# The Shape of Space: Nets

## Shape in 3 Dimensions

In the beginning, children view solids (three-dimensional shapes-3D) as entities instead of seeing the parts of the solid as a collection of related shapes. By manipulating solids and being asked to think about them, children learn that the faces (the sides, top and bottom) are composed of two dimensional shapes including rectangles, circles or triangles. They also learn that the size and shape of each face are dependent upon the size and shape of the other faces. There are a number of ways to find out how children think about shape. Two of the best ways are to draw and build shapes.

The homework activities are designed to assist you in finding out about how your child thinks about three-dimensional shapes. Making shapes is one way to learn how children think about solids and develop spatial reasoning. Cereal boxes can be used for this purpose. In order to make the manufacturing process of the cereal box more efficient, the surface of the box has been stamped out in the form of a net. A net is an arrangement of two-dimensional shapes that can be folded up and connected to create 3-D shapes. The child in the photograph has taken two cereal boxes apart.

Notice that he has taken these boxes apart in different ways. Each way has resulted in a different 2-D configuration even though the two flattened boxes would make the same 3-D shape. Do you think that your child knows that there is more than one way to form a net for a box? You can try the homework and see!

The development of children's ideas about nets and their uses of nets as ways to understand a three dimensional figure varies from child to child. However, the following kinds of milestones are usually attained:

1.) Children learn to represent the shape of the different faces of the 3-D shape.

For example, a cube has 6 faces.

2. ) Children learn to visualize how the shapes of the net will fold together to form the faces of the 3-D figure.

This generally requires a lot of exploration, for which we use tools like paper and polydrons.
Polydrons are pieces of molded plastic that snap together to form 3-D shapes.
We have included some in our mathematics backpacks.

3. ) Children learn to form more than one net of the same shape.

This requires many opportunities to draw nets and to use paper or polydrons to construct 3-D figures.

4. ) Although children typically begin with fairly simple shapes, some eventually progress to modeling more complex shapes with nets, like houses or other buildings.

Child's Name____________________________ Teacher______________________________

Please choose one of the following activities for homework.
Please use the back to write on if there is not enough room on the front.
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Activity 1.) Comparing Solids

Keep empty cereal boxes and other kinds of containers (cylinders like those used for oatmeal or coffee are very nice too).
Line up your collection of solids and have your child describe which of them are most alike and why.
Ask your child to describe the number of faces and the shape of each face for each container.
What did your child say was the same?

Activity 2.) Depicting Solids

Have your child choose one box and one cylinder and have them draw the solid on paper.
How does s/he depict the different faces of the solid?
Does s/he use any perspective to represent three-dimensionality?

Activity 3.) Taking Solids Apart

Have your child cut apart a cereal box - try to cut only along the edges (the "corner" lines connecting 2 sides).
What are the shapes that form the faces of the solid? How are these different faces related - either in size or shape? When the box is flattened out can your child identify the front, back, sides, top and bottom of the box?

Activity 4.) Creating Solids