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- Pre-Algebra (2005)

# Pre-Algebra (2005)

### 1. The Tools of Algebra

1.3. Variables and Expressions

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. Variables and Equations

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

1.6. Ordered Pairs and Relations

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

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

1.7. Scatter Plots

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

### 2. Integers

2.1. Integers and Absolute Value

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview

Rational Numbers, Opposites, and Absolute Values

Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview

2.2. Adding Integers

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

2.3. Subtracting Integers

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

2.6. The Coordinate System

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. Equations

3.3. Solving Equations by Adding or Subtracting

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview

3.4. Solving Equations by Multiplying and Dividing

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

3.5. 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

3.7. Using Formulas

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

### 4. Factors and Fractions

4.1. Factors and Monomials

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

4.3. 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

4.5. Simplifying Algebraic Fractions

Dividing Exponential Expressions

Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

4.6. Multiplying and Dividing Monomials

Multiplying Exponential Expressions

Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview

### 5. Rational Numbers

5.1. Writing Fractions as Decimals

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

5.2. Rational Numbers

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

5.3. Multiplying Rational Numbers

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview

5.4. Dividing Rational Numbers

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview

5.7. Adding and Subtracting Unlike Fractions

Fractions with Unlike Denominators

Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview

5.8. 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

5.9. Solving Equations with Rational Numbers

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

5.10. 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

### 6. Ratio, Proportion, and Percent

6.1. Ratios and Rates

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

6.2. Using Proportions

Beam to Moon (Ratios and Proportions)

Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

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

6.4. Fractions, Decimals, and Percents

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

6.5. Using the Percent Proportion

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

6.7. Using Percent Equations

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

6.8. Percent of Change

Percent of Change

Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview

6.9. Probability and 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

### 7. Linear Equations, Inequalities, and Functions

7.1. Solving Equations with Variables on 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

7.4. Solving Inequalities by Adding or Subtracting

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

7.5. Solving Inequalities by Multiplying or Dividing

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

### 8. Functions and Graphing

8.1. 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

8.2. Linear Equations in two Variables

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

8.4. Slope

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

8.6. 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

8.8. Best-Fit Lines

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

8.9. Solving Systems of Equations

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 *x*, *y*)

8.10. Graphing Inequalities

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

### 9. Applying Algebra to Geometry

9.1. Squares and Square Roots

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

Ordering and Approximating Square Roots

Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview

9.4. Triangles

Triangle Angle Sum

Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview

Isosceles and Equilateral Triangles

Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

Classifying Triangles

Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview

9.5. The Pythagorean Theorem

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

9.6. 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

9.8. Sine, Cosine, and Tangent Ratios

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

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

### 10. Two-Dimensional Figures

10.1. Line and Angle Relationships

Investigating Angle Theorems

Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

10.2. Congruent Triangles

Congruence in Right Triangles

Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview

10.3 Transformations on the Coordinate Plane

Rotations, Reflections, and Translations

Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview

10.4. Quadrilaterals

Classifying Quadrilaterals

Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview

10.5. Area: Parallelograms, Triangles, and Trapezoids

Area of Parallelograms

Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview

10.6. Polygons

Polygon Angle Sum

Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview

10.7. Circumference and Area: Circles

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 5 Minute Preview

### 11.1. Three-Dimensional Figures

11.2. Volume: Prisms and Cylinders

Prisms and Cylinders

Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview

11.3. Volume: Pyramids and Cones

Pyramids and Cones

Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview

11.4. Surface Area: Prisms and Cylinders

Surface and Lateral Areas of Prisms and Cylinders

Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview

11.5. Surface Area: Pyramids and Cones

Surface and Lateral Areas of Pyramids and Cones

Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview

11.7. Precision and Significant Digits

Triple Beam Balance

Learn how to determine the mass of an object using a triple beam balance. The mass of a variety of objects can be determined using this simulated version of a common real-world laboratory tool for measurement. 5 Minute Preview

### 12. Extending Algebra to Statistics and Polynomials

12.1. Stem-and-Leaf Plots

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

12.2. Measures of Variation

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. 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. Histograms

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

12.6. Counting Outcomes

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

12.7. 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

12.8. Odds

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

12.9. Probability of Compound 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

### 13. Polynomials and Nonlinear Functions

13.2. Adding Polynomials

Addition of Polynomials

Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

13.3. Subtracting Polynomials

Addition of Polynomials

Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

13.5. Linear and Nonlinear 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

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

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

13.6. Graphing Quadratic and Cubic 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

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

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