Math Thematics: Book 3 (2005)

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

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

Chords and Arcs

Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview

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

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

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

Perimeter and Area of Rectangles

Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview

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

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

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

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

Adding and Subtracting Integers

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

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

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

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

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

Order of Operations

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

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

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

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

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

Constructing Parallel and Perpendicular Lines

Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview

Constructing Congruent Segments and Angles

Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview

Solving Equations on the Number Line

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

Proving Triangles Congruent

Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview

Rotations, Reflections, and Translations

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

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

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

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

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

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

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

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

Multiplying Exponential Expressions

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

Dividing Exponential Expressions

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

Investigating Angle Theorems

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

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

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

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

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

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

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

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

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

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

Investigating Angle Theorems

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

Exploring Linear Inequalities in One Variable

Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 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

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

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

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

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

Modeling One-Step Equations

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

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

Introduction to Exponential Functions

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 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

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview

Rotations, Reflections, and Translations

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

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

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

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

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

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

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

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