Intro: Tetrahedron Platonic Solid | | : United States 3rd

Intro: Tetrahedron Platonic Solid

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United States 3rd

Discover the tetrahedron, 1 of the 5 Platonic solids that have intrigued mathematicians, architects, and philosophers for thousands of years. This three-dimensional shape is formed by only 4 equilateral triangles. Learn to build this basic 3D shape as a starting point for many more future projects.

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 properties of the tetrahedron as one of the Platonic solids.

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.3.G.A.1 introduce the icosahedron, characterized by having 20 equilateral triangle faces. Help them understand that shapes from different categories may share certain attributes. For example, the square has four sides, making it a quadrilateral. Encourage your students to recognize rhombuses, rectangles, and squares as examples of quadrilaterals and have them draw examples of quadrilaterals that don't belong to these subcategories.

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.3.GR.1.2 - MATHEMATICS (B.E.S.T.) describe relationships between lines and classify quadrilaterals. Start by introducing your students to the featured platonic solid. Some of these geomeAlthough it's not a quadrilateral itself, it's a great visual aid. Discuss the relationships between lines within the tetrahedron. For instance, how many lines of symmetry does it have? Then, relate this to quadrilaterals like parallelograms, rhombi, rectangles, squares, and trapezoids.

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 tetrahedron with 4 triangular 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.3.G.A.1

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Third graders, through STEAM, can delve deeper into categorizing shapes, utilizing tools or materials that exemplify shared attributes. This could be achieved through constructing shape families or using technological tools that display the interconnectedness of shapes, enabling a vivid understanding of how smaller categories fit into larger geometric hierarchies.

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.3.GR.1.2

Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.

Through tactile activities, mold and assemble various drawn quadrilaterals. Utilize flexible construction pieces to create and compare shapes like parallelograms, rhombi, rectangles, squares, and trapezoids, discovering their unique properties.

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