Library
Courses
Geometry to Engineering Design
Intro: Icosahedron Platonic Solid
Cover image
Lesson
Preview

Intro: Icosahedron Platonic Solid

ByStrawbees Team

Model the icosahedron, 1 of the 5 Platonic solids that have intrigued mathematicians, architects, and philosophers for thousands of years. Learn to build this symmetrical, 3D shape that features 20 triangular faces. Discover how the icosahedron is found in nature and ways it has been used by people.

Topics
Geometry
Get Started
  • Common Core Mathematics
    Grade: 2nd
    Geometry, Reason with shapes and their attributes.
    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.
    Grade: 3rd
    Geometry, Reason with shapes and their attributes.
    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.
    Grade: 4th
    Geometry, Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
    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.
    Grade: 5th
    Geometry, Classify two-dimensional figures into categories based on their properties.
    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.
    Grade: 6th
    Geometry, Solve real-world and mathematical problems involving area, surface area, and volume.
    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.
    Grade: 7th
    Geometry, Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
    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.
    Grade: 8th
    Geometry, Understand congruence and similarity using physical models, transparencies, or geometry software.
    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.
  • ISTE Students
    Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models or simulations.
  • Florida - NGSSS
    Grade: 2nd
    Geometric Reasoning, Identify and analyze two-dimensional figures and identify lines of symmetry.
    Identify and draw two-dimensional figures based on their defining attributes. Figures are limited to triangles, rectangles, squares, pentagons, hexagons and octagons.
    Grade: 3rd
    Geometric Reasoning, Describe and identify relationships between lines and classify quadrilaterals.
    Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.
    Grade: 4th
    Geometric Reasoning, Draw, classify and measure angles.
    Informally explore angles as an attribute of two-dimensional figures. Identify and classify angles as acute, right, obtuse, straight or reflex.
    Grade: 5th
    Geometric Reasoning, Classify two-dimensional figures and three-dimensional figures based on defining attributes.
    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.
    Grade: 6th
    Geometric Reasoning, Model and solve problems involving two-dimensional figures and three-dimensional figures.
    Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.
    Grade: 7th
    Geometric Reasoning, Solve problems involving two-dimensional figures, including circles.
    Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.
    Grade: 7th
    Geometric Reasoning, Solve problems involving three-dimensional figures, including right circular cylinders.
    Solve real-world problems involving surface area of right circular cylinders.
    Grade: 7th
    Geometric Reasoning, Solve problems involving three-dimensional figures, including right circular cylinders.
    Solve mathematical and real-world problems involving volume of right circular cylinders.
    Grade: 8th
    Geometric Reasoning, Understand similarity and congruence using models and transformations.
    Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship.
  • TEKS Technology Applications
    Grade: 3rd
    identify and communicate a problem or task and break down (decompose) multiple solutions into sequential steps;
    The student explores the core concepts of computational thinking, a set of problem-solving processes that involve decomposition, pattern recognition, abstraction, and algorithms.
    Grade: 3rd
    demonstrate personal skills and behaviors, including effective communication, following directions, and mental agility, needed to implement a design process successfully; and
    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.
    Grade: 3rd
    apply a design process with components such as testing and reflecting to create new and useful solutions to identify and solve for authentic problems.
    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.
    Grade: 4th
    decompose story problems into smaller, manageable subproblems and discuss and document various solutions to the problems;
    The student explores the core concepts of computational thinking, a set of problem-solving processes that involve decomposition, pattern recognition, abstraction, and algorithms.
    Grade: 4th
    explain the importance of and demonstrate personal skills and behaviors, including problem solving and questioning, effective communication, following directions, mental agility, and metacognition, that are needed to implement a design process successfully; and
    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.
    Grade: 4th
    apply an appropriate design process that includes components to improve processes and refine original products for authentic problems.
    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.
    Grade: 5th
    decompose a real-world problem into smaller, manageable subproblems using graphic organizers such as learning maps, concept maps, or other representations of data;
    The student explores the core concepts of computational thinking, a set of problem-solving processes that involve decomposition, pattern recognition, abstraction, and algorithms.
    Grade: 6th
    decompose real-world problems into structured parts by using visual representation;
    The student explores the core concepts of computational thinking, a set of problem-solving processes that involve decomposition, pattern recognition, abstraction, and algorithms.
    Grade: 5th
    explain the importance of and demonstrate personal skills and behaviors, including persistence, effective communication, following directions, mental agility, metacognition, problem solving and questioning, that are needed to implement a design process successfully; and
    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.
    Grade: 5th
    apply an appropriate design process that includes components to generate multiple solutions for an authentic problem and develop original products.
    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.
    Grade: 6th
    resolve challenges in design processes independently using goal setting and personal character traits such as demonstrating courage and confidence;
    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.
    Grade: 6th
    discuss and implement a design process using digital tools to compare, contrast, and evaluate student-generated outcomes; and
    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.
    Grade: 7th
    decompose real-world problems into structured parts using flowcharts;
    The student explores the core concepts of computational thinking, a set of problem-solving processes that involve decomposition, pattern recognition, abstraction, and algorithms.
    Grade: 7th
    resolve challenges in design processes independently using goal setting and personal character traits such as demonstrating responsibility and advocating for self appropriately;
    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.
    Grade: 7th
    discuss and implement a design process that includes planning and selecting digital tools to develop and refine a prototype or model through trial and error; and
    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.
    Grade: 8th
    decompose real-world problems into structured parts using pseudocode;
    The student explores the core concepts of computational thinking, a set of problem-solving processes that involve decomposition, pattern recognition, abstraction, and algorithms.
    Grade: 8th
    demonstrate innovation in a design process using goal setting and personal character traits, including demonstrating calculated risk-taking and tolerance;
    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.
    Grade: 8th
    discuss and implement a design process that includes planning, selecting digital tools to develop, test, and evaluate design limitations, and refining a prototype or model; and
    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.
  • TEKS Mathematics
    Grade: 3rd
    solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction;
    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.
    Grade: 3rd
    represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting;
    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.
    Grade: 3rd
    classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language;
    The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties.
    Grade: 4th
    apply mathematics to problems arising in everyday life, society, and the workplace;
    The student uses mathematical processes to acquire and demonstrate mathematical understanding.
    Grade: 4th
    use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
    The student uses mathematical processes to acquire and demonstrate mathematical understanding.
    Grade: 4th
    select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
    The student uses mathematical processes to acquire and demonstrate mathematical understanding.
    Grade: 4th
    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.
    The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties.
Age range
7-14+
Duration
1:00:00
Assets
Guide - Platonic Solids

Overview and Objectives

Lesson Structure

When students go through this lesson in each section, the objectives they will learn are:

  • Imagine – Discover the icosahedron and learn about this Platonic solid.
  • Build – Build a symmetrical icosahedron, a Platonic solid with 20 faces.

Overview

Model the icosahedron, 1 of the 5 Platonic solids that have intrigued mathematicians, architects, and philosophers for thousands of years. Learn to build this symmetrical, 3D shape that features 20 triangular faces. Discover how the icosahedron is found in nature and ways it has been used by people.