UNIT 3: Area, Surface Area and Volume
Area, Surface Area and Volume[color=#198f88][/color]
Table of Contents
- Area
- Activity 1a: Area of a Parallelogram
- Activity 1b. Parallelograms with Given Area: Quick Formative Assessment
- Activity 2a: Area of a Triangle (Discovery)
- Activity 2b: Create a Triangle with Given Area (Quick Formative Assessment)
- Activity 3a: Trapezoid Area
- Activity 3b: Create a Trapezoid with Given Area (Quick Formative Assessment)
- Circles (Circumference and Area)
- Activity 4a: Circumference (Animation)
- Activity 4b: Circumference = (Animation II)
- Activity 5: Circle Area (by Peeling)
- Nets of 3-dimensional figures
- Investigating NETS
- Surface Area of Rectangular Prisms
- Activity 7a: Surface Area: Introductory Exercises
- Activity 7b: Creating Rectangular Prisms with Given Surface Area
- Maximizing Surface Area: Open Middle Cube Problem (V1)
- Volume of Rectangular Prisms
- Activity 9: Volume (Intuitive Introduction)
Activity 1a: Area of a Parallelogram
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. [br]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.
Activity 4a: Circumference (Animation)
[b][color=#1551b5]Let's try to find the circumference of a circle by wrapping diameters around it.[/color][/b][br][br][b][color=#c51414]Hit the "Start Animation!" button below and carefully observe what happens.[/color][/b][br][i][color=#0a971e](Be sure to answer the 2 questions that follow.)[/color][/i]
Investigating NETS
In your Maths workbook
1. Take out [i][b]Investigating Nets[/b][/i] worksheet.[br][br]2. Explore the below interactive activities and complete the worksheet.[br][br]3. Draw each 3D object and ONE 2D net on your sheet. Ensure you label the 3D object clearly and accurately. Use as full page for the 2 diagrams for each object. [i] (Note: you MUST use a ruler and protractor - as appropriate)[br][br][/i]4. Using a colour-coded key, highlight the faces, edges, and vertices on your drawings.
Activity 1: Net of a CUBE
Need a quick refresher? Visit Hotmaths!
[url=https://www.hotmaths.com.au/lessonSection/lesson.action?loc=d9wxrB15J3RhwfmyzHRh2g%3D%3D&hash=#/resources/31393/]Hotmaths - 3D Objects Nets & Models[br][/url]
Activity 2: Create your own nets for a CUBE
Important Note:
Take a screenshot of your 11 different 2D nets of a cube from the above activity and SAVE into your own Maths folder on the school network. [br][color=#ff0000][b]Print the screenshot and glue into your workbook.[/b][/color]
Activity 3: Net of a RECTANGULAR PRISM
Activity 4: Net of a TRIANGULAR PRISM
Activity 5: Net of a SQUARE BASED PYRAMID
Activity 6: Net of a CYLINDER
Activity 7 - Net of a CONE
EXTENSION 1: Net of a HEXAGONAL PRISM
EXTENSION 2: Net of a DODECAHEDRON
Investigating Nets
Activity 7a: Surface Area: Introductory Exercises
Take a few minutes to interact with the rectangular prism shown here. After doing so, create one that has a length = 4 units, width = 5 units, and height = 3 units.
How many square units (i.e. "squares") appear on 1 [b][color=#ff00ff]pink face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b][color=#bf9000]gold face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b]white face[/b]?
Use your answers for (1) to determine the TOTAL SURFACE AREA of this rectangular prism. [br]That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism?
Now create a rectangular prism that has a length = 8 units, width = 3 units, and height = 5 units.
How many square units (i.e. "squares") appear on 1 [b][color=#ff00ff]pink face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b][color=#bf9000]gold face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b]white face[/b]?
Use your answers for (3) to determine the TOTAL SURFACE AREA of this rectangular prism. [br]That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism?
Overall, how we can determine the total surface area (number of squares) that cover the entire surface of a rectangular prism? Describe.
Activity 9: Volume (Intuitive Introduction)
STUDENTS:
Interact with the applet below for a few minutes. Then answer the questions that follow. [br][br][b][color=#1e84cc]To explore this resource in Augmented Reality, see the directions beneath the questions listed below. [/color][/b]
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.
TO EXPLORE IN AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device. [br][br]2) Go to the[b] MENU (horizontal bars)[/b] in the upper left corner. Select [b]OPEN[/b]. [br] In the Search GeoGebra Resources input box, type [b]dp6ghmvv[/b][br] (Note this is the resource ID = last 8 digits of the URL for this resource.)[br][br]3) In the resource that uploads, zoom out and/or adjust the [br] LENGTH, WIDTH, & HEIGHT sliders to create a prism with dimensions you like. [br][br] Press the [b]AR[/b] button in the lower right corner of your 3D screen. Follow the directions that appear.