TJB GeoGebra Sampler

Tim Brzezinski, Oct 30, 2015

[b]Contains a sample of applets that show how GeoGebra can be used as a powerful tool to[/b] [color=#c51414][b](a) Foster Discovery Learning[/b][/color] [color=#0a971e][b](b) Differentiate Instruction[/b][/color] [color=#1551b5][b](c) Provide Students With Opportunities for Meaningful Remediation,[/b][/color] and [color=#d69210][b](d) Provide Students With Numerous Opportunities for Informal Assessment [/b][/color]

Table of Contents

  1. Sample Discovery (and/or "re-discovery") Learning Applets
    1. Distance in the Coordinate Plane (With Hints)
    2. Messing With Lisa
    3. Slope Triangle Rotation (VA)
    4. Alternate Interior Angles: Quick Investigation
    5. Congruent Corresponding Angles to Start? (Quick Investigation)
    6. Where to Sit? (I)
    7. Where to Sit (II)?
    8. Inscribed Angle Theorem: Take 2!
    9. Inscribed Angle Theorem (V1)
    10. Function Transformations
    11. Blueprint Equation of a Line (I)
    12. Right Triangle Trigonometry: Intro
  2. Sample Applets That Illustrate Differentiation of Instruction
    1. Distance in the Coordinate Plane (II)
    2. Rise & Run
    3. Rhombus Template with Investigation Questions
    4. Rhombus Template (Scaffolded Discovery)
    5. Points of Concurrency: Investigation
    6. Circumcenter & Circumcircle Action!
    7. 3 Special Points!
    8. Angle Formed by 2 Chords (I)
    9. Angle Formed by 2 Chords (II)
    10. 9 Point Circle Action
    11. Thebault Action!!!
    12. How Fast are You Spinning?
    13. Exterior Angles of a Heptagon
    14. NCTM Calendar Problem (11-2-2016)
  3. Sample Dynamic Reference Applets Useful for Meaningful Remediation
    1. Vertical Angles Exploration (1)
    2. Slope: Intuitive Introduction
    3. Perpendicular Lines Investigation (VA)
    4. Perpendicular Lines Investigation (VB)
    5. Triangle Angle Theorems
    6. Circle Terminology
    7. 3-Way Color-Changing Derivative Grapher
    8. TRUE MEANING of π
    9. Area of a Triangle (Discovery)
    10. Trapezoid: Area (I)
    11. Trigonometric Ratios (Right Triangle Context)
    12. Complementary Meaning?
    13. A Special Triangle & Its Properties (I)
  4. Sample Informal Assessment Applets
    1. Plotting Points (x,y): Quiz
    2. Slope (Quiz) I
    3. Slope (Quiz) II
    4. Finding Slope Given 2 Points: Question Generator
    5. Graphing Linear Equations: Question Generator (V2)
    6. Working With Percents
    7. Working with Percent Change
    8. Simplifying Radicals (II)
    9. Linear Equation Generator
    10. Interval Notation Quiz: Single Sets, Conjunctions, Disjunctions
    11. Solving Exponential Equations (I)
    12. Graph y = a sin(x) + d (Quiz)
    13. Application Problems: Solving Linear Equations (1)
    14. Perimeter of a Rectangle: Solving Linear Equations
    15. Application Problems: Solving Linear Equations (3)
    16. Friends and Money: Solving Linear Equations

1.

Sample Discovery (and/or "re-discovery") Learning Applets

  • 1. Distance in the Coordinate Plane (With Hints)
  • 2. Messing With Lisa
  • 3. Slope Triangle Rotation (VA)
  • 4. Alternate Interior Angles: Quick Investigation
  • 5. Congruent Corresponding Angles to Start? (Quick Investigation)
  • 6. Where to Sit? (I)
  • 7. Where to Sit (II)?
  • 8. Inscribed Angle Theorem: Take 2!
  • 9. Inscribed Angle Theorem (V1)
  • 10. Function Transformations
  • 11. Blueprint Equation of a Line (I)
  • 12. Right Triangle Trigonometry: Intro

1.1.

Distance in the Coordinate Plane (With Hints)

Discovery Lesson (Can be used without interactive figure below)
– Tim Brzezinski

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1.10.

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1.11.

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1.12.

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2.

