Facilitate Self-Directed Learning in Secondary Math

Anthony OR 柯志明, 21 Jan 2022

Facilitate Self-Directed Learning using GeoGebra

Table of Contents

  1. Handoout
    1. Using GeoGebra to Facilitate Self-Directed Learning in Secondary Mathematics
  2. Examples of GeoGebra Resources
    1. Area of Two Rectangles
    2. Exterior Angles of Polygons
    3. Errors in Measurement
    4. Area of Circles
    5. Volume of Spheres with Proof
    6. Addition of Directed Numbers - Counters Model
    7. Subtraction of Directed Numbers - Counters Model
    8. Addition of Directed Numbers - Elevator Model
    9. Subtraction of Directed Numbers - Elevator Model
    10. Quiz on Solving Right Triangles (Combined) 解直角三角形：合併測驗
    11. Quiz on Special Lines in Triangles 三角形內的特殊線：測驗
  3. Exploring Congruence of Triangles
    1. Q1
    2. Q2
    3. Q3
    4. Q4
    5. Q5
    6. Q6
  4. Drawing Figures and Graphs
    1. Graph Plotter 2020
  5. Creating Simple GeoGebra Applets
    1. Rotation on the Coordinate Plane
    2. y = a sin x°

1.

Handoout

  • 1. Using GeoGebra to Facilitate Self-Directed Learning in Secondary Mathematics

1.1.

Using GeoGebra to Facilitate Self-Directed Learning in Secondary Mathematics

Using GeoGebra to Facilitate Self-Directed Learning in Secondary Mathematics
– Anthony OR 柯志明

2.

Examples of GeoGebra Resources

  • 1. Area of Two Rectangles
  • 2. Exterior Angles of Polygons
  • 3. Errors in Measurement
  • 4. Area of Circles
  • 5. Volume of Spheres with Proof
  • 6. Addition of Directed Numbers - Counters Model
  • 7. Subtraction of Directed Numbers - Counters Model
  • 8. Addition of Directed Numbers - Elevator Model
  • 9. Subtraction of Directed Numbers - Elevator Model
  • 10. Quiz on Solving Right Triangles (Combined) 解直角三角形：合併測驗
  • 11. Quiz on Special Lines in Triangles 三角形內的特殊線：測驗

2.1.

Area of Two Rectangles

[size=150]Drag P so that the two red rectangles have equal area.[/size]
At what positions of P would the two rectangles have equal areas?
[size=150]Prove your assertion in the space of the applet.[/size]
– Anthony OR 柯志明, GeoGebra Institute of Hong Kong

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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3.

Exploring Congruence of Triangles

  • 1. Q1
  • 2. Q2
  • 3. Q3
  • 4. Q4
  • 5. Q5
  • 6. Q6

3.1.

Q1

– Anthony OR 柯志明

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Drawing Figures and Graphs

  • 1. Graph Plotter 2020

4.1.

Graph Plotter 2020

Instructions
[list=1][*]Click the full-screen button at the lower right corner to use this applet.[/*][*]After modifying the parameters in the control panel, click any space in the graphics view to activate it. Input the functions to plot.[/*][*]Show and edit the axis labels and text labels if necessary.[/*][*]Set the margins required.[/*][*]Save the picture as PNG or SVG formats.[/*][/list]
Version 1 (for general functions)
Examples
[code]If(-2<x<8, -0.25(x-4)^2+16)[br]If((x-3)^2-1<=20, (x-3)^2-1)[br]If(-2<x<1, x+5, 1<x<4, 6, 4<x<8, 3x-6)[/code]
Version 2 (for trigonometric functions)
Examples
[code]If(0<=x<=720, cos(x deg))[/code]
This applet is modified from [url=https://www.geogebra.org/m/mVWXRtt9]an applet[/url] made by Anthony Or of GeoGebra Institute of Hong Kong.[br][br]gMath 互動數學教室[br][url=http://www.gmath.hk]http://www.gmath.hk[/url]
– Alex CHIK

5.

Creating Simple GeoGebra Applets

  • 1. Rotation on the Coordinate Plane
  • 2. y = a sin x°

5.1.

Rotation on the Coordinate Plane

– Anthony OR 柯志明

5.2.

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Information