Sorting 3-D Shapes

Est. Class Sessions: 2–3

Developing the Lesson

Part 1. Analyzing Properties of 3-D Shapes

Build a Shape Finder Chart. Display a set of Power Solids® so the set is visible to the class. Students should be ready to write down the possible 3-D shapes that fit a particular property.

Display the Shape Finder chart you prepared and explain:

I will name a property of a shape. A property is an attribute or characteristic of a shape that helps you identify it. For example, I might say, “Find a shape with six faces” or “Find a shape with a right angle.” Find a shape that has that property. Is there more than one answer?

Have students read the Shape Finder Chart section on the Sorting 3-D Shapes pages in the Student Guide.

Say:

Look at the properties listed in Question 1. Find as many shapes as you can that have the properties listed on this page and write down the names of the 3-D shapes on your scratch paper. There may be more than one answer for each property. Be ready to show or tell how you made your choice.

Have students work in pairs to find at least one shape that has each property and prepare explanations for their choices. Use Figure 2 to check students' responses.

For each property, have students demonstrate how they decided which shapes have that property and tape the pictures of the shapes under the “Possible Shapes” column on the Shape Finder chart. Use the shapes from the five sets of the 3-D Shape Sort Cards Master you prepared. The table in Figure 2 provides a list of properties, examples of shapes, and possible explanations for identifying each property. It lists some properties to use on the Shape Finder chart, but you may want to come up with other properties that are not listed.

The Shape Finder chart will compile a record of the properties and corresponding shapes that students can use in the Guess My Shape game. See Figure 3 for the beginning of a sample chart.

It is not necessary for the class to find every shape that has a given property. However, continue the discussion long enough to find different shapes with the same property.

Play Guess My Shape. Keep the 2 sets of Power Solids® on display and the Shape Finder chart posted so students can refer to them to play Guess My Shape. Model how to play the game by engaging the whole class in a group game using the display set of the Large 3-D Shapes Master. Select a shape and keep the shape a secret. Students take turns asking “yes” or “no” questions using properties and characteristics of the shape (e.g., number of vertices). They are not allowed to point to a shape and ask, “Is this the shape?” Rather, they should continue to ask questions about the shape's properties until the choices are reduced to one shape. Students can jot down and change their predictions of the solution on paper as properties are affirmed until the shape is revealed. You may want to limit the number of “yes” or “no” questions students can ask or keep a record of how many questions they ask before they guess the shape. Sample Dialog 1 is an example of a class discussion about a triangular prism.

Use this Sample Dialog to model how to play Guess My Shape using a triangular prism.

Teacher: Today we are going to play the game Guess My Shape. I will select a shape from the 3-D Shape Sort Cards and I will keep it a secret. You will have to guess my secret shape by asking me questions about the properties of the shapes. Use the Shape Finder chart to help you think of properties of the shapes. I can only answer your questions by saying “yes” or “no.” After I answer “yes” or “no,” you have to explain which shapes fit that property. I will keep a tally of how many questions the class asks before you guess the secret shape. One rule for this game is that you are not allowed to point to a shape and ask if that is the secret shape until we have narrowed it down to one shape.

Brenda: Does your shape have any triangle faces?

Teacher: Yes. Which shapes fit that property?

Brenda: If I look at the Shape Finder chart, I can see that the shape can be a hexagonal pyramid, square pyramid, triangular prism, or a triangular pyramid.

Teacher: Great answer! Who else has a question?

Javier: Is the shape a triangular prism?

Teacher: The rule is that you are not allowed to ask if the secret shape is a particular shape until we have narrowed it down to one shape, and we have 4 possible shapes left.

Javier: Does it have any right angles?

Teacher: No. Can you eliminate any shapes?

Javier: I can eliminate the hexagonal pyramid and the triangular pyramid because they do not have right angles.

Teacher: If we eliminated 2 shapes, does anyone have a question about which shape you think it is?

Ashley: Does it have a set of parallel faces?

Teacher: Yes.

Ashley: So that eliminates the square pyramid. Is it a triangular prism?

Teacher: Yes! Great job! Now play the game with your partner.

Have student pairs or small groups play the game using two sets of 3-D Shape Sort Cards. One set of cards is stacked face down on the playing surface and the other set is used as a reference for members of the group. Students take turns being the leader until each has had a turn. The leader looks at the top card from the face-down pile keeping the shape a secret from the other members of the group. The other students follow the “yes” or “no” questions procedure until the shape is guessed and the leader reveals the hidden shape.

Conduct a class discussion in which students tell how they determined their solution for each hidden shape. Encourage students to explain all the possibilities they were considering and how they eliminated some before making a final choice.

Mystery Sort. Begin this part of the lesson by giving student pairs time to explore how they can sort the shapes on the 3-D Shape Sort Cards page in the Student Activity Book into two groups.

Say:

Work with your partner to sort the 3-D Shapes Sort Cards into two groups based on properties. The first group will have 3-D shapes that have a particular property and the other group will have the shapes that do not fit in the first group. Think about the properties of the 3-D shapes that we discussed for the Shape Finder chart.

Give pairs about ten minutes to sort their shape cards. As students work, talk with them about their sorts. How they choose to sort the shapes is up to students at this point. However, it is important that they are able to give reasons for the sort based on the properties of the 3-D shapes.

Next, use the display of 3-D Shape Sort Cards or the Large 3-D Shapes Masters (for a larger display) to do a “mystery sort” and engage the whole class in a discussion of how you sorted shapes into two groups. For example, you can sort the 3-D shapes into “cylinders” and “not cylinders.” See Figure 4.

Cylinders have two parallel and congruent faces with parallel lines that join the faces. Using this definition, cylinders, cubes, hexagonal prisms, rectangular prisms, square prisms, and triangular prisms fit into the category “cylinders.”

A circular cylinder has two faces that are circles. Prisms are also cylinders, but the two faces are polygons. All prisms are cylinders but not all cylinders are prisms, because prisms have polygons for faces.

Ask:

I sorted the shapes into 2 groups. I want you to guess how I sorted them. How are the shapes in the first group alike? (Possible responses: All the shapes in the first group have faces that are parallel and that are the same size and shape. The shapes in the second group do not have parallel faces.)
How can we label the two groups? (Possible response: I would label them “Parallel Faces” and “Not Parallel Faces.”) Accept any answer that is correct. At this point, you may decide to say that you sorted them into cylinders and not-cylinders and explain that cylinders have two parallel and congruent faces with parallel lines joining those faces.

Give students time to play Mystery Sort in pairs. Directions and 3-D Shape Sort Cards are in the Student Activity Book. Using the 3-D Shape Sort Cards, the first partner sorts the shapes into 2 groups and the other partner tries to figure out how the first partner sorted them.

Observe students as they play Mystery Sort: 3-D Shapes to assess their ability to describe and analyze 3-dimensional shapes [E2]; classify three-dimensional shapes using their properties [E4]; and to justify their sorts using the geometric properties of the three-dimensional shapes [E7].

For targeted practice, students can play Mystery Sort: 3-D Shapes in the Student Activity Book or you can place prepared copies of the 3-D Shape Sort Cards Master and the Mystery Sort: 3-D Shapes Master in a learning center so students can continue to practice sorting shapes according to their properties.