Dynamic Algebra™ Explorations
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JavaSketchpad™ is a dynamic environment that lets you interact with algebra and geometry constructions on the Internet. This page contains a JavaSketch. If this is the first JavaSketch you’ve encountered since starting your browser, it may take a few minutes to load. Once the illustration appears at right, you can interact with it by dragging the red points.
| JavaSketchpad is an extension of The Geometer’s Sketchpad®. You do not need The Geometer’s Sketchpad to use these explorations, but you do need to have a Java™-compatible web browser. To learn more about The Geometer’s Sketchpad or JavaSketchpad, visit The Geometer's Sketchpad area of Keymath.com. |
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With the Dynamic Algebra Explorations below, you can investigate a variety of concepts from Discovering Algebra: An Investigative Approach. Each exploration has one or more JavaSketches, along with instructions and questions to guide your work. While some explorations are similar to investigations in Discovering Algebra, most are intended to expand or deepen your understanding.
Click the links below to go directly to these free online explorations. You might want to keep notes about your work and written answers to the questions. These explorations do not come with answers, but you can check your work by sharing your results with a classmate, a family member, or your teacher.
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 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. |
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 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. |
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 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 (pages 199201). |
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 On the Road Again Explore linear plots for the time-distance relationships of three vehicles. This exploration is similar to the investigation on pages 207208 of Discovering Algebra. |
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 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 251255). |
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 Inequalities Use a dynamic sketch to analyze what addition, subtraction, multiplication, and division do to an inequality. This exploration reinforces the investigation on pages 340 and 341 of Discovering Algebra. |
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 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, pages 367370 of Discovering Algebra and will prepare you for exponential equations later in Chapter 7. |
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 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 (pages 483, 484, and 487). |
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 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 on pages 551556 of Discovering Algebra. |
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 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. |
