# PATTERN CUBE – Hexahedron, Pattern, Space

Students use markers to create a different pattern for each of the 6 faces on a hexahedron net, and then build it into a cube.

80 Minutes

Language Arts
Mathematics
Visual Arts

#### Vocabulary

3-dimensional space face hexahedron pattern platonic solid polygon polyhedron vertex

#### Materials

Markers Glue Sticks Scissors Hexahedron Nets Cardstock Paper - 21.6 cm x 27.9 cm (8.5" x 11")

## Steps

### Step One

1. Use line, colour, shape, and your own creative rules to make a different pattern on each face of the hexahedron.

### Step Two

1. Cut the net out carefully.

### Step Three

1. Make crisp folds at each of the dotted lines.
2. Fold the tabs and glue them under the edges so they cannot be seen.
3. View your cube from all sides.

## Learning Goals

Students will be able to:

• use line, colour and shape to create 6 different patterns;
• build a cube using a hexahedron net;
• describe the characteristics of a hexahedron;
• demonstrate technical accomplishment and creativity.

## Extensions

Have students:

• work in small groups to create a variety of polygons in different sizes;
• use the polygons to create a group sculpture;
• write a description of the process;
• draw the sculpture from different points of view;
• share their work with their peers.

## Prepare

1. Prior to this lesson have students explore patterns using the pattern worksheet available on this website. (Downloads – Pattern_Worksheet.pdf)
2. 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.
3. Photocopy hexahedron nets on cardstock paper – one for each student. (Downloads - Hexahedron_Net.pdf)
4. Create a large hexahedron out of plain Bristol board.

## Introduction

1. View the large hexahedron and have students describe its characteristics, e.g.,
6 faces
- each face has 4 edges
- each face is a square
- it has 12 edges in total
- it has 8 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, cube, 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. Introduce the challenge.

## Activities

### The Challenge

1. Use line, colour and shape to create 6 different patterns.
2. Build a cube using a hexahedron net.
3. Describe the characteristics of a hexahedron.
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:
a hexahedron
- a different pattern on each face of the hexahedron

- patterns with lines, colours and/or shapes
- crisp folds
- tabs glued so they cannot be seen
- a carefully constructed hexahedron
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 designs are complete display them for a group discussion.
Look closely at the cubes.
- Choose one that interests you for some reason.
- Share thoughts about the work.
2. During the discussion include references to:
colours - How do the colours contribute to the effectiveness of the overall design?
- pattern - How are the patterns different? How are they similar?
- technical accomplishment – How does careful construction contribute to the overall effectiveness of the cube?
3. Have students identify the characteristics of the hexahedron by pointing to the areas on their cube and using correct mathematical terminology.

## 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.