logo

Dynamic Explorations

Chapter 0

  • Slope
    Use a dynamic sketch to review how to calculate the slopes of lines on the coordinate plane. This exploration complements the review of slope in Lesson 0.1 of Discovering Advanced Algebra.

Chapter 1

  • Sequence Graphs
    Use dynamic sketches to explore the graphs of arithmetic and geometric sequences. This exploration can help you deepen your understanding of concepts from Lesson 1.4 of Discovering Advanced Algebra.

Chapter 2

  • Box Plots
    Drag data plots and observe a box plot changing dynamically in this exploration of the properties of box plots. This exploration reinforces the concepts in Lesson 2.1 of Discovering Advanced Algebra.
  • Standard Deviation
    In this exploration, you will use a dynamic sketch to investigate standard deviation and better understand how it measures the spread of a data set. This exploration can deepen your understanding of concepts in Lesson 2.2 of Discovering Advanced Algebra.
  • Histogram Puzzles
    Find the data set that produces a histogram by experimenting with different bin width and starting values. This exploration will give you more practice interpreting histograms, which are covered in Lesson 2.3 of Discovering Advanced Algebra.

Chapter 3

  • Fitting a Line to Data
    Use a movable line to improve your skill at finding a line of fit for a data set. This exploration complements the material in Lesson 3.3 of Discovering Advanced Algebra.
  • Residuals
    Use dynamic sketches to explore residuals and root mean square error and to evaluate how well a model fits a set of data. This exploration will deepen your understanding of the concepts in Lesson 3.5 of Discovering Advanced Algebra.

Chapter 4

  • Translations of Parabolas
    Explore the relationship between the equation of a translated parabola and the coordinates of its vertex. This will help you fully understand the paragraph that closes Lesson 4.4 on page 197 of Discovering Advanced Algebra.
  • Rotation as a Composition of Transformations
    Explore rotation as a composition of other transformations and write rules for rotating figures on the coordinate plane. These dynamic sketches can help you complete the Exploration Rotation as a Composition of Transformations in Chapter 4 of Discovering Advanced Algebra.
  • Stretches and Shrinks of Shapes and Functions
    Use dynamic graphs to investigate how graphs can be stretched and shrunk horizontally and vertically by changing their equations. This exploration will reinforce the concepts in Lesson 4.6 of Discovering Advanced Algebra.

Chapter 5

  • An Application of Exponential Decay
    Model the motion of a pendulum using an exponential function. This exploration can be used to deepen your understanding of Example B in Lesson 5.4 of Discovering Advanced Algebra.
  • Building Inverses of Functions
    Use dynamic sketches to explore the relationship between the graph of a function and its inverse. This exploration can enhance your understanding of the concepts in Lesson 5.5 of Discovering Advanced Algebra.

Chapter 6

  • Systems of Inequalities
    Use dynamic sketches to investigate the graphs of systems of linear and nonlinear inequalities. This exploration reinforces the concepts in Lesson 6.5 of Discovering Advanced Algebra.

Chapter 7

  • Vertex Form and Factored Form of Quadratic Equations
    Enrich your understanding of Lesson 7.2 (pages 368???376) by exploring how the vertex and factored forms of quadratic equations relate to the graphs of parabolas. These dynamic sketches also give you an example for Exercise 16 on page 446 of Discovering Advanced Algebra.
  • The Box Factory
    Use a dynamic sketch to explore the relationship between the dimensions of a box and a graph of its volume. This exploration can be used to augment the Investigation Box Factory and to help you solve Exercise 5 in Lesson 7.6 of Discovering Advanced Algebra.

Chapter 8

  • Right Triangle Trigonometry
    Use dynamic sketches to review the properties of similar triangles and the definitions of trigonometric ratios. This exploration will reinforce the concepts in Lesson 8.3 of Discovering Advanced Algebra.
  • The Law of Cosines
    Use a dynamic sketch to validate the Law of Cosines, which is covered in Lesson 8.7 of Discovering Advanced Algebra.

Chapter 9

  • Constructing an Ellipse
    Extend Lesson 9.2 (pages 496???508) of Discovering Advanced Algebra by exploring a geometric construction of an ellipse. This sketch also supports the Geometer's Sketchpad Exploration Constructing the Conic Sections.
  • Constructing a Parabola
    Extend Lesson 9.3 (pages 507???513) of Discovering Advanced Algebra by exploring a geometric construction of a parabola. This sketch also supports the Geometer's Sketchpad Exploration Constructing the Conic Sections.
  • Constructing a Hyperbola
    Extend Lesson 9.4 (pages 514???522) of Discovering Advanced Algebra by exploring a geometric construction of a hyperbola. This sketch also supports the Geometer's Sketchpad Exploration Constructing the Conic Sections.
  • Properties of Hyperbolas
    Deepen your understanding of the definition of hyperbolsa by exploring a dynamic sketch. This exploration will deepen you understanding of the material in Lesson 9.4 of Discovering Advanced Algebra.

Chapter 10

  • Defining the Circular Functions
    Explore the definitions and graphs of the circular functions sine and cosine. The sketches on this page will give you a deeper understanding of Lesson 10.1, pages 565???572, of Discovering Advanced Algebra.
  • Radian Measure
    Use dynamic sketches to deepen your understanding of the definition of radian. This exploration will reinforce the concepts in Lesson 10.2 of Discovering Advanced Algebra.
  • Double Ferris Wheel
    Explore the motion of a double Ferris wheel. This will help you solve Exercise 12 on page 607 of Discovering Advanced Algebra. It may also give you some ideas for how to create your own simulation for Exercise 13.

Chapter 11

  • Infinite Geometric Series
    Use a geometric model to deepen your understanding of infinite series. This exploration enriches your understanding of the concepts in Lesson 11.2 of Discovering Advanced Algebra, and offers a different model from the Exploration Seeing the Sum of a Series in Chapter 11.

Chapter 12

  • Permutations and Combinations
    Use dynamic sketches to investigate properties of permutations and combinations. This exploration will reinforce the concepts in Lessons 12.5 and 12.6 of Discovering Advanced Algebra.

Chapter 13

  • Normal Distributions
    See how the mean and standard deviation impact the bell-shaped normal curve. This will give you a deeper understanding of Lesson 13.2, pages 734???742, of Discovering Advanced Algebra.
  • The Least Squares Line
    Use a dynamic data set and movable line to enrich your understanding of the least squares line. This exploration will reinforce the concepts in Lesson 13.6 of Discovering Advanced Algebra.