Sorting 3D Shapes by a Single Attribute

Solid shapes like cubes, cones, cylinders, spheres, pyramids, and rectangular prisms all look different, but they also share properties that can be measured or described. An attribute is just one property of a shape, such as how many flat faces it has, how many edges or corners it has, or whether it has a curved surface. Sorting by a single attribute means choosing just one of these properties and using it, and only it, to decide which group each shape belongs to.

This is different from describing a shape completely. When sorting by a single attribute, two shapes can look nothing alike and still belong in the same group, as long as they share that one chosen property. For example, a cone and a cylinder look different, but both have at least one curved surface, so they can be sorted together under the attribute "has a curved surface."

Before sorting, it helps to know which properties of a solid shape are easiest to compare. The most common attributes used with young learners are:

• Number of faces: a flat surface on a solid shape. A cube has 6 faces, while a cone has only 1 flat face.
• Number of edges: a line where two faces meet. A cube has 12 edges, while a sphere has none.
• Number of vertices: a corner point where edges meet. A rectangular prism has 8 vertices, while a cylinder has none.
• Curved surface or flat surface only: shapes like spheres, cones, and cylinders have at least one curved surface, while cubes, prisms, and pyramids are made only of flat faces.
• Rolls, stacks, or slides: a shape with a curved surface can roll, while a shape with flat faces can stack or slide.

One of the easiest attributes to start with is whether a shape has a curved surface. Look at the shapes below. Some are made entirely of flat faces, and some have at least one curved part.

Notice that the sphere, cone, and cylinder all landed in the same group even though they are very different sizes and shapes overall. They were sorted using only one attribute: the presence of a curved surface. This is the key idea behind sorting by a single attribute; every other difference between the shapes is ignored.

Another common attribute is the number of flat faces a shape has. This works well for solids made only of flat surfaces, like cubes, rectangular prisms, and pyramids, but it can also be used to compare curved shapes.

This example shows something important: a cube and a rectangular prism have different shapes overall, but they share the same number of faces, so they sort together. Meanwhile, a shape like a square pyramid has fewer faces and belongs in a different group, even though it is also made only of flat surfaces.

1. Choose one attribute to sort by, such as number of faces, edges, vertices, or curved surface.
2. Look at each shape and figure out the value of that attribute only, ignoring size and color.
3. Place shapes with the same value into the same group.
4. Check the finished groups by explaining the rule out loud, such as "every shape in this group has a curved surface."
5. Try sorting the same set of shapes again using a different attribute to see how the groups change.

That last step is worth practicing, since it shows that the same collection of solids can be grouped in several valid ways, depending on which single attribute is chosen. A shape does not belong to only one group forever; its group depends entirely on the attribute being used.

Suppose a set contains a sphere, a cube, a cylinder, and a rectangular prism. Sort them by whether they can roll.

A sphere rolls easily in every direction because its entire surface is curved. A cylinder can roll along its curved side but stays still when standing on a flat end. A cube and a rectangular prism cannot roll at all, since every face is flat. Sorting by the single attribute "can roll" gives two groups: the sphere and cylinder together, and the cube and rectangular prism together.

Now sort the same four shapes by number of vertices instead. The sphere and cylinder both have 0 vertices, so they stay grouped together again, but the cube has 8 vertices and the rectangular prism also has 8 vertices, so this attribute still groups the cube and prism together. Trying a third attribute, like number of faces, would separate the cube (6 faces) from a triangular prism (5 faces) if one were added to the set, showing how each attribute creates its own grouping.

Sorting by a single attribute builds the foundation for describing shapes precisely and for comparing shapes later on. It is closely related to sorting 2D shapes by a single attribute, except that solid shapes add depth and can have curved surfaces, extra faces, and more edges and vertices to consider. Once shapes can be reliably sorted and described by their properties, that same understanding of faces and vertices becomes useful when composing 3D shapes out of smaller solids.

Related lessons

• Math 1