## Polyhedra Activity.docx - Section 4: Developing Euler's Formula

# Creating and Identifying Polyhedra

Lesson 7 of 11

## Objective: SWBAT create and identify polyhedra.

*50 minutes*

#### Do Now

*10 min*

I will post two polyhedra on the board for the Do Now problem (See Polyhedra Do Now). Students will had to categorize the polyhedra and describe the characteristics that helped them categorize them.

Students will have 5 minutes for the Do Now and then we will discuss the solids as a class. I will randomly select students to share their answers.

Students should categorize the first solid as a pentagonal pyramid. The characteristics are: triangular sides, one polygon base with an opposite vertex, and a base that is a pentagon.

Students should categorize the second solid as an octagonal prism. The characteristics are: rectangular sides and two octagonal bases that are parallel to one another.

#### Resources

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#### Class Activity

*10 min*

In the previous lesson, students learned important vocabulary and the characteristics of pyramids and prisms. For this activity, students will explore these solids to help reinforce their knowledge.

Students will be paired, with a high level and low level math student together. This will promote discussion and questioning among the pairs. Each pair will use a laptop computer. I will post the Interactive 3D Shapes website on the board. Students will have 10 minutes to explore the different types of prisms and pyramids. They should focus on the characteristics of the polyhedra and their nets.

As students review the website, I will circulate throughout the pairs monitoring their focus and answering/asking questions.

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#### Creating Polyhedras

*15 min*

For this activity each student will receive a net of a polyhedron (See Nets for 3D Shapes website). Before I give students their net, I've already removed the name of their net. Students will receive the following directions:

1. Identify your polyhedron based on the net

2. Cut out the net, but only on the outside lines

3. Fold the net along the lines

4. Use tape to hold the polyhedron together

5. Write down how many edges, faces, and vertices your polyhedron has

Students will have 10 minutes to complete the steps above. It is helpful to have an example polyhedron to show students what the end result will look like.

After 10 minutes, we will reconvene as a class. Together we will complete the Polyhedra Table based on students observations. For each polyhedron, I will ask students to share how many edges, faces and vertices they counted. There are several students with each polyhedron who should be able to confirm the count.

#### Resources

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#### Developing Euler's Formula

*10 min*

As a class, we will complete the Polyhedra Activity based on students observations. For each polyhedron, I will ask students to share how many edges, faces and vertices they counted. There are several students with each polyhedron who should be able to confirm the count.

As we complete the table, students may start to notice a pattern/rule.

*Can you figure out a relationship between the number of faces, vertices and edges of 3-Dimensional Figures?*

Students may observe that if we add the number of faces and vertices and subtract 2, we will have the number of edges. This will lead to Euler's Formula.

**Euler's Formula**

F + V - 2 = E

#### Resources

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#### Exit Ticket

*5 min*

Students will complete the Nets Worksheet as an exit ticket. They will identify the polyhedron for each net. This will assess how well students understand the relationship between nets and polyhedra.

The results of the exit ticket will determine future groupings and which students need additional help with nets.

#### Resources

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- UNIT 1: First Week of School
- UNIT 2: Properties of Math
- UNIT 3: Divisibility Rules
- UNIT 4: Factors and Multiples
- UNIT 5: Introduction to Fractions
- UNIT 6: Adding and Subtracting Fractions
- UNIT 7: Multiplying and Dividing Fractions
- UNIT 8: Algorithms and Decimal Operations
- UNIT 9: Multi-Unit Summative Assessments
- UNIT 10: Rational Numbers
- UNIT 11: Equivalent Ratios
- UNIT 12: Unit Rate
- UNIT 13: Fractions, Decimals, and Percents
- UNIT 14: Algebra
- UNIT 15: Geometry

- LESSON 1: Developing the Area Formulas for Regular Polygons
- LESSON 2: Applying the Area Formulas for Regular Polygons
- LESSON 3: Area of Irregular Polygons, Method 1
- LESSON 4: Area of Irregular Polygons, Method 2
- LESSON 5: Area of Shaded Regions
- LESSON 6: Categories and Characteristics of 3D Solids
- LESSON 7: Creating and Identifying Polyhedra
- LESSON 8: Surface Area of 3D Solids
- LESSON 9: Volume of Rectangular Prism
- LESSON 10: Area of Polygons Quiz
- LESSON 11: Geometry Town Project