Intro: Dodecahedron Platonic Solid | | : United States 4th

Intro: Dodecahedron Platonic Solid

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United States 4th

Discover the dodecahedron, 1 of the 5 Platonic solids that have intrigued mathematicians, architects, and philosophers for thousands of years. Build this 3D model with 12 pentagonal faces, and find out about real-life examples and uses of this shape in history.

Cover image

Overview and Objectives

05:00

Facilitators set the groundwork for students to understand the purpose and components of the project with a well-defined set of learning objectives. By delving into the lesson's fundamentals, students gain the confidence and insight to craft their unique renditions of the project.

Assign this lesson as a student resource. Have students read and watch the video.

This section prepares students to engage the lesson. Throughout the teaching of this entire lesson, the facilitator provides an opportunity for students to collaborate with each other and provide feedback on their individual or group project.

Preparation

30:00

Equip students for before starting the lesson by familiarizing them with frequently used vocabulary words, enhancing their writing skills, and engaging in constructive building exercises.

Get familiar with the Platonic Solids guide and vocabulary. Assign this lesson as student resources. Have students read the list and watch the video.

Imagine

10:00

Learn about the dodecahedron, the only Platonic solid with pentagons.

Imagine section is a critical phase where students are encouraged to conceptualize, and visualize their ideas before diving into the building and prototyping stage in Build section. Pause to have a short group reflection.

Common Core Mathematics

For CCSS.MATH.CONTENT.4.G.A.2 introduce the tetrahedron, a 3D shape composed of four equilateral triangles. Challenge your students to classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines and angles of specific sizes. Make sure they can recognize right triangles as a category. Keep an eye out for these properties as you explore the tetrahedron together.

Platonic Solids List (bold is the featured shape in this lesson):

  • Tetrahedron: A tetrahedron is a three-dimensional geometric shape with four faces, and each face is an equilateral triangle. It has four vertices and six edges.
  • Hexahedron (Cube): The hexahedron, often referred to as a cube, is characterized by having six square faces. It has eight vertices and twelve edges.
  • Octahedron: An octahedron is a polyhedron with eight faces, and each face is an equilateral triangle. It has six vertices and twelve edges.
  • Dodecahedron: The dodecahedron has twelve regular pentagonal faces. It features twenty vertices and thirty edges.
  • Icosahedron: An icosahedron is a three-dimensional shape composed of twenty equilateral triangle faces. It has twelve vertices and thirty edges.

Florida - NGSSS

For MA.4.GR.1.1 - MATHEMATICS (B.E.S.T.) draw, classify, and measure angles using the tetrahedron as an example for geometric reasoning. Although the tetrahedron primarily consists of triangles, we can still explore angles within its faces. Discuss how angles are an attribute of two-dimensional figures and relate this to the triangular faces of the tetrahedron. Are there any acute, right, obtuse, straight, or reflex angles within these triangles?

Platonic Solids List (bold is the featured shape in this lesson):

  • Tetrahedron: A tetrahedron is a three-dimensional geometric shape with four faces, and each face is an equilateral triangle. It has four vertices and six edges.
  • Hexahedron (Cube): The hexahedron, often referred to as a cube, is characterized by having six square faces. It has eight vertices and twelve edges.
  • Octahedron: An octahedron is a polyhedron with eight faces, and each face is an equilateral triangle. It has six vertices and twelve edges.
  • Dodecahedron: The dodecahedron has twelve regular pentagonal faces. It features twenty vertices and thirty edges.
  • Icosahedron: An icosahedron is a three-dimensional shape composed of twenty equilateral triangle faces. It has twelve vertices and thirty edges.

Build

15:00

Build a symmetrical dodecahedron, a Platonic solid with 12 faces.

Watch the video to get an idea of the project's structure and a demonstration of how it works. Some may figure out how to construct the project just from pausing the video or looking at a few images from the steps. The instructions are helpful for new builders or those seeking general guidance.

Florida - NGSSS

For SC.35.CS-CS.1.2 - COMPUTER SCIENCE introduce students to the concept of computational thinking, emphasizing problem decomposition, and the importance of breaking complex problems into smaller parts. Explain how this will be applied to building the animal. They can create fins, ears, increasing body size, claws, etc. for iterating on its adaptation. And for SC.35.CS-CC.1.3 - COMPUTER SCIENCE direct students to test how their animals would live by crafting the biome and their habitat.

NGSS

For 3-5-ETS1-1 - ENGINEERING DESIGN, students will consider constraints, such as the materials they have available, the time they have to complete the project, and any limitations when starting to build. For 3-5-ETS1-2 - ENGINEERING DESIGN, students understand how to design and build functional prototypes, as well as how to evaluate and refine their design through testing. And for 3-5-ETS1-3 - ENGINEERING DESIGN students engaged in this learning experience helps students understand how to design and build functional prototypes, as well as how to evaluate and refine their design through testing.

Common Core Mathematics

CCSS.Math.Content.4.G.A.2

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Fourth graders can harness the power of STEAM to delve into the nuances of two-dimensional figures. Through hands-on manipulatives or digital platforms, learners can physically or virtually manipulate figures to discern properties related to parallelism, perpendicularity, and angle size. The dynamic interaction with these concepts fosters a deeper, experiential comprehension of classification.

ISTE Students

1.6.c Creative Communicator

Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models or simulations.

Introduce students to a variety of digital tools and media that can enhance their communication. This could include graphic design software, multimedia creation tools, video editing software, or presentation platforms. Help students choose the appropriate tools based on their communication goals and the requirements of their project.

Florida - NGSSS

MA.4.GR.1.1

Informally explore angles as an attribute of two-dimensional figures. Identify and classify angles as acute, right, obtuse, straight or reflex.

Fabricate hands-on models representing different angles. By physically adjusting and measuring these angles, intuitively understand classifications such as acute, right, obtuse, straight, or reflex.

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