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.

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.6.G.A.4 start by introducing featured platonic soild. Show your students how to represent the three-dimensional figure making a nets made up of these faces. Explain that these nets can help find the surface area of complex shapes. Explain how nets are used in real-world problem-solving:

• Engineers and designers use nets for prototyping and modeling purposes. By creating paper or cardboard models based on nets, they can visualize physical objects, test their design concepts, and make necessary adjustments before manufacturing the actual product.
• In architectural fields, architects and builders use nets as part of their design and planning processes. Nets help them conceptualize and plan structures, ensuring that architectural components fit together correctly.

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.6.GR.2.2 - MATHEMATICS (B.E.S.T.) though the featured platonic soild is a 3D shape, its faces can help us understand how to calculate the area of triangles and quadrilaterals within each. Encourage your students to decompose these shapes into triangles or rectangles to find their areas. A real-life example is planning the layout of a room, considering the area of furniture pieces (rectangles) and the space available.

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.

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.

NGSS

For MS-ETS1-1 - ENGINEERING DESIGN present the problem to the students: design an invention to improve the natural habitiat for the animal made in Build can efficiently thrive in. Discuss the criteria (e.g., efficiency, cost-effectiveness, environmental impact) and constraints (e.g., available materials, budget) for their designs. Discuss relevant scientific principles with the students. And for MS-ETS1-2 - ENGINEERING DESIGN guide students in evaluating their prototype's performance against the defined criteria and constraints. Students should also consider potential impacts on the environment and people. Based on the evaluation, ask students to refine and improve their designs. This iterative process allows them to make modifications to their water wheels to increase efficiency or address any shortcomings.

CCSS.Math.Content.6.G.A.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

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.

MA.6.GR.2.2

Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.