Name: ___________________________

 

Activity 1
Exploring Cubes

 
1. Where have you seen objects like these before?
What do you call them?
What are some objects like these that you have seen in your home, school, and community?

Here are a square prism and a rectangular prism.
Are these cubes? Why or why not?

2. Create your own skeletal models of a cube using toothpicks and mini marshmallows. Compare your model with others in your group. Ask these questions:
How many toothpicks did you use?

How many marshmallows did you use?

Are there any parallel lines? Perpendicular lines? Skew lines? Explain.



Are there any parallel planes? Perpendicular planes? Explain.

Discuss and record the different properties each member of the group observes.

3. One way to sketch a cube is to draw two squares as shown below and then to connect the corresponding vertices of the squares. (An alternative approach is to sketch cubes by using isometric dot paper as shown.)

Make a sketch of your cube in the space below and label the vertices with different capital letters. Using your diagram -

name a pair of parallel lines;
name a pair of perpendicular lines;
name a pair of skew lines;
name a square;
determine how many squares are needed to form a cube;
name a right angle;
name a face diagonal;
name a diagonal of the cube.

Is it possible to name a rectangle in your diagram that is not a square? Explain.

 

 

4. Here are some pictures of number cubes. 

Which of the pictures above could be a view of a number cube that is made by folding a pattern like this?

This flattened-out pattern of a cube is called a "network" of a cube.
How many squares are needed to form the network of a cube?


5. A flat pattern (or network) made up of five squares where each square must share an edge with another square is called a pentomino. Here are some examples of pentominoes:

On pieces of square grid or dot paper, each member of the group should sketch some pentominoes.

How many different pentominoes are there?

How many of these pentominoes can be folded to form an open box?

6. Models of buildings are frequently created using cubes, and then front, side, and top views of the model are drawn.

For example:

Can you make out of cubes a "building" that has these top, front, and side views? Sketch your result.

Sometimes the "floor plan" can be recorded by showing the number of cubes needed in each part.

For example:

Does this "floor plan" match your "building"?




7. Challenge: How many cubes were needed to build the design in this figure? Explain several different ways of solving this problem.