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Geometric World

Develop spatial reasoning by creating and identifying geometric shapes.

Learning Objectives

  • Develop spatial reasoning skills; think about objects in two and three dimensions, draw conclusions from limited information
  • Recognize geometry in the world and how it can be used
  • Create and scale geometric structures; identify and improve weak points
  • Learn about the properties of self-similarity and the dimensions of shapes
  • Study and identify the fractals and patterns in nature and art


30 minutes before starting the lesson

  • Create an example of the intended activity
  • Gather and prepare support materials


  • “What is geometry?
  • “How is geometry used in our everyday lives?”
    • Nature – honeycombs, pinecones, trees, snowflakes, ferns
    • Art – creating depth on a flat surface
    • Architecture – the Giza pyramids or a bridge for structural integrity
    • Robotics – mapping the path of a robot’s hand on an assembly line, 3D printing
    • Chemistry – in the shapes of all atoms and molecules in existence
  • “Can geometric shapes be broken down into other shapes?”
  • “What happens if you break a geometric shape into smaller or larger versions of itself?” (Self-similarity)
  • “What is triangulation?”
  • “Is there a shape that can’t be broken into triangles?”


Students can:

  • Create a set of shapes and trade with another group and see what each group can build with them.
  • Build shapes to make a self-similar structure like a tree full of branches, a snowflake, a cube made out of smaller cubes or the Sierpinski Pyramid. To start, encourage students to draw self-similar shapes and lines on paper.
  • Build collaboratively to make large geometric structures (such as an enormous honeycomb, snowflake, etc.)


Students can:

  • Invent a new geometric shape. Try to build a complex or even an impossible shape.
  • Cut and attach paper panels on the faces of shapes. For example, create a “class clubhouse” by cutting out large sheets of triangles from paper and attaching them to the sides of a Sierpinski pyramid large enough to have different rooms inside of it.
  • Experiment with changing the construction pipe size, or changing its angle using a different Strawbees connector, and observe and describe what happens.
  • Transform the shapes and lines of your geometric objects into items of your daily life, imagination or to use as a prop on another activity.
  • Have students pair up. One student can be the builder and the other can be the reader. The reader will choose a 3-D geometric image out of a hat. The reader must describe the image and how to build it. The builder will try to create the same geometric model based solely on verbal instructions.


You can have your students:

  • Engage in a “show-and-tell”, inviting student groups to describe the various shapes and/or artwork they created.
  • After building and identifying a variety of geometric shapes, collaboratively connect them into a unique “sculpture” the class can move through.


  • “What shapes did you enjoy using most for your building block set? Why?”
  • “What did you notice when another student built something with your block set?”
  • “What was the most difficult part of creating a set of 3-D building blocks?”
  • “Can you make your geometric structures grow infinitely?”
  • “Where else have you seen self-similarity in nature?”

Other Lesson Plans