In the philosophy of Greek philosopher Plato, he saw geometry and mathematics existing in their own ideal world. The 5 Platonic solids are connected to nature through the association of natural elements earth, fire, air, water, and the universe from which the world was made. Explore how humans interact with geometry and mathematics and realize the beauty behind them in everyday life.

Intro: Tetrahedron Platonic Solid

Intro: Hexahedron Platonic Solid

Intro: Octahedron Platonic Solid

Intro: Dodecahedron Platonic Solid

Intro: Icosahedron Platonic Solid

Construct a Sierpinski Pyramid

STEAM Classroom

United States

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Common Core Mathematics

CCSS.Math.Content.2.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.

CCSS.Math.Content.3.G.A.1

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.

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

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.

CCSS.Math.Content.5.G.B.3

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.

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

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

CCSS.Math.Content.7.G.B.6

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

CCSS.Math.Content.8.G.A.2

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

ISTE Students

1.6.c Creative Communicator

Identify and draw two-dimensional figures based on their defining attributes. Figures are limited to triangles, rectangles, squares, pentagons, hexagons and octagons.

Florida - NGSSS

MA.2.GR.1.1

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

MA.3.GR.1.2

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

MA.4.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.

MA.5.GR.1.1

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

MA.6.GR.2.2

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

MA.7.GR.1.2

Solve real-world problems involving surface area of right circular cylinders.

MA.7.GR.2.2

Solve mathematical and real-world problems involving volume of right circular cylinders.

MA.7.GR.2.3

Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship.

MA.8.GR.2.1

The student explores the core concepts of computational thinking, a set of problem-solving processes that involve decomposition, pattern recognition, abstraction, and algorithms.

TEKS Technology Applications

3.1A

The student takes an active role in learning by using a design process to solve authentic problems for a local or global audience, using a variety of technologies.

3.3A

3.3B

4.1A

4.3A

4.3B

5.1A

6.1A

The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy.

TEKS Mathematics

3.4A

3.4E

The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties.

3.6A

The student uses mathematical processes to acquire and demonstrate mathematical understanding.

4.1B

4.1C

The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties.

4.6D

5.3A

5.3B

The student takes an active role in learning by using a design process and creative thinking to develop and evaluate solutions, considering a variety of local and global perspectives.

Beautiful Geometry