Skills: Geometry, polygons, measurement …. and creativity.
Levels: Junior School & Middle School
In this activity students will create their own, preferably life-sized cardboard igloo. Igloo structures can be complicated or simple and in this project students must design and then build an igloo using a standard hexagon. Here are some inspiring designs.
The first igloo was built using computer generated constructive geometry. It uses a basic – but distorted – hexagonal cardboard unit and was built by by the students of the Faculty of Architecture, University of Porto. You can see the construction method below. More info here.
The next cardboard igloo is based entirely on circles. It was designed by students of ETH Zurich in Switzerland. More info here.
The following cardboard igloo based on triangles looks simple but has a very strong construction. More info here.
But the Granddaddy of the geometric or geodesic dome was Buckminster Fuller, who has been honoured by having a carbon-based nano-molecule named after him. They’re called Bucky Balls. If you look at the geodesic dome below you can see the HEXAGONAL PATTERN also visible int he Bucky Balls.
Skills: Geometry, measurement, polyhedrons, symmetry and creativity
Year Level: Year 7-9
Ask students to design and make a GEOMTRIC FASHION STATEMENT. This could involve a dress, hat or hair. Then they stage run a MATHS FASHION parade. The point is the fashion statement must involve specific maths such as geometry or trigonometry, calculus, quadratic equations … any maths you like.
Here from Lancia Trend Visions is the work of Amila Hrustic, a fashion design student in Sarajevo. These samples come from her “Plato’s Collection” inspired by the idea of Platonic solids. Her collection includes dress based on tetrahedrons, cubes, octahedrons, dodecahedrons, icosahedrons.
Skills:Geometry, measurement, cylinders, area, symmetry and creativity.
Year Level: Year 4 – whatever
Ask students to build their own cardboard armour and helmet. Give prizes in the category of Scariest, most Mathematically-Complex, Star Wars Potential, Most Historical, Most Creative and any other category that crops up. You can source cardboard from your nearest Self-Storage Warehouse.
Mathspig was at Womadelaide Music Festival 2013 and saw the Box Wars at work. The Box Wars guys, Joss, Josh and Hoss, started in Melbourne and now travel to Music Festivals around Australia. Boxwars builds sculptures, armour, props and sets and airplanes , tanks, cannons and the rest.
They stage battles of destruction … but destruction isn’t always the outcome.
If you want to interest kids especially boys 8 – 12 years of age in maths, get them building armour.
Mathspig saw dozens of them at WOMAD and they so loved their armour they wouldn’t take it off in 39Cº.
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Sometimes it is just lots and lots of fun. Here is a recently staged BOX WARS in Canberra. You only need watch a few minutes of the video to get the idea.
Now, my Sweeties, I want you to understand something important about the way people, who use maths, think.
It is vital that architects can walk around inside an imaginary building in their heads, that engineers can see in their imagination where the support columns need to be placed in a building/bridge, that chemists can visualise 3D mirror images of molecules, that fashion designers can see the axis of symmetry and also invert an item of clothing inside out (because that is how clothes are sewn), that designers can rotate objects in their imagination (not just to look pretty, but to make sure the object can stand up) and it is important that computer programmers can see patterns to write their repeating algorithms (More later).
The maths involved here includes:
Symmetry
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2D patterns
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2D & 3D mirror images
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3D Rotations
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Algorithms
You will find these fab world maps @ BLDG BLOG, which uses an algorithm to map the 3D world into different 2D shapes, which can then be reconstructed into 3D objects. Wow!
Sometimes mathