CCSS Gr. 6 Nets and Surface Area

Jack D. Gittinger, Nov 22, 2015

[color=#c51414][i][b]Common Core Standards for Grade 6-Geometry[/b][/i][/color] [b]Solve real-world and mathematical problems involving area, surface area, and volume.[/b] 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. [b]Apply and extend previous understandings of numbers to the system of rational numbers.[/b] Extend coordinate axes familiar from previous grades to represent points on the plane with negative number coordinates.[list] [*]Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. [*]Find and position pairs of integers and other rational numbers on a coordinate plane. [/list]


  • 1. FINDING THE SURFACE AREA OF 3-D SHAPES:  THE CUBE 
  • 2. FINDING THE SURFACE AREA OF 3-D SHAPES:  THE PYRAMID
  • 3. FINDING THE SURFACE AREA OF THE CYLINDER

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FINDING THE SURFACE AREA OF 3-D SHAPES:  THE CUBE 

Instructions
[center][/center][b]Introduction[/b][b] [br][br][/b]Finding the total area of the surface of a 3-D shape like a cube can be very useful.  It can answer questions like, “How much paint do I need to cover the surface?” or “How much wrapping paper do I need to wrap this container?” [br][br]There are formulas that you can memorize and use when needed. However, it is easy to forget a formula that you only use once in a great while. Is there another way to solve a surface area problem without memorizing the formula?  In this [i]GeoGebra [/i]lab you will explore another method for finding surface area. [br][br][b]Step 1.  Create and Experiment a Net[br][br][/b]Use the MOVE tool to use the red slider to set the length of an edge on the cube to 3 units.  Now base, width, and height of the cube are all 3 units. Now [i][u]slowly [/u][/i]use the blue slider to create a [b][i]net[/i][/b] of the cube.  A net is created by imagining that you cut and unfold the 3-D shape into one, flat shape. [br][br]Using the slider, the net can be folded back into the original 3-D shape.   [br][br][b]Step 2.  Find the Surface Area[/b] [br][br]Move the blue slider all the way to the right to completely unfold the cube and display the net. The net for a cube is a connected set of what 2-D polygon? ___________________________ [br][br]You already know the method for calculating the area of a square.  Use that method for finding the surface area of the entire cube.  Explain your solution:   [br][br][br]Once you have computed the surface area of this cube, click on the [i]Check Surface Area Solution[/i] check-box to see the surface area as computed by [i]GeoGebra[/i]. [br][br][b]Step 3.  Practice[/b] [br][br]Turn off the Check Surface Area Solution check-box. Make or print the table shown below. Use the red slider to create three cubes with sides of differing lengths.  Use the net to help you calculate the surface area of each new cube.  Use the [i]Check Surface Area Solution[/i] check-box to check your solutions. [br][br][b]Conclusion[/b] [br][br]For a cube, the“official” formula is: [b]surface area = 6 X side[sup]2[/sup][br][br][/b]But if you forget the formula, you can always use reasoning and a net to help you compute the[br]surface area.
– Jack D. Gittinger

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