Intro: Octahedron Platonic Solid | | : United States 5th

Intro: Octahedron Platonic Solid

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United States 5th

Discover the octahedron, 1 of the 5 Platonic solids that have intrigued mathematicians, architects, and philosophers for thousands of years. Model and build this symmetrical, 3D shape with 8 triangular faces, and find out about real-life examples and uses of this shape.

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 what makes the properties of the octahedron a Platonic solid.

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.5.G.B.3 introduce the featured platonic soild. Explain that attributes belonging to a category of two-dimensional figures also apply to all subcategories of that category. For example, all rectangles have four right angles, and squares are rectangles, so all squares have four right angles. Encourage your students to think about how these ideas relate to the platonic solid.

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.5.GR.1.1 - MATHEMATICS (B.E.S.T.) introducing the featured platonic soild. While it's a 3D shape, each face is a 2D figure. Discuss how you can classify these faces based on their attributes. Then, relate this to the classification of triangles and quadrilaterals into different categories. Challenge them to explain why a particular triangle or quadrilateral belongs or does not belong to a specific category. An example are architectural blueprints or floor plans where there's many types of triangles and quadrilaterals used in the design of buildings and houses.

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

Make an octahedron with 8 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.5.G.B.3

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Fifth graders, tapping into the interdisciplinary essence of STEAM, can explore the attributes of two-dimensional figures. Constructing models or utilizing technology, they can superimpose shapes, visually discerning shared attributes. The activity highlights the hierarchical nature of geometric categories, driving home the principle that subcategories inherently possess the attributes of their parent category.

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.5.GR.1.1

Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category.

Craft tangible models of triangles and quadrilaterals, classifying them based on shared defining attributes. Use flexible connectors or other materials to demonstrate why a shape conforms or deviates from a specific category.

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