# TINY TETRAHEDRONS – Geometry, Pattern, Balance

Students create small sculptures using tiny, marker painted tetrahedrons they have built with nets.

80 Minutes

Language Arts
Mathematics
Science
Visual Arts

#### Vocabulary

balance edge geometric solid negative space pattern positive space sculpture vertex

#### Materials

Crayola Broad Line Markers Crayola Paint Brushes Crayola White Glue Crayola Glue Sticks Crayola Scissors Toothpicks Water Containers Plastic Container Lids for Palettes Paper Towels

## Steps

### Step One

1. Draw marker ink on a plastic lid.
2. Dip the paintbrush in water.
3. Don't get it too wet.
4. Pick up the marker ink with the wet paintbrush.
5. Paint different patterns and colours on each face of the tetrahedron.

### Step Two

1. Carefully cut out each painted net.

### Step Three

1. Glue the net together.
2. Use a toothpick to apply pressure from inside the net by gently placing it into a vertex and pushing the outside edge against the toothpick.
3. Make at least 6 tetrahedrons.

### Step Four

1. Start gluing your tiny tetrahedrons together to make a stable, balanced sculpture.
2. Put a small amount of Crayola Washable Glue on the end of a tetrahedron and hold it in place for a few seconds until it sticks.
3. Look at your sculpture from all directions to see how the spaces and shapes move your eye around and through the whole piece.
4. Make sure it can stand on its own.

### Step Five

1. Give your sculpture a title.
2. Write the title on a card and place it with the sculpture.
3. Place all the sculptures on a table so they are part of the group, but still have their own space.

## Learning Goals

Students will be able to:

• use nets to build a variety of tetrahedrons;
• create 6 different patterns;
• create a stable sculpture using at least 6 tetrahedrons;
• demonstrate technical accomplishment and creativity.

## Extensions

Set up an 'Add a Shape' station –

• place a starter sculpture of 3 tetrahedrons glued together, a stack of paper, a bottle of glue, and scissors at the side of the room
• invite students to add a shape whenever they need a break or have finished their work early
• leave the 'Add a Shape' station set up for at least a month and see how big the sculpture can grow
- allow it to change shape and fall to a new base so it grows organically
- let it be a conversation piece and have students draw it from different points of view
- from time to time discuss what is happening with the sculpture as it gets larger and changes
- use it as a story starter, for example, What if you were small enough to travel through this space?  What adventures would you have?
• once you decide to stop the station, ask students what they learned by participating in the 'Add a Shape'.

## Prepare

1. Prior to this lesson have students explore patterns using the pattern worksheet available on this website. (Downloads – Pattern_Worksheet.pdf)
2. Prior to this lesson have students explore geometric solids.
3. Gather books and pictures about geometry and polyhedrons, for example, Amazing Math: Introduction to Platonic Solids, by Sunil Tanna; Beginner's Book of Modular Origami Polyhedra: The Platonic Solids, by Rona Gurkewitz, and Bennett Arnstein; Building Platonic Solids: How to Construct Sturdy Platonic Solids from Paper or Cardboard and Draw Platonic Solid Templates with a Ruler and Compass, by Sympsionics Design; Cubes, Cones, Cylinders, & Spheres, by Tana Hoban; The Greedy Triangle, by Marilyn Burns; Mummy Math: An Adventure in Geometry, by Cindy Neuschwander;  and Shapes, Shapes, Shapes, by Tana Hoban.
4. Photocopy tetrahedron nets on regular copy paper – two for each student. (Downloads - Tetrahedron_nets.pdf)
Aston
Clemson
Greenfield
Martyn
Rubinoff
6. Create a large tetrahedron out of plain Bristol board.

## Introduction

1. View the large tetrahedron and have students describe its characteristics, e.g.,
- 3 faces
- each face has 3 edges
- each face is a triangle
- it has 16 edges in total
- it has 4 vertices
2. Explain that It is one of the Platonic solids.
a 3-dimensional shape
each face is the same regular polygon
- the same number of polygons meet at each vertex
- only 5 – tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron
3. Review patterns and the design vocabulary they used in the worksheet.
pattern is the arrangement of shapes or elements according to a set of rules
- design vocabulary for making patterns includes loops, circles, spirals, crossed lines, teardrops, squiggles, waves, right angles, dots
4. View and discuss the abstract sculptures.
- use of positive and negative space
- balance
- movement of the eye in and around the whole sculpture
- variety and harmony
5. Introduce the challenge.

## Activities

### The Challenge

1. Use nets to build a variety of tetrahedrons.
2. Create 6 different patterns.
3. Create a stable sculpture using at least 6 tetrahedrons.
4. Demonstrate technical accomplishment and creativity.

### The Process

1. Ensure that everyone understands the challenge.
2. Establish success criteria with your students, for example,
I know I am successful when I have made:
at least 6 different patterns
- at least 6 tetrahedrons

- spaces and shapes that move your eye around and through the whole sculpture
- a sculpture that can stand on its own
- the sculpture carefully
3. Guide students through the steps outlined in this lesson plan.
4. Observe students as they work.
5. Provide individual assistance and encouragement.

## Sharing

1. Once all the sculptures are complete display them for a group discussion.
Look closely at the sculptures.
- Choose one that interests you for some reason.
- Share thoughts about the work.
2. During the discussion include references to:
variety – How do the different sizes of tetrahedrons contribute to the effectiveness of the overall design?
- pattern – How are the patterns different? How are they similar? How do they help move the eye in and around the sculpture?
- balance – How does the placement and size of tetrahedrons affect the stability of the sculpture?

- technical accomplishment – How does careful construction contribute to the overall effectiveness of the sculpture?

## Assessment

1. Observe students as they work – thoughtful focus, discriminating, seeking more information, elaborating, experimenting.
2. Observe students as they discuss the art works – active listening, insightful contributions, supporting ideas with evidence found in the artwork and from personal experience.