Tessellations, Hands-on Math

Intro: Tessellations, Hands-on Math

This project is made to give students the opportunity to design there own tessellations and understant the math behind that. Explore the unique feature of "Calçada Portuguesa" a beautiful and useful way to use tessellations.

STEP 1: Design the Polygons

You can use any 3D sotware to design this. I choose Openscad because it's free and very precise.

Let's use this formula:
{circle(20,$fn=8);%circle(20,$fn=90);}

Now you have a 2d shape.

STEP 2: Add Volume to Polygons

It's time to add volume so add this line before the previous one:
linear_extrude(height = 3, center = true, convexity = 0)

And you obtain your first polygon

STEP 3: Make Other Polygons

You can make different polygons by change the value that apears above the green bar in the next photos.

Now you need to print them!

STEP 4: Stl Files and Print Settings

This is my print settings:

Printer: Bq Witbox

Rafts: No

Supports: No

Resolution: 0,2mm

Infill: 20%

Notes: Filament: PLA | Print Speed: 60mm/s | Bed adhesive: hair spray

STEP 5: Teacher's Notes

Project Name
Tessellations, hands-on math is made to give students the opportunity to design there own tessellations and understant the math behind that. Explore the unique feature of "Calçada Portuguesa" a beautiful and useful way to use tessellations.

Overview & Background

This project give me more knowledge about math. I was a medium math student and now with 3D printers at a reasonable price it's a great opportunity to everyone knows more about math and have hands on activities in schools.

Objectives

At the end of this project students wil be abble to:

• Identify polygons
• Identify Regular Tessellations
• Identify Semi Regular Tessellations
• Build there own tessellations

Audiences

This project is made for 5th grade

Subjects

Math

Skills Learned

• Math of polygons
• Tessellations
• "Calçada Portuguesa", a brief history

Lesson/Activity

There is a powerpoint you can use as guideline for the activity.

STEP 6: Classroom Activity - What Is a Polygon?

List of things to get before activity starts:

• Plastic polygons printed or ordered by the teacher
• A media projector and a computer
• Pencil for students
• A webcam or a camera
• A printer
• Glue
• Scissores
• Make groups of 4 or 5 students

What is a polygon?

The teacher should ask first to students if they know what is a polygon. From there the activity should start.

STEP 7: Classroom Activity - Identify Polygons

The teacher should give to each student the “Identify polygons” worksheet and let them do the work.

STEP 8: Classroom Activity - Tessellations

The teacher should now introduce the concept of tessellation. Explain the difference between regular and semi-regular tessellations.

STEP 9: Classroom Activity - Identify Regular Tessellations

The teacher should give to each student the “Identify Regular Tessellations” worksheet and let them do the work

STEP 10: Classroom Activity - Identify Semi Regular Tessellations

The teacher should give to each student the “Identify SemiRegular Tessellations” worksheet and let them do the work

STEP 11: Classroom Activity - Build Your Own Tessellation

The teacher should give to each student the “Build your own Tessellation” worksheet and invite students to use the plastic pieces to make there own tessellations. After that the teacher our the students should use the camera to take a picture of the tessellation, print it and glue it on the worksheet

STEP 12: Classroom Activity - "Calçada Portuguesa" a Brief History

From here to end the teacher should tell a little story about "Calçada portuguesa" and show the beautiful images in the powerpoint of this wonderful use of tessellation.

Comments

[dave.vaness.79]

I like the hexagons attacked by triangles and squares. It seems like someone should be able to use it as a game board. Any ideas board game designers?

[charlessenf-gm]

A version of Go, perhaps?? But how might one win?

[jeanniel1]

Go wins by number of spaces covered by one color so it'd be possible!

[charlessenf-gm]

I played with the color choices - I liked the one design, but not the colors! In changing them about (I was thinking of a Mosaic design element for a shower!) it occurred to me that you might want to involve your Art instructors in choosing the colors (or create each shape in each color as well as employ at least three values (?) of each color and maybe whites, grays and a black?
I am not an Art major, but I believe there is a 'rule' about color values and how they may be used to manipulate or perception of a given image. In my blue versions, it seemed that changing the value of the center most piece gave one the impression that the piece was three dimensional. Not sure the three .bmp images I uploaded are appearing!