Algebra 2 (2011)
1: Expressions, Equations, and Inequalities
1.1: Patterns and Expressions
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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
1.4: Solving Equations
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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
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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: Absolute Value Equations and Inequalities
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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: Functions, Equations, and Graphs
2.1: Relations and Functions
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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
2.2: Direct Variation
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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
2.3: Linear Functions and Slope-Intercept Form
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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
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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
2.4: More About Linear Equations
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
2.5: Using Linear Models
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Determining a Spring Constant
Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring. 5 Minute Preview
2.6: Families of Functions
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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
2.7: Absolute Value Functions and Graphs
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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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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
2.8: Two-Variable Inequalities
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Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
3: Linear Systems
3.1: Solving Systems Using Tables and Graphs
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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
3.2: Solving Systems Algebraically
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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
3.3: Systems of Inequalities
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Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview
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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
3.4: Linear Programming
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Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
4: Quadratic Functions and Equations
4.1: Quadratic Functions and Transformations
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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
4.2: Standard Form of a Quadratic Function
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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
4.4: Factoring Quadratic Expressions
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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
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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
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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
4.5: Quadratic Equation
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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
4.7: The Quadratic Formula
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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
4.9: Quadratic Systems
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Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview
5: Polynomials and Polynomial Functions
5.1: Polynomial Functions
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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
5.2: Polynomials, Linear Factors, and Zeros
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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
5.4: Dividing Polynomials
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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: Radical Functions and Rational Exponents
6.1: Roots and Radical Expressions
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Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
6.2: Multiplying and Dividing Radical Expressions
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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
6.8: Graphing Radical Functions
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
7: Exponential and Logarithmic Functions
7.1: Exploring Exponential Models
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Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
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Half-life
Investigate the decay of a radioactive substance. The half-life and the number of radioactive atoms can be adjusted, and theoretical or random decay can be observed. Data can be interpreted visually using a dynamic graph, a bar chart, and a table. Determine the half-lives of two sample isotopes as well as samples with randomly generated half-lives. 5 Minute Preview
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
7.2: Properties of Exponential Functions
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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
7.3: Logarithmic Functions as Inverses
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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
7.4: Properties of Logarithms
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Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview
8: Rational Functions
8.1: Inverse Variation
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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
8.3: Rational Functions and Their Graphs
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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
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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
9: Sequences and Series
9.1: Mathematical Patterns
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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
9.2: Arithmetic Sequences
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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
9.3: Geometric Sequences
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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
10: Quadratic Relations and Conic Sections
10.2: Parabolas
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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
10.3: Circles
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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
10.4: Ellipses
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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
10.5: Hyperbolas
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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
11: Probability and Statistics
11.1: Permutations and Combinations
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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
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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
11.2: Probability
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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
11.3: Probability of Multiple Events
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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
11.4: Conditional Probability
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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
11.5: Analyzing Data
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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
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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
11.7: Samples and Surveys
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Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
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Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
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Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
12: Matrices
12.5: Geometric Transformations
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
12.6: Vectors
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Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
13: Periodic Functions and Trigonometry
13.2: Angles and the Unit Circle
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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
13.4: The Sine Function
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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
13.5: The Cosine Function
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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
13.6: The Tangent Function
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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
13.7: Translating Sine and Cosine Functions
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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
14: Trigonometric Identities and Equations
14.1: Trigonometric Identities
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Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
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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
14.3: Right Triangles and Trigonometric Ratios
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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
14.6: Angle Identities
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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
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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