Create , Visualize & Explore

Sangeeta Gulati, Tutorified.com, Dec 14, 2019

This workbook was created for the workshop "Create , Visualize & explore with GeoGebra and Desmos" for secondary and senior secondary mathematics teachers conducted on November 27 & 28, 2015. This workshop was held at Sanskriti School , New Delhi, India and led by Sangeeta Gulati. Over the past years, I have created and curated many other useful applets related to CBSE curriculum for use of teachers and students.

Table of Contents

  1. Geometry
    1. Drawings, Constructions, and Drag Test
    2. Construction vs Drawing
    3. Pythagoras Theorem for Regular n-gons
    4. Disection Proof - Pythagoras Theorem
    5. Corners of Squares
    6. Pentagrams
    7. Angle Sum Property by Rotation
    8. Isosceles Triangles - Examples and Non-Examples
    9. Midpoint Triangles
    10. Intro to Area Using Unit Squares
    11. Dividing a line segment into 4 equal parts
    12. Exterior Angles of a Regular Polygon
    13. Consistency of Linear equations in Two Variables
    14. Perimeter - Area Challenges
    15. Arc Length 1
    16. Forest Hills (8.G.5 Parallel lines)
    17. ACCESS - Sum of Angles in Triangle
    18. Create Tool - Pentagram
    19. Pythagorean Theorem Proof without Words
  2. PreCalculus
    1. Function Matching
    2. Radians, Number line and the Unit Circle
    3. Right Triangle Trigonometry Ratios
    4. Sine Curve with Points
    5. Domain of Functions
    6. Horizontal Line Test
    7. Trigonometric Functions and Unit Circle
    8. Inverse of a Function-Reflection on y = x
    9. Vertical Line Test
    10. Histogram with GeoGebra
    11. Copy of Trigonometry: Basic and More
    12. Measuring angles using radians
    13. Arc Length 2
    14. Function Machine 1
    15. Function Machines
    16. Function Or Not?
    17. trig ceilings and floors
    18. Solving Absolute Value Inequalities Visually, Greater Than
    19. Exploring Quadratic Functions
    20. Will It Hit The Hoop?
    21. Sine & Cosine of a Sum: Discovery
    22. Linear Inequalities of 2 Variables: Illustrator
    23. Trigonometric Functions-Graphs
  3. Calculus
    1. Understanding Differentiability
    2. Derivative as Slope Function
    3. Increasing and Decreasing Functions-Intervals
    4. Definite Integral - Upper and Lower Sum
    5. GeoGebra Calculus Applets
    6. Maximizing Area
    7. Box Problem
    8. Derivative of Sine & Cosine Functions (Quick Investigation)
    9. Limit Quiz
  4. Linear Programming
    1. Linear Programming- Problem 2- Minimum Cost
    2. Linear Programming-Transport Problem
    3. Линейни неравенства.
    4. graph linear inequalities in two variables
    5. WHY the VERTICES? Linear Programming: A Closer Look
  5. Vectors & Three Dimensional Geometry
    1. Definition of vector addition
    2. Translations along vector
    3. Vector Sum - Parallelogram Law
    4. Skew Lines and Line of Shortest Distance
    5. Three Dimensional Coordinate System with Axes Planes
    6. Point in 3D Coordinate System
    7. Vector Projections (1)
    8. Projection of a Vector
    9. Adding Vectors Geometrically
  6. Conics
    1. Parabola
    2. Ellipse
  7. Maths is Beautiful
    1. 8 Point Star
    2. Square Root Spiral
    3. Golden Spiral
    4. Caso 5
    5. Sierpinski Triangle
    6. Ever Present Equilateral Triangle
    7. Curve of Pursuit
    8. Snowflakes with GeoGebra
    9. Kaleidoscope
    10. 3-Way Color-Changing Derivative Grapher
    11. Treasure Island Puzzle
    12. Four color challenge
  8. GeoGebra Guides
  9. Classes 6-10
    1. Golden Spiral
    2. Angle Sum Property by Rotation
    3. Quadratic Functions: the effect of "b"
    4. Friends and Money: Solving Linear Equations
    5. Graphing Linear Equations -1
    6. Application Problems: Solving Linear Equations (5)
    7. Matching Verbal Statements to Algebraic Statements (V1)
    8. Exploring Right Triangles
    9. ACCESS - Rhombus
    10. Nets of Solids
    11. Example Activity: Orthocenter of a Triangle
    12. Linear Equation in two variables
    13. Completing the Square (2)
    14. Introduction to Probability ---- The Rolling of a Die
    15. Exterior Angles (Revisited)
    16. Convex vs. Concave
    17. Field of Fractions

1.

