3-D Shapes

Est. Class Sessions: 2

Developing the Lesson

Part 1. 3-D Shape Hunt

Identify Differences Between 2-D and 3-D Shapes. Explain that two-dimensional shapes can be drawn on a flat surface. You can illustrate this by drawing examples of a triangle, a circle, a square, and a rectangle. Remind students of two-dimensional shapes they learned about in previous lessons. Point out that three-dimensional, or 3-D, shapes are not flat because they have depth, as well as length and width.

Introduce 3-D Shapes. Read and discuss the vignette and Questions 1–2 on the 3-D Shapes page in the Student Guide.

Show students examples of each of three-dimensional shapes that you have gathered for this lesson.

As you introduce each shape, ask:

What can you tell me about this three-dimensional shape? (Encourage students to note geometric properties of shapes they learned in previous lessons: number of sides, parallel sides, angles.)

Continue to do the same for each shape you introduce.

There is a great deal of variability in the ages at which children move through the van Hiele Levels of Geometric Thought. In the primary grades, students will begin at Level 0 but within the same classroom, you may have students at Levels 0–2.

During the discussion use the terms cone, cube, cylinder, rectangular prism, sphere, square pyramid, triangular pyramid, and triangular prism. As you model the use of the mathematical vocabulary, most students will readily incorporate the new words into their everyday language. However, do not expect them to memorize the geometric terms. Students can invent their own terminology or use terms they already know, such as “box” for rectangular prism and “ball” for sphere.

When introducing different types of shapes, show various examples of each. Students need to see that all pyramids and prisms are not alike. For example, a triangular pyramid can have bases other than equilateral triangles and a rectangular pyramid can have a square base, as well as a nonsquare rectangular base. See Figure 2.

Next have student pairs preview the data table and the three-dimensional shapes illustrated on the 3-D Shape Hunt page in the Student Activity Book. Have them search the classroom for examples of each shape. Offer models of these shapes as a reference during the search. Tell partners to record the objects they find in the data table and record a few examples on a display of this page. Conclude this part of the activity by having students analyze the three-dimensional objects they identified.

Pose the following questions to prompt discussion:

Which shapes were difficult to find?
Which shapes were easy to find?
Did you and your partner have difficulty deciding what 3-D shapes some objects were?

During the 3-D Shape Hunt, if a student selects a trash can or other objects with different-sized circles for a cylinder or a cone, point out that a cylinder has 2 congruent circles and a cone has a vertex or top vertex. If students are unsure if an object is a cylinder or cone, tell them to ask the following questions:

Does it have 2 congruent circles? If the answer is no, it is not a cylinder.
Does it have a vertex (top vertex)?

If the answer is no, it is not a cone. You may want to tell them that it is a truncated cone because it does not have a top vertex.

As students complete the 3-D Shape Hunt page in the Student Activity Book, observe students as they explore shapes to assess their skills in analyzing similarities and differences between three-dimensional shapes and describing their properties [E2].

Types of 3-D Shapes. A pyramid is a three-dimensional shape having a polygon for a base and triangular faces with a common vertex. See Figure 2.

A prism is a three-dimensional shape that has two faces (called the bases) that are congruent and parallel. All other faces are parallelograms. If all other faces are rectangles, the prism is called a right prism.

A cube is a special kind of rectangular prism where all edges are the same length.