Polygons and Polyhedra

May 22, 2014 | by Albert J. and B. Michael

Primary Market

Education, Secondary Ed

Character Focus

Communication, Cooperation, Teamwork

Items Needed

1 Toobeez set, 1 piece of chart paper per group, graph paper, pen or pencil

The Activity Time

1 hour

- Introduce students to 2-D and 3-D geometric figures
- Define polygons and polyhedra
- Learn nomenclature associated with 2-D and 3-D geometric figures
- Observe and identify features characteristic of various geometric shapes
- Work cooperatively with others in a teambuilding style

Character Focus

Teamwork/Cooperation & Communication

The Challenge

Students should be able to identify and name various polygons and polyhedra.

Preparation

**Setup Time: **5 minutes

**Mini-Lesson Time: **15 – 20 minutes

**Materials**

- 1 Toobeez set
- 1 piece of chart paper per group
- graph paper
- pen or pencil

Activity Plan

**Time:** 1 hour

**Instruction:** Whole class and Individual

**Space:** Medium

1. Teachers should build a 2-D triangle and a cube from Toobeez tubes (as pictured).

1. Ask students to evaluate the two shapes and record observations in their notebooks. Lead a discussion which allows students to share their observations about the two figures. Teacher Note: The crucial observation points are as follows:

- One figure is 2-D and the other is 3-D
- None of the lines in either figure intersect

2. After the discussion in Step 1, the teacher should identify the triangle as a polygon and the cube as a polyhedron. Based upon the discussion, the teacher should guide the class in a discussion to define the polygon and polyhedron. Any definitions that encompass the following concepts are acceptable:

- Polygon: A 2-D figure made up of a closed chain of points linked together by non-intersecting straight lines
- Polyhedron: A 3-D figure made up of a closed chain of points linked by non-intersecting straight lines

3. Remove one of the Toobeez tubes from the triangle models. Ask the class, “Is this a polygon?” Follow up with, “If it is not, explain why?” and “What quality does the polygon have that distinguishes it from a polyhedron?”

4. After establishing the definitions, remove one tube from the cube model constructed in the setup. Ask the class: “Is this a polyhedron?” Follow up with: “If it is not, explain why?” and “Does removal of the one Toobeez tube convert it into a polygon? If not, why?”

5. Have students record their conclusions and observations from this discussion in their notebooks.

6. Teachers should inform students that different types of polygons and polyhedra have different names.

7. Students should brainstorm in preparation for the activity to identify what qualities would best serve in classifying these two types of geometric figures.

**Helpful Hints**

- Be sure to review these tips prior to beginning the activity, and if necessary, share reminders with the group during the activity.

- Teachers should often remind students of the two definitions established during the “Activity Setup” discussion
- The teacher should emphasize the differences between the two classes of geometric shapes
- Have students share their results for the potential parameters for classification from the discussion in the “Activity Setup.”
**Teacher Note:**Try to guide students in a discussion to eliminate incorrect hypotheses and to include any missed classification parameters

*Here are available Training Options!*

**1. Divide the students into groups.
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**2. Read aloud the following Activity Challenge Box to the group.
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**Challenge**: Students should be able to identify and name various polygons and polyhedra.

**3. If accurate classification parameters for polygon and polyhedron were not arrived at through the setup discussion, the following parameters should be introduced:
**

- Polygons are classified and named by the number of sides
- Polyhedra are classified and named by the number of faces

**Teacher Note:** To eliminate any confusion, review other classification parameters suggested by students and have the class discuss them.

**4. After the parameters for classification and naming are established, the following table should be posted on the chalkboard for students to record:
**

**Teacher Note:** Point out the Greek origin of these prefixes.

**5. After allowing students to review the chart in Step 4, point out that the number of sides in a polygon and the number of faces in a polyhedron the appropriate prefix is used in naming the figure.
**

**6. Next, guide the students in the general rules for naming polygons and polyhedra.**

- Polygon – Use the appropriate prefix for the number of sides and add “–gon” to the end (for example, eight-sided polygon = octagon)
- Polyhedron – Use Use the appropriate prefix for the number of faces and add “–hedron” to the end (for example, four-faced polyhedron = tertrahedron)

**Teacher Note:** Be sure to point out some exceptions to this rule such as triangle and cube.

**7. Using Toobeez, have each team build any random polygons, name them and record any additional observations about their polygons.
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**8.** **Have each group present their results to the class. Using their models, groups should explain their reasoning for naming the polygon.
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**9. Have the students break into their groups again and build various random polyhedra with Toobeez. Groups should then name the models and record any additional observations.
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**10. Have each group present their results to the class. Using their models, groups should explain their reasoning for naming the polyhedron.
**

**11. After the activity, gather the class together and pose the following questions for discussion: “What are the differences between polygons and polyhedra? How is this difference reflected in the naming strategies for the two types of geometric figures?”
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**12. Finally, move to the “Activity Discussion and Processing” section of the activity.**

- On graph paper, have students draw various polygons, assign them names, and explain the name assignment
- On graph paper, have students draw various polyhedra, assign them names, and explain the name assignment

To close the lesson, end with a group discussion about what was learned during the activity. Circle up the group and work through the following questions. If possible, record the group’s responses on flip chart paper so all comments are displayed.

- What is the difference between the standard rules for naming polygons and polyhedra?
- Why is a foreign language used as the basis for naming polygons and polyhedra?
- Why is it important to have a systematic method for naming various geometrical figures?
- How are polygons and polyhedra useful in real world scenarios?
- What important aspect of communication does the naming system for polygons and polyhedra demonstrate?

Here are some additional topics for discussion:

- The difference between polygons and polyhedra
- The parameters for naming and classifying polygons and polyhedra
- The Greek-based system utilized in naming these figures
- The team effort used in building and naming geometric models

**1. A spatial analysis.
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Have students measure the various dimensions of their Toobeez polygons and polyhedra. Have them calculate the area of the polygons and the volume for the polyhedra. Provide them with a listing of the appropriate equations. Ask them to explore why it is impossible to provide a volume for polygons. Also have them calculate the area of each face of a polygon (a cube is the easiest) and then calculate the sum of these areas. Explore why this sum is not equivalent to the calculated volume.

**2. Extension/Follow up.
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For homework, assign students various polygons to draw on graph paper. Instruct them to measure and record both side length and degrees of angles. Have them record any observations from their results. **Teacher Note:** Require students to draw four examples of each type of polygon assigned so that any mathematical qualities can be observed.