Dynamic Explorations

Chapter 0

  • The Hat Curve
    Use dynamic sketches to study the hat curve that is introduced in Lesson 0.3 of Discovering Algebra.
  • The Sierpinski Attractor
    Explore the attractor of a recursive routine based on a triangle. This exploration will help you with the investigation in Lesson 0.5 of Discovering Algebra.

Chapter 1

  • Finding the Center
    Learn more about the mean and median of data sets as you change the data values. This exploration will help you understand the measures of center you learned about in Lesson 1.2 of Discovering Algebra.
  • The Box Plotter
    Adjust data values and see the box plot of the resulting data set in a dynamic sketch. This exploration will help you understand more about properties of the box plot that you learned about in Lesson 1.3 of Discovering Algebra.

Chapter 2

  • Gone Fishin'
    Use a dynamic sketch to simulate the capture of several fish, some of which are tagged, similar to the investigation in Lesson 2.2 of Discovering Algebra.
  • Population Estimator
    Use percents and proportions to estimate populations, as in Lesson 2.2 of Discovering Algebra.
  • Geometric Probability
    Use geometry to estimate probabilities, and probabilities to estimate geometric quantities such as area. The ideas in this exploration are closely related to the ideas in Lessons 2.6 and 2.7 of Discovering Algebra.

Chapter 3

  • Direct Variation
    Use a dynamic graph to study direct variation. Then use the graph to solve the example on page 148 and a few exercises on page 149 of Discovering Algebra.
  • Shadows and Similar Triangles
    Investigate the similar triangles that are formed when objects block sunlight and cast shadows. This exploration will help you extend Exercise 9 on page 160 of Discovering Algebra.

Chapter 4

  • Recursive Sequences
    Use a dynamic sketch to explore recursive sequences. You can use this exploration to complete the examples and investigation in Lesson 4.3 of Discovering Algebra.
  • On the Road Again
    Explore linear plots for the time-distance relationships of three vehicles. This exploration is similar to the investigation in Lesson 4.4 of Discovering Algebra.

Chapter 5

  • A Formula for Slope
    Explore the concept of slope and develop a formula for the slope of the line through two points. This exploration is similar to the investigation and examples in Lesson 5.1 of Discovering Algebra (pages 251???255).
  • Line Drill
    Use dynamic sketches to improve your skills at finding intercept and point-slope forms of equations of lines. This exploration is related to Exercise 3 in Lesson 5.2 and the investigation in Lesson 5.4 of Discovering Algebra.
  • Using Q-Lines to Model Data
    Drag data points, and observe the effect on the Q-line, one line of fit for data. This exploration will help deepen your understanding of Q-lines, which are introduced in Lesson 5.6 of Discovering Algebra.

Chapter 6

  • The Eliminator
    Use a dynamic sketch to explore the elimination method of solving two linear equations. This exploration reinforces the concepts and can be used to solve some of the problems in Lesson 6.3 of Discovering Algebra.
  • Inequalities
    Use a dynamic sketch to analyze what addition, subtraction, multiplication, and division do to an inequality. This exploration reinforces the investigation in Lesson 6.5 of Discovering Algebra.
  • Systems of Inequalities
    Use dynamic sketches to explore graphs of inequalities in two variables and solve systems of inequalities. This exploration reinforces the concepts in Lesson 6.7 and may be helpful in doing some of the exercises on pages 358???359 of Discovering Algebra.

Chapter 7

  • Recursive Routines with Repeated Multiplication
    Investigate how growth and decay can be modeled by recursive routines with repeated multiplication. This exploration reinforces the concepts in Lesson 7.1 of Discovering Algebra and will prepare you for exponential equations later in Chapter 7.
  • Koch Curve Growth and Exponential Equations
    Use dynamic sketches to explore the growth of the Koch curve, as in the investigation on pages 374???376 of Discovering Algebra. This exploration also provides practice with exponental functions and may help you do the exercises in Lesson 7.2.

Chapter 8

  • The Code Maker
    Use a dynamic graphsto code and decode messages, as in Exercise 14 in Lesson 8.4 of Discovering Algebra.
  • Related to Squaring
    Use dynamic graphs to explore the squaring function and how it relates to the absolute value and square root functions. This exploration will help you with the investigation and Example in Lesson 8.7 of Discovering Algebra.

Chapter 9

  • Translating Graphs
    Use dynamic graphs to explore translations of functions. This exploration closely follows the investigation and Example B in Lesson 9.2 of Discovering Algebra.
  • Transformation Drill
    Practice expression transformations of functions, based on viewing the original graph and the transformed graph. This exploration is closely related to Examples B and C in Lesson 9.3 of Discovering Algebra.
  • Stretching and Shrinking Graphs
    Use sliders to stretch and shrink graphs, and observe the effects on the coordinates of points on the graph and on the equation of the graph. This exploration provides practices with the concepts introduced in Lesson 9.4 of Discovering Algebra.

Chapter 10

  • Factored Form of Quadratic Equations
    Explore the relationships between the factored form of a quadratic equation, the graph of the equation, and the roots when the equation is set equal to zero. This exploration corresponds to Lesson 10.4 of Discovering Algebra.
  • Parabola by Definition
    Explore the geometric definition of a parabola and see a few real-world situations that can be modeled by a parabola. This exploration extends the project on page 559 of Discovering Algebra, but it can be used at anytime to enrich Chapter 10: Quadratic Models.

Chapter 11

  • A Distance Formula
    Use an interactive sketch to better understand the distance formula that is based on the Pythagorean Theorem. This exploration can help you with the examples and exercises in Lesson 11.6 of Discovering Algebra.
  • Similar Triangles and Trigonometric Functions
    Use dynamic sketches to investigate relationships between similar triangles, and use the properties you discover to define and understand the trigonometric functions sine, cosine, and tangent. This exploration is related to Lesson 11.7 of Discovering Algebra.