Sunday, August 17, 2014

Nets of 3D Shapes Part 1- Cubes: More practice with Procedures using Pro-Bot

This programming assignment is intended to provide more practice with Procedures using Pro-Bot. We shall use a Procedure to store the program for a square. We shall then write programs for Pro-Bot to draw nets of a 3-Dimensional object, a cube in this case, using the Procedure. 

Computer Science concepts involved:   Sequential programming, Repeat loops, Nested Loops, Procedures

Math concepts involved:   Cubes; Nets of 3D objects: visualizing cubes on a 2D plane, identifying multiple nets per cube, properties of nets of a cube; Squares, Measurement, Angles

Material required:  Card paper/thin cardboard to draw the nets on

Extension activity:   Make the cube by cutting out the net from the card paper and folding along the edges 

Grade levels:   3, 4

Hours required:   2 (or more)

Nets of 3-Dimensional Figures

A 3-Dimensional (3D) shape is a shape that has length, width and depth. They are also called solid figures or solid shapes. The length, width and depth are the three dimensions. Most of the objects that we see around us are 3-Dimensional. For example: your books, school bag, a box of crayons, Pro-Bot, table, chairs, water bottle, soccer ball, even yourselves are all 3D shapes.

How do these shapes differ from 2-Dimensional (2D)  figures, like the ones that you draw on paper? Think about how a cube or a sphere differs from a square or a circle drawn on paper. Well, the difference is that they have depth, unlike the 2D figures drawn on paper, which have only length and width. 3D shapes do not lie flat on a plane surface and they are difficult to draw on a piece of paper. 

But what if we could open up the 3D shapes and lay them out flat on paper? This would show us exactly how these solid shapes are made. A net can help us convert a 3D shape to a 2D figure. Nets are the flattened shapes of 3D objects. The net shows every edge and every face of the 3D figures laid out flat on paper. The net has only length and width; it does not have depth. It makes it easier for us to study and analyze some of the properties of a 3D object. You can cut out the net from the paper and fold it along the edges to create the 3D object. The same 3D object may be flattened into more than one net.

Let’s look at a very common 3D shape, a cube, and draw its nets. We shall use Pro-Bot to draw the nets on thin cardboard. You can then cut out the nets and fold them to create the 3D object.

Nets for a Cube

Have you seen the dice that you use for board games? It has the shape of a cube. A cube is one of the most common 3D figures, with 6 square faces, 12 edges and 8 vertices. 

What would the cube look like if you cut it open along some of its edges and laid it out flat on a piece of paper, so that you can see every face and every edge? The flattened version of the cube would be its net. There can be more than one net for a given 3D shape. Can you guess how many nets exist for a cube?

In the figure below are a couple of nets for a cube of sides 6 cm each. 

You can see from the figure that each net is made up of multiple squares; each square representing a face of the cube. All the squares are similar, with edges measuring 6 cm each. If you fold the above nets along the edges/lines drawn in the figure, you would end up with a cube.

Programming Assignment

  1. Write a program to draw a 6 cm side square. Remember to use Repeat Loops in your program for the square. Store your program as a Procedure.   (Since the same square is used multiple times in each net, it would be easier for you as the programmer, to write the program for the square just once, store it in a Procedure and then call that Procedure from your main program whenever you need it.) 
  2. Write the programs for Pro-Bot to draw the nets for the cube as given in the figure above. Use the Procedure for the square that you previously wrote while writing the programs.
  3. There are 11 possible nets for a cube, two of which are given above. Can you identify the other 9 nets for the cube as well? 
  4. Write a program for Pro-Bot to draw each net that you identify, using the Procedure for the square in your program.
  5. Once you are done drawing each net using Pro-Bot, cut out the nets from the paper. Fold the paper along the lines drawn and create a cube from each net.You could even draw the numbers/dots on the six squares as seen on a pair of dice. 
  6. List the properties that seem to be common for the various nets that you came up with.
  7. Compare the area and perimeter of the different nets. 

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