# HEXA-HEXAFLEXAGONS – Pattern, Colour, Geometry

Students create a hexa-hexaflexagon and decorate the faces using markers, then they flex their hexa-hexaflexagons to explore probability.

120 Minutes

Language Arts
Mathematics
Visual Arts

#### Vocabulary

colour contrast flexagon hexa-hexaflexagon pattern polygon

#### Materials

Construction Paper Strips - 4 cm x 48 cm (1.5" x 18") - Light Colours Markers Scissors Glue Sticks Rulers Pencils

## Steps

### Step One

1. Follow the instructions to make a hexa-hexaflexagon using a light colour of construction paper. (Downloads - Hexahexaflexagon.pdf)

### Step Two

1. Erase the numbers on the face of the hexa-hexaflexagon.
2. Use markers to draw a pattern on the first face.

### Step Three

1. Flex the hexa-hexaflexagon to reveal a new face.
2. Draw a new design on this face.
3. Keep flexing the hexa-hexaflexagon and drawing new patterns until you have done all 6 faces.

### Step Four

1. Flex your hexa-hexaflexagon and notice:
- how many patterns show up
- how the structures of the patterns change
- which patterns show up the most
- which patterns rarely show up
2. Try to figure out the probability of a specific pattern showing up when the hexa-hexaflexagon is flexed.

## Learning Goals

Students will be able to:

• follow instructions to create a hexa-hexaflexagon;
• use markers to create 6 different patterns;
• flex the hexa-hexaflexagon to show all faces;
• determine the probability of a specific pattern showing up when the hexa-hexaflexagon is flexed;
• demonstrate technical accomplishment and creativity.

## Extensions

Have students:

• research the discovery of flexagons;
• experiment with other types of flexagons, for example, tri-hexaflexagons and tetraflexagons and compare them with their hexa-hexaflexagon;
• create a video to teach others how to make flexagons;
• create an advertisement using a flexagon to get their message across;
• share their ideas with their peers.

## Prepare

1. Prior to this lesson you may want students to explore pattern using the Patterns worksheet available on this website. (Downloads - PATTERN_worksheet.pdf)
2. Review or teach about polygons.
3. Review or teach about probability, the Probability Line and how to figure out the probability of an event happening.
- the probability of an event happening = number of ways it can happen divided by the total number of outcomes
4. Gather and make available books about flexagons, for example, Fantastic Flexagons: Hexaflexagons and Other Flexible Folds to Twist and Turn, by Nick Robinson; The Magic of Flexagons: Paper Curiosities to Cut Out & Make, by David Mitchell; and Cool Flexagon Art: Creative Activities that Make Math & Science Fun for Kids!, by Anders Hanson.
5. Make a sample hexa-hexaflexagon.
6. Pre-cut a variety of colours of construction paper into 4 cm x 48 cm strips.
7. Photocopy the instructions for making a hexa-hexaflexagon, enough for each student. (Downloads - HexaHexaflexagon.pdf)

## Introduction

1. Show students your hexa-hexaflexagon and flex it a few times so they can see how different patterns appear.
2. Introduce students to Arthur Stone - the university student who made a discovery in 1939 while playing with a strip of paper.
- he had folded it in such a way that is created a hexagon
- as he folded and played with the paper he noticed that he could make a third face appear by flexing it in a certain way
- he was intrigued by this and kept thinking about it overnight
- he kept playing with the idea and figured out how to make a hexa-hexaflexagon that would reveal 6 faces
- he shared his ideas with his friends and soon other kinds of flexagons were discovered
3. Introduce the challenge.

## Activities

### The Challenge

1. Follow instructions to create a hexa-hexaflexagon that works.
2. Use markers to create a different pattern on each face of the hexa-hexaflexagon - 6 in total.
3. Flex the hexa-hexaflexagon to show all faces.
4. Determine the probability of a specific pattern showing up when the hexa-hexaflexagon is flexed.
5. Conduct a trial to see if you get the outcome you expected.
6. Compare your results with two other people.
7. Demonstrate technical accomplishment and creativity.

### The Process

1. Make sure everyone understands the challenge.
2. Establish success criteria with your students, for example,
I know I am successful when I have:
- followed the instructions accurately
- created a hexa-hexaflexagon that works
- created 6 different patterns
- flexed my hexa-hexaflexagon to reveal all faces
- kept the paper in good condition
- explored probability using my hexa-hexaflexagon
3. Demonstrate how to fold the construction paper to make an equilateral triangle.
4. Guide students through the steps outlined in this lesson plan.
5. Observe students as they work.
6. Provide individual assistance and encouragement.

## Sharing

1. Place students into small groups.