Geometry

Worksheets suitable for middle and secondary school mathematics.

  • 1. Drawings, Constructions, and Drag Test
  • 2. Construction vs Drawing
  • 3. Pythagoras Theorem for Regular n-gons
  • 4. Disection Proof - Pythagoras Theorem
  • 5. Corners of Squares
  • 6. Pentagrams
  • 7. Angle Sum Property by Rotation
  • 8. Isosceles Triangles - Examples and Non-Examples
  • 9. Midpoint Triangles
  • 10. Intro to Area Using Unit Squares
  • 11. Dividing a line segment into 4 equal parts
  • 12. Exterior Angles of a Regular Polygon
  • 13. Consistency of Linear equations in Two Variables
  • 14. Perimeter - Area Challenges
  • 15. Arc Length 1
  • 16. Forest Hills (8.G.5 Parallel lines)
  • 17. ACCESS - Sum of Angles in Triangle
  • 18. Create Tool - Pentagram
  • 19. Pythagorean Theorem Proof without Words

1.1.

Drawings, Constructions, and Drag Test

Discussion
[b][font=Tahoma, sans-serif][color=#000000]What is the difference between a drawing and a construction?[/color][/font][/b][br][font=Tahoma, sans-serif][color=#000000] Adrawing is only a connection of points and lines that can be shaped[br]in the form of a geometric figure, while a construction is a solid[br]object with constraints and properties.[/color][color=#000000][br][br][b]What is the “drag test” and why is it important?[/b][/color][/font][br][font=Tahoma, sans-serif][color=#000000] [/color][color=#000000]To see if the construction is fully defined. [/color][color=#000000]Tocheck if the construction is correct.[/color][color=#000000][br][br][b]Why is it important to construct figures instead of just drawing them[br]in interactive geometry software?[/b][/color][/font][br][font=Tahoma, sans-serif][color=#000000] [/color][color=#000000]To be able to work with them, so the construction can influence other[br]objects and vice versa.[/color][color=#000000][br][br][b]What do we have to know about the geometric figure before we are able[/b][br]to construct it using dynamic mathematics software?[/color][/font][br][font=Tahoma, sans-serif][color=#000000] [/color][color=#000000]Dimensions,number of vertices. [/color][color=#000000][br][/color][/font][br][br]
– Jose Alvarado

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2.

PreCalculus

[color=#1551b5]Worksheets to teach and explore Trigonometry , Trigonometric functions, Domain and Range of functions, Graphs of Functions[/color]

  • 1. Function Matching
  • 2. Radians, Number line and the Unit Circle
  • 3. Right Triangle Trigonometry Ratios
  • 4. Sine Curve with Points
  • 5. Domain of Functions
  • 6. Horizontal Line Test
  • 7. Trigonometric Functions and Unit Circle
  • 8. Inverse of a Function-Reflection on y = x
  • 9. Vertical Line Test
  • 10. Histogram with GeoGebra
  • 11. Copy of Trigonometry: Basic and More
  • 12. Measuring angles using radians
  • 13. Arc Length 2
  • 14. Function Machine 1
  • 15. Function Machines
  • 16. Function Or Not?
  • 17. trig ceilings and floors
  • 18. Solving Absolute Value Inequalities Visually, Greater Than
  • 19. Exploring Quadratic Functions
  • 20. Will It Hit The Hoop?
  • 21. Sine & Cosine of a Sum: Discovery
  • 22. Linear Inequalities of 2 Variables: Illustrator
  • 23. Trigonometric Functions-Graphs

2.1.

Function Matching

This activity is a matching test. Drag the correct function to its graph.[br][br]Displayed in English as Daniel Mentrard gave permission.[br][url]http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/MDfonctioalg.html[/url]
By Daniel Mentrard, Créé avec GeoGebra [url]http://dmentrard.free.fr/GEOGEBRA/index.htm[\url][br]Translation by A. B. Cron
– Auston B Cron

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3.