Sample Applets That Illustrate Differentiation of Instruction

  • 1. Distance in the Coordinate Plane (II)
  • 2. Rise & Run
  • 3. Rhombus Template with Investigation Questions
  • 4. Rhombus Template (Scaffolded Discovery)
  • 5. Points of Concurrency: Investigation
  • 6. Circumcenter & Circumcircle Action!
  • 7. 3 Special Points!
  • 8. Angle Formed by 2 Chords (I)
  • 9. Angle Formed by 2 Chords (II)
  • 10. 9 Point Circle Action
  • 11. Thebault Action!!!
  • 12. How Fast are You Spinning?
  • 13. Exterior Angles of a Heptagon
  • 14. NCTM Calendar Problem (11-2-2016)

2.1.

Distance in the Coordinate Plane (II)

[color=#000000]In the coordinate plane below, you'll notice that the axes and gridlines are missing. [br][br]You can move the [b]BIG BLACK POINTS[/b] anywhere you'd like. [br]Use this applet to help guide you through the questions on your activity sheet. [br][br]After completing your activity sheet, please answer the questions that appear after the applet. [/color]
[b][color=#0000ff]Questions:[/color][/b][br][br][color=#274e13]1) How can you calculate the length of the green segment, or [b]|RISE|[/b], WITHOUT counting spaces (or gridlines)? [br][/color][br][color=#cc0000]2) How can you calculate the length of the red segment, or [b]|RUN|[/b], WITHOUT counting spaces (or gridlines)? [/color][br][br][color=#000000]3) Let's call "[i][b]d[/b][/i]" the distance between point [i]A[/i] and point [i]B[/i]. Write an equation that expresses the relationship among [i][b]d[/b][/i], [/color][color=#274e13][b]|RISE|[/b][/color][color=#000000], and[/color] [color=#cc0000][b]|RUN|[/b][/color][color=#000000].[/color] [br][br][color=#000000]4) Use the relationship you wrote for (3) to calculate the distance between [i]A[/i](-3, 4) and [i]B[/i](2, -6) [i]without[/i] using the applet above. After you arrive at your answer, use the applet to check your work. [/color]
– Tim Brzezinski

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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3.

Sample Dynamic Reference Applets Useful for Meaningful Remediation

  • 1. Vertical Angles Exploration (1)
  • 2. Slope: Intuitive Introduction
  • 3. Perpendicular Lines Investigation (VA)
  • 4. Perpendicular Lines Investigation (VB)
  • 5. Triangle Angle Theorems
  • 6. Circle Terminology
  • 7. 3-Way Color-Changing Derivative Grapher
  • 8. TRUE MEANING of π
  • 9. Area of a Triangle (Discovery)
  • 10. Trapezoid: Area (I)
  • 11. Trigonometric Ratios (Right Triangle Context)
  • 12. Complementary Meaning?
  • 13. A Special Triangle & Its Properties (I)

3.1.

Vertical Angles Exploration (1)

Interact with this app for a few minutes. Be sure to drag the LARGE POINT around and be sure to move the 2 sliders you see.
Notice anything interesting? Describe as best as you can.
What happens if you make the size of the [b][color=#ff00ff]angle[/color][/b] BIGGER or smaller? [br][br][b][color=#ff00ff](You can change the size of the manila angle by using the manila-colored slider). [/color][/b]Does your response to the question above change? Why? Why not? Describe.
– Tim Brzezinski

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3.8.

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3.10.

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3.11.

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4.

Sample Informal Assessment Applets

  • 1. Plotting Points (x,y): Quiz
  • 2. Slope (Quiz) I
  • 3. Slope (Quiz) II
  • 4. Finding Slope Given 2 Points: Question Generator
  • 5. Graphing Linear Equations: Question Generator (V2)
  • 6. Working With Percents
  • 7. Working with Percent Change
  • 8. Simplifying Radicals (II)
  • 9. Linear Equation Generator
  • 10. Interval Notation Quiz: Single Sets, Conjunctions, Disjunctions
  • 11. Solving Exponential Equations (I)
  • 12. Graph y = a sin(x) + d (Quiz)
  • 13. Application Problems: Solving Linear Equations (1)
  • 14. Perimeter of a Rectangle: Solving Linear Equations
  • 15. Application Problems: Solving Linear Equations (3)
  • 16. Friends and Money: Solving Linear Equations

4.1.

Plotting Points (x,y): Quiz

[b][color=#000000]Students:[/color][/b] [b][color=#1e84cc]Repeat this exercise as many times as you need in order to master this concept! [/color][/b]
Quick (Silent) Demo
– Tim Brzezinski

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