Visual Geometry for Grade 9

Alfonso Garcia, Nov 11, 2020

A collection of activities to support conceptual understanding of Area in 2D and area and volume in 3D shapes.

Table of Contents

  1. Area - Parallelogram, Triangle, Trapezoid, Circle
    1. Area of Parallelogram Made Easy
    2. Area of a Triangle (Discovery)
    3. Another Look: Area of a Triangle
    4. Area of Trapezoid - Building from what we already know
    5. Meaning of π & its connection to the circumference
    6. Area of a circle from what we already know
  2. Surface Area & Volume
    1. Visual Volume: Intuitive Introduction
    2. Volume of cylinder
    3. Exploring Triangular Prism Volume
    4. Connecting volume of cylinder and cone
    5. Volume of Pyramid and Cube
    6. Connecting Volume of Prism and Pyramid
    7. Visual Surface Area: Intuitive Introduction
    8. Visual Exploration - Nets of Three Solids
    9. Surface Area - Unwrapping a Cylinder
    10. Consolidating Surface Area - Net of a Cylinder
    11. Surface Area Visually - Net of a Cone

1.

Area - Parallelogram, Triangle, Trapezoid, Circle

  • 1. Area of Parallelogram Made Easy
  • 2. Area of a Triangle (Discovery)
  • 3. Another Look: Area of a Triangle
  • 4. Area of Trapezoid - Building from what we already know
  • 5. Meaning of π & its connection to the circumference
  • 6. Area of a circle from what we already know

1.1.

Area of Parallelogram Made Easy

Directions:
In the app below, use the [b]filling[/b] slider to make the parallelogram light enough so that you can see the white gridlines through it. [b]But don't touch anything else yet! [/b][br][br]After you set the [b]filling[/b] slider, try to count the number of squares inside this parallelogram, this represents the area. Be sure to include partial squares! Provide a good estimate in the question box below.
Try to count the number of squares inside this parallelogram. How many squares (i.e. square units) do you estimate to be inside this parallelogram?
Slide the "[b]Slide Me" [/b]slider now. Carefully observe what happens. What shape do you see now?
How does the area of this new shape compare with the area of the original parallelogram? How do you know this?
How many squares do you now count in the newer shape that was formed? How many squares were in the original parallelogram?
Without looking it up on another tab in your browser, describe how we can find the area of ANY PARALLELOGRAM.
– Alfonso Garcia, Tim Brzezinski

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2.

Surface Area & Volume

  • 1. Visual Volume: Intuitive Introduction
  • 2. Volume of cylinder
  • 3. Exploring Triangular Prism Volume
  • 4. Connecting volume of cylinder and cone
  • 5. Volume of Pyramid and Cube
  • 6. Connecting Volume of Prism and Pyramid
  • 7. Visual Surface Area: Intuitive Introduction
  • 8. Visual Exploration - Nets of Three Solids
  • 9. Surface Area - Unwrapping a Cylinder
  • 10. Consolidating Surface Area - Net of a Cylinder
  • 11. Surface Area Visually - Net of a Cone

2.1.

Visual Volume: Intuitive Introduction

STUDENTS:
Interact with the applet below for a few minutes. Then answer the questions that follow. [br][br]
1.
In the applet above, create a rectangular prism that has its first layer measuring 3 units long by 4 units wide. Suppose this rectangular prism is 2 layers high. How many cubes make up this prism?
2.
In the applet above, create a rectangular prism that has its first layer measuring 5 units long by 3 units wide. How many cubes make up this prism if this prism is 2 layers high? 3 layers high? 10 layers high?
3.
How can we EASILY determine the number of cubes that fit inside ANY rectangular prism? Describe.
– Alfonso Garcia, Tim Brzezinski

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2.9.

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2.11.

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