Avenues: The World School GeoGebra Book of Resources

Carmel Schettino, Jul 22, 2017

This is a book of resources for the Mathematics Department for grades 6-12 at Avenues: The World School. It is supplementary to the materials they use for their curriculum.

Table of Contents

  1. Grade 6 Supplement
    1. Balloons and Sandbags
    2. Equivalent Fractions Visual
    3. Expressions Using Variables
    4. Is it a square?
    5. Surface Area: Intuitive Introduction
    6. What's the Name of the Solid?
    7. Question 1
    8. Measurement of Angle with a Protractor
    9. Measuring Angles Using Protractor
    10. Polygon Pieces for Chain of Changes Problem
    11. Building Parallelograms with Given Area: Quick Formative Assessment
    12. TR KAY - Equivalent Fractions
    13. Avenues Polygon Synthesizer
  2. Grade 7 Supplement
    1. Cube Roots
    2. TR (KAY) - Ισοδύναμα κλάσματα
    3. Copy of Indirect Proportion Exploration
    4. Parallels & Perpendiculars: Ex. 7
    5. Parallel Lines & Related Angles
    6. Animation 171
    7. Quadrilateral Angle Theorems
    8. Circle Area (By Peeling!)
    9. Area of a Circle - Wedge/Sector Demonstration
    10. Graph data sets and use a line to model the data
  3. Math 1 Supplement
    1. Rectangle Perimeter Exploration
    2. Working with Point-Slope Form
    3. Linear Inequality Generator (1B)
    4. Inequalities in Standard Form (Illustrator)
    5. Equation of a Line: Dynamic Illustrator
    6. Multiplying Binomials
    7. Exponents: Product Rule (with Negatives)
    8. Zero Product Property Exploration
    9. Completing the Square (1)
  4. Math 2 Supplement
    1. Activity 2: Messing With Mona: Introduction to Transformations
    2. Introducing Congruence
    3. Square Dissection Puzzle Dilemma
    4. IM2 Folding Paper Problem
    5. Activity 5: Exploring Altitudes
    6. IM2 Changing m in point/slope form
    7. IM2 Justify the type of transformation
    8. IM2 Different type of transformations - diagram
    9. IM2 glide reflection justification diagram
    10. IM2 How many congruent triangles?
    11. IM2 Showing angle are congruent with coordinates - diagram
    12. Activity 6: Exploring Medians and the Centroid
    13. IM2 Proving angles congruent on graph
    14. Graph of Parabola from Distance Definition
    15. Dilated triangles and ratio of areas
    16. Activity 7: Perpendicular Bisectors of a Triangle
    17. IM2 Similar or Dilation Distinction
    18. Similar Triangles and Area Comparison
    19. Activity #8: Transversal Intersects Parallel Lines (Investigation)
    20. Activity 9: Triangle Exterior Angle
    21. What is the Sentry Theorem?
    22. Activity #10: Three Parallels Theorem
    23. IM2 inscribed vs central angles in circles
    24. IM2 Right, Obtuse or Acute? Test of Triangle Type
    25. Activity #11: Angle Bisector Proportionality Theorem
    26. Cavalieri's Principle
    27. IM2 Right Triangle Similarity Visualization
    28. Activity 12: Introduction to Dilations
    29. IM2 Truth about altitude x base?
    30. IM2 Ratio of Areas with same Base within a triangle
    31. Animation 74
    32. Circle Area (By Peeling!)
    33. Exploring the configuration of the points that keep an angle constant
    34. IM2 Different type of transformations - diagram
    35. Triangle Inequality Theorem Exploration
    36. IM2 Squares for Pythagorean Puzzle
  5. Triangle Congruence Applets for Math 2
    1. Discovery of SSS
    2. SAS Congruence Demo
    3. Why may SSA / ASS triangles be incongruent?
    4. Triangle SSA
    5. Triangle Congruence Criteria: Side - Side - Side
    6. Triangle Congruence Criteria: Side - Angle - Side
    7. Triangle Congruence Criteria: Angle-Angle-Angle
  6. Math 3 Supplement
    1. Unit Circle and Angles
    2. Graphs of Trig Functions from Unwrapping the Unit Circle
    3. Ferris Wheel Unit Circle
    4. Transforming the Sine Function
    5. Volume of Spheres with Proof
    6. Exploring Trigonometric Ratios on the Unit Circle
    7. 580 -Exploring Exponential Function and Slope at (0,1)
    8. Archimedes Volume of a Sphere
    9. Unit Circle and Sine Graph
    10. Unit Circle and Cosine Graph
    11. Unit Circle and Tangent Graph
  7. Math 4 Supplement
    1. Position, Velocity, and Acceleration vs. Time Graphs
    2. Continuity Questions
    3. Average Rate Of Change
    4. 3-Way Color-Changing Derivative Grapher
    5. 580 -Exploring Exponential Function and Slope at (0,1)
    6. Pascal's Triangle Explorer
  8. Calculus Supplement
    1. Derivative Function: Without Words
    2. Upper and Lower Sum