Calculus

Abstract concepts of Calculus are best illustrated with dynamic applets made by GeoGebra

  • 1. Understanding Differentiability
  • 2. Derivative as Slope Function
  • 3. Increasing and Decreasing Functions-Intervals
  • 4. Definite Integral - Upper and Lower Sum
  • 5. GeoGebra Calculus Applets
  • 6. Maximizing Area
  • 7. Box Problem
  • 8. Derivative of Sine & Cosine Functions (Quick Investigation)
  • 9. Limit Quiz

3.1.

Understanding Differentiability

Drag the point B (x, f(x)) to see how a Secant Becomes a Tangent Use the check boxes to see the slopes of the Secant line and of the Tangent line

This applte shows how a Secant Becomes a Tangent and it shows the slopes of the Secant line and of the Tangent line , thus establishing a correspondence between differentiability geometrically and algebraically.
– Sangeeta Gulati

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4.

Linear Programming

These applets are based on the Linear Programming problems of class XII text book.

  • 1. Linear Programming- Problem 2- Minimum Cost
  • 2. Linear Programming-Transport Problem
  • 3. Линейни неравенства.
  • 4. graph linear inequalities in two variables
  • 5. WHY the VERTICES? Linear Programming: A Closer Look

4.1.

Linear Programming- Problem 2- Minimum Cost

Minimum Cost- Verification
– Sangeeta Gulati

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Vectors & Three Dimensional Geometry

  • 1. Definition of vector addition
  • 2. Translations along vector
  • 3. Vector Sum - Parallelogram Law
  • 4. Skew Lines and Line of Shortest Distance
  • 5. Three Dimensional Coordinate System with Axes Planes
  • 6. Point in 3D Coordinate System
  • 7. Vector Projections (1)
  • 8. Projection of a Vector
  • 9. Adding Vectors Geometrically

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Definition of vector addition

Dynamic demonstration of vector addition.
– Malin Christersson

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Conics

  • 1. Parabola
  • 2. Ellipse

6.1.

Parabola

Parabola formed as envelope of straight lines.
Parabola
– Sangeeta Gulati

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7.

Maths is Beautiful

[color=#1551b5]There are many math wonders that one can discover and recreate with the help of technology , especially GeoGebra. Here is a collection of some of them.[/color]

  • 1. 8 Point Star
  • 2. Square Root Spiral
  • 3. Golden Spiral
  • 4. Caso 5
  • 5. Sierpinski Triangle
  • 6. Ever Present Equilateral Triangle
  • 7. Curve of Pursuit
  • 8. Snowflakes with GeoGebra
  • 9. Kaleidoscope
  • 10. 3-Way Color-Changing Derivative Grapher
  • 11. Treasure Island Puzzle
  • 12. Four color challenge

7.1.

8 Point Star

Maths is fun!
8 Point Star
– Sangeeta Gulati

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GeoGebra Guides

[color=#c51414]Collection of GeoGebra help guides with tutorials to help you learn GeoGebra[/color] [url]http://tube.geogebra.org/material/simple/id/1403161[/url]


    This chapter does not contain any resources yet.

9.

Classes 6-10

Applets suitable for Classes VI-X ( CBSE)

  • 1. Golden Spiral
  • 2. Angle Sum Property by Rotation
  • 3. Quadratic Functions: the effect of "b"
  • 4. Friends and Money: Solving Linear Equations
  • 5. Graphing Linear Equations -1
  • 6. Application Problems: Solving Linear Equations (5)
  • 7. Matching Verbal Statements to Algebraic Statements (V1)
  • 8. Exploring Right Triangles
  • 9. ACCESS - Rhombus
  • 10. Nets of Solids
  • 11. Example Activity: Orthocenter of a Triangle
  • 12. Linear Equation in two variables
  • 13. Completing the Square (2)
  • 14. Introduction to Probability ---- The Rolling of a Die
  • 15. Exterior Angles (Revisited)
  • 16. Convex vs. Concave
  • 17. Field of Fractions

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– Sangeeta Gulati

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