/img/blank.gif)
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
10.2. Conic Sections: Circles
![Screenshot of Circles](/Assets/img/blank.gif)
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
10.3. Ellipses
![Screenshot of Ellipses](/Assets/img/blank.gif)
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
10.4. Hyperbolas
![Screenshot of Hyperbolas](/Assets/img/blank.gif)
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
10.5. Parabolas
![Screenshot of Parabolas](/Assets/img/blank.gif)
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
11. Polynomial Functions
11.2. The Remainder and Factor Theorems
![Screenshot of Dividing Polynomials Using Synthetic Division](/Assets/img/blank.gif)
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
11.3. Theorems About Roots
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
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
11.6. Graphs of Polynomial Functions
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
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
12. Inverse Relations and Functions
12.2. Exponential and Logarithmic Functions
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
12.3. Exponential and Logarithmic Relationships
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
12.4. Properties of Logarithmic Functions
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
12.8. Natural Logarithms and the Number e
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
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
13. Matrices
13.1. Matrices and Systems of Equations
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
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
13.2. Addition and Subtraction of Matrices
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
14. Sequences, Series, and Mathematical Induction
14.2. Arithmetic Sequences and Series
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
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
14.3. Geometric Sequences and Series
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
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
15. Counting and Probability
15.1. Counting Problems and Permutations
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
15.3. Combinations
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
15.5. Probability
![Screenshot of Geometric Probability](/Assets/img/blank.gif)
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
15.6. Compound Probability
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
15.7. Simulating Events
![Screenshot of Binomial Probabilities](/Assets/img/blank.gif)
Binomial Probabilities
Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview
![Screenshot of Probability Simulations](/Assets/img/blank.gif)
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
![Screenshot of Theoretical and Experimental Probability](/Assets/img/blank.gif)
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
16. Statistics and Data Analysis
16.1. Statistics: Organizing Data
![Screenshot of Stem-and-Leaf Plots](/Assets/img/blank.gif)
Stem-and-Leaf Plots
Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview
![Screenshot of Histograms](/Assets/img/blank.gif)
Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
16.2. Using Measures of Central Tendency
![Screenshot of Mean, Median, and Mode](/Assets/img/blank.gif)
Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
![Screenshot of Describing Data Using Statistics](/Assets/img/blank.gif)
Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
![Screenshot of Mean, Median, and Mode](/Assets/img/blank.gif)
Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
17. Trigonometric Functions
17.1. Trigonometric Functions in Triangles
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
17.2. More Trigonometric Functions
![Screenshot of Sine Function](/Assets/img/blank.gif)
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
17.5. Graphs of Trigonometric Functions
![Screenshot of Sine Function](/Assets/img/blank.gif)
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Tangent Function](/Assets/img/blank.gif)
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Cosine Function](/Assets/img/blank.gif)
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
17.6. Trigonometric Function Relationships
![Screenshot of Simplifying Trigonometric Expressions](/Assets/img/blank.gif)
Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
17.7. More Trigonometric Graphs
![Screenshot of Translating and Scaling Sine and Cosine Functions](/Assets/img/blank.gif)
Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
18. Trigonometric Identities and Equations
18.1. Sum and Difference Identities
![Screenshot of Sum and Difference Identities for Sine and Cosine](/Assets/img/blank.gif)
Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
18.3. Proving Identities
![Screenshot of Simplifying Trigonometric Expressions](/Assets/img/blank.gif)
Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
18.6. Right Triangles and Problem Solving
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
How Free Gizmos Work
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Start teaching with 20-40 Free Gizmos. See the full list.
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Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
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All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
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Free Gizmos change each semester. The new collection will be available January 1 and July 1.
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
Find Your Solution
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