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- Applications and Connections: Course 2 (2001)

# Applications and Connections: Course 2 (2001)

### 1. Problem Solving, Algebra, and Geometry

1.2. Order of Operations

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview

1.3. Integration: Algebra (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

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

1.4. Integration: Algebra (Powers and Exponents)

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview

1.5. Integration: Algebra (Solving 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

Modeling One-Step Equations

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

1.7. Integration: Geometry (Area)

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

### 2. Applying Decimals

2.1. Comparing and Ordering Decimals

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

2.4. Multiplying Decimals

Multiplying with Decimals

Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview

2.7. Decimals and Fractions

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

### 3. Statistics: Analyzing Data

3.1. Frequency Tables

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

3.2. Making Predictions

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

3.3. Line Plots

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

3.4. Mean, Median, and Mode

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

3.5. 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

3.6. 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

### 4. Using Number Patterns, Fractions, and Percents

4.2. 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

4.3. Integration: Patterns and Functions (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

4.5. Simplifying Fractions and Ratios

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

4.6. Ratios and Percents

Percents, Fractions, and Decimals

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

4.7. 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

4.8. Integration: Probability (Simple Events)

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

4.10. Comparing and Ordering Fractions

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. Algebra: Using Integers

5.1. Integers

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

5.2. Comparing and Ordering Integers

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

5.3. Integration: Geometry (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

5.4. Adding Integers

Adding and Subtracting Integers

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

5.5. Subtracting Integers

Adding and Subtracting Integers

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

5.8. Integration: Geometry (Graphing Transformations)

Rotations, Reflections, and Translations

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

### 6. Algebra: Exploring Equations and Functions

6.1. Solving Addition and Subtraction Equations

Modeling One-Step Equations

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

6.3. 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

6.4. Writing Expressions and Equations

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

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

6.5. Inequalities

Solving Linear Inequalities in One Variable

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

6.6. Functions and Graphs

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

6.7. Functions and Equations

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

### 7. Applying Fractions

7.1. Estimating with Fractions

Estimating Sums and Differences

Estimate the sum or difference of two fractions using area models. Compare estimates to exact sums and differences. 5 Minute Preview

7.2. Adding and Subtracting 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

7.4. Multiplying Fractions and Mixed 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

Multiplying Mixed Numbers

Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

7.6. Integration: Geometry (Perimeter)

Circumference and Area of Circles

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

7.7. Integration: Measurement (Circles and Circumference)

Circumference and Area of Circles

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

7.9. Dividing Fractions and Mixed Numbers

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

### 8. Using Proportional Reasoning

8.1. Ratios

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

8.3. Solving 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

8.5. Percents and Fractions

Percents, Fractions, and Decimals

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

8.6. Percents and Decimals

Percents, Fractions, and Decimals

8.7. Percents Greater Than 100% and Percents Less Than 1%

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview

8.8. Percent of a Number

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

8.9. 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

### 9. Geometry: Investigating Patterns

9.2. 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

9.3. Integration: Algebra (Similar Polygons)

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

9.4. Triangles and 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

9.7. Reflections

Reflections

Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview

### 10. Geometry: Exploring Area

10.1. 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

10.2. Estimating Square Roots

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

10.3. The Pythagorean Theorem

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

10.5. Area of 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. Area of Circles

Circumference and Area of Circles

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

10.7. Integration: Probability (Area Models)

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

### 11. Applying Percents

11.1. Percent and Estimation

Percents, Fractions, and Decimals

11.5. 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

11.6. Discount and Sales Tax

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

11.7. Simple Interest

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

### 12. Geometry: Finding Volume and Surface Area

12.1. Drawing Three-Dimensional Figures

3D and Orthographic Views

Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view. 5 Minute Preview

12.2. Volume of Rectangular Prisms

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

12.3. Volume of 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

12.4. Surface Area of Rectangular Prisms

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

12.5. Surface Area of 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

### 13. Exploring Discrete Math and Probability

13.1. Theoretical and Experimental Probability

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

13.2. Tree Diagrams

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

13.3. The Counting Principle

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

13.4. 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

13.5. 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

13.6. 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

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