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- Algebra 1 (2008)
Algebra 1 (2008)
1: Patterns and Multiple Representations
1.1: Patterns and 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
1.2: Finding the 10th Term of a Sequence
Pattern Flip (Patterns)
In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview
1.6: Using Multiple Representations, Part 1
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
1.7: Using Multiple Representations, Part 2
Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
1.8: Using Tables, Graphs, and Equations, part 1
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
1.9: Using Tables, Graphs, and Equations, Part 2
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
2: Proportional Reasoning, Percents, and Direct Variation
2.1: Using Samples, Ratios, and Proportional to Make Predictions
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
2.2: Ratios, Rates, and Mixture Problems
Measuring Motion
Go on an African safari and observe a variety of animals walking and running across the savanna. Videotape the animals, and then play back the videotape to estimate animal speeds. Which animals run fastest? 5 Minute Preview
2.3: Proportions and Indirect Measurement
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
2.4: Ratios and Part-to-Whole Relationships
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.5: Ratios, Part-to-Part Relationships, and Direct Variation
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
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
2.6: Using Percents
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
2.7: Percents and Taxes
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
3: Solving Linear Equations
3.1: Solving One-Step Equations
Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
3.2: Solving Two-Step equations
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
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
3.3: Using the Percent Equation
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
3.6: Integers and Integer Operations
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
3.7: The Coordinate Plane
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
3.8: Using a Graph of an Equation
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
4: Linear Functions and Inequalities
4.1: Solving and Graphing Inequalities in One Variable
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
4.2: Relations and Functions
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
4.4: The Distributive Property
Chocomatic (Multiplication, Arrays, and Area)
Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview
4.7: Solving Absolute Value Equations and Inequalities
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
5: Writing and Graphing Linear Equations
5.3: Finding the Slope of a line
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
5.4: Slope-Intercept Form
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
5.5: Writing Equations of Lines
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
5.6: Linear and Piecewise Functions
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
5.7: Standard Form of a Linear Equation
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
5.8: Solving Literal Equations
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: Lines of Best Fit
6.1: Drawing the Line of Best Fit
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
6.2: Using Lines of Best Fit
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
6.3: Performing an Experiment
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
6.4: Correlations
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
6.5: Using Technology to Find a Linear Regression Equation, Part 1
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
6.6: Using Technology to Find a Linear Regression Equation, Part 2
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
7: Systems of Equations and Inequalities
7.1: Using a Graph to Solve a Liner System
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
7.2: Graphs and Solutions o Linear Systems
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
7.4: Using Linear Combinations to Solve a Linear System
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
7.8: Writing and Graphing an Inequality in Two Variables
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
7.9: Solving Systems of Linear Inequalities
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
8: Quadratic Functions
8.1: Introduction to Quadratic Functions
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
8.2: 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
8.4: Square Roots and Radicals
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
8.6: Using the Quadratic Formula to Solve Quadratic Equations
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
8.7: Using a Vertical Motion Model
Golf Range
Try to get a hole in one by adjusting the velocity and launch angle of a golf ball. Explore the physics of projectile motion in a frictional or ideal setting. Horizontal and vertical velocity vectors can be displayed, as well as the path of the ball. The height of the golfer and the force of gravity are also adjustable. 5 Minute Preview
Pendulum Clock
Find the effect of length, mass, and angle on the period of a pendulum. The pendulum is attached to a clock that can be adjusted to tell time accurately. The clock can be located on Earth or Jupiter to determine the effect of gravity. 5 Minute Preview
8.8: Using Quadratic Functions
Ray Tracing (Lenses)
Observe light rays that pass through a convex or concave lens. Manipulate the position of an object and the focal length of the lens and measure the distance and size of the resulting image. 5 Minute Preview
9: Properties of Exponents
9.1: Powers and Prime Factorization
Finding Factors with Area Models
Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree. 5 Minute Preview
9.2: Multiplying and Dividing Powers
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
9.3: Zero and Negative Exponents
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
9.5: Properties of Powers
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
10: Polynomial Functions and Rational Expressions
10.1: Polynomials and 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
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
10.2: Adding and Subtracting Polynomials
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
Addition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
10.5: Factoring Polynomials
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
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
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
11: Probability
11.1: Introduction to Probability
Spin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview
11.2: Theoretical and Experimental Probabilities
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: Using Probabilities to Make Predictions
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
11.4: Graphing Frequencies of Outcomes
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
11.5: Counting and Permutations
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
11.6: Permutations and Combinations
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
11.7: Independent and Dependent Events
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
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
11.8: Geometric Probabilities
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
12: Statistical Analysis
12.1: Measures of Central Tendency
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
12.3: Quartiles and Box-and-Whisker Plots
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
12.4: Sample Variance and Standard Deviation
Sight vs. Sound Reactions
Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview
13: Quadratic and Exponential Functions and Logic
13.1: The Pythagorean Theorem and Its Converse
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
13.2: The Distance and Midpoint Formulas
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
13.4: Vertex Form of a Quadratic Equation
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
13.5: Graphing by Using Parent 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
13.6: Introduction to 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
13.7: Exponential Growth and Decay
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
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
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
13.8: Special Topic: Logic
Biconditional Statements
Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
Conditional Statements
Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
How Free Gizmos Work
Start teaching with 20-40 Free Gizmos. See the full list.
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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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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.
Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
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