1.

Grade 6 Supplement

  • 1. Balloons and Sandbags
  • 2. Equivalent Fractions Visual
  • 3. Expressions Using Variables
  • 4. Is it a square?
  • 5. Surface Area: Intuitive Introduction
  • 6. What's the Name of the Solid?
  • 7. Question 1
  • 8. Measurement of Angle with a Protractor
  • 9. Measuring Angles Using Protractor
  • 10. Polygon Pieces for Chain of Changes Problem
  • 11. Building Parallelograms with Given Area: Quick Formative Assessment
  • 12. TR KAY - Equivalent Fractions
  • 13. Avenues Polygon Synthesizer

1.1.

Balloons and Sandbags

Contact us at [url=mailto:ptierneyfife@edc.org]ptierneyfife@edc.org[/url] if this resource should be updated, or with questions or suggestions. We appreciate your help maintaining the quality of this resource.
– EDC in Maine

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2.

Grade 7 Supplement

  • 1. Cube Roots
  • 2. TR (KAY) - Ισοδύναμα κλάσματα
  • 3. Copy of Indirect Proportion Exploration
  • 4. Parallels & Perpendiculars: Ex. 7
  • 5. Parallel Lines & Related Angles
  • 6. Animation 171
  • 7. Quadrilateral Angle Theorems
  • 8. Circle Area (By Peeling!)
  • 9. Area of a Circle - Wedge/Sector Demonstration
  • 10. Graph data sets and use a line to model the data

2.1.

Cube Roots

– Edward Knote

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3.

Math 1 Supplement

GeoGebra Files for Algebra 1 Problem Book

  • 1. Rectangle Perimeter Exploration
  • 2. Working with Point-Slope Form
  • 3. Linear Inequality Generator (1B)
  • 4. Inequalities in Standard Form (Illustrator)
  • 5. Equation of a Line: Dynamic Illustrator
  • 6. Multiplying Binomials
  • 7. Exponents: Product Rule (with Negatives)
  • 8. Zero Product Property Exploration
  • 9. Completing the Square (1)

3.1.

Rectangle Perimeter Exploration

Rectangle Perimeter Exploration
– Carmel Schettino

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4.

Math 2 Supplement

  • 1. Activity 2: Messing With Mona: Introduction to Transformations
  • 2. Introducing Congruence
  • 3. Square Dissection Puzzle Dilemma
  • 4. IM2 Folding Paper Problem
  • 5. Activity 5: Exploring Altitudes
  • 6. IM2 Changing m in point/slope form
  • 7. IM2 Justify the type of transformation
  • 8. IM2 Different type of transformations - diagram
  • 9. IM2 glide reflection justification diagram
  • 10. IM2 How many congruent triangles?
  • 11. IM2 Showing angle are congruent with coordinates - diagram
  • 12. Activity 6: Exploring Medians and the Centroid
  • 13. IM2 Proving angles congruent on graph
  • 14. Graph of Parabola from Distance Definition
  • 15. Dilated triangles and ratio of areas
  • 16. Activity 7: Perpendicular Bisectors of a Triangle
  • 17. IM2 Similar or Dilation Distinction
  • 18. Similar Triangles and Area Comparison
  • 19. Activity #8: Transversal Intersects Parallel Lines (Investigation)
  • 20. Activity 9: Triangle Exterior Angle
  • 21. What is the Sentry Theorem?
  • 22. Activity #10: Three Parallels Theorem
  • 23. IM2 inscribed vs central angles in circles
  • 24. IM2 Right, Obtuse or Acute? Test of Triangle Type
  • 25. Activity #11: Angle Bisector Proportionality Theorem
  • 26. Cavalieri's Principle
  • 27. IM2 Right Triangle Similarity Visualization
  • 28. Activity 12: Introduction to Dilations
  • 29. IM2 Truth about altitude x base?
  • 30. IM2 Ratio of Areas with same Base within a triangle
  • 31. Animation 74
  • 32. Circle Area (By Peeling!)
  • 33. Exploring the configuration of the points that keep an angle constant
  • 34. IM2 Different type of transformations - diagram
  • 35. Triangle Inequality Theorem Exploration
  • 36. IM2 Squares for Pythagorean Puzzle

4.1.

Activity 2: Messing With Mona: Introduction to Transformations

Note: LARGE POINTS are MOVEABLE.
– Carmel Schettino, Tim Brzezinski

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5.

Triangle Congruence Applets for Math 2

  • 1. Discovery of SSS
  • 2. SAS Congruence Demo
  • 3. Why may SSA / ASS triangles be incongruent?
  • 4. Triangle SSA
  • 5. Triangle Congruence Criteria: Side - Side - Side
  • 6. Triangle Congruence Criteria: Side - Angle - Side
  • 7. Triangle Congruence Criteria: Angle-Angle-Angle

5.1.

Discovery of SSS

Discovery of SSS Triangle Congruence.[br][br]Complete the below activity with a partner.
save the file as[br][br]lastname.SSS
– Melissa Hertel

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6.

Math 3 Supplement

  • 1. Unit Circle and Angles
  • 2. Graphs of Trig Functions from Unwrapping the Unit Circle
  • 3. Ferris Wheel Unit Circle
  • 4. Transforming the Sine Function
  • 5. Volume of Spheres with Proof
  • 6. Exploring Trigonometric Ratios on the Unit Circle
  • 7. 580 -Exploring Exponential Function and Slope at (0,1)
  • 8. Archimedes Volume of a Sphere
  • 9. Unit Circle and Sine Graph
  • 10. Unit Circle and Cosine Graph
  • 11. Unit Circle and Tangent Graph

6.1.

Unit Circle and Angles

GeoGebra Tutorial Example 62 - Unit Circle and Angles
GeoGebra Tutorial Example 62 - Unit Circle and Angles
– GGBin

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7.

Math 4 Supplement

  • 1. Position, Velocity, and Acceleration vs. Time Graphs
  • 2. Continuity Questions
  • 3. Average Rate Of Change
  • 4. 3-Way Color-Changing Derivative Grapher
  • 5. 580 -Exploring Exponential Function and Slope at (0,1)
  • 6. Pascal's Triangle Explorer

7.1.

Position, Velocity, and Acceleration vs. Time Graphs

Adjust the Initial Position and the shape of the Velocity vs. Time graph by sliding the points up or down. Watch how the graphs of Position vs. Time and Acceleration vs. Time change as they adjust to match the motion shown on the Velocity vs. Time graph.
– Markus Hohenwarter, Tom Walsh

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8.

Calculus Supplement

  • 1. Derivative Function: Without Words
  • 2. Upper and Lower Sum

8.1.

Derivative Function: Without Words

In the applet below, a function [i]f [/i]is shown (black). [br]Its derivative function, f', is shown in gray. [br][br]Feel free to input any function you'd like. [br][br]Slide the slider to see the physical meaning of the derivative of a function (at a certain input value: x-coordinate of white point) within this graphical context. [br][br][i]How can we sketch the graph of the derivative of a function? Explain. [/i]
Quick Demo (BGM: Andy Hunter)
– Tim Brzezinski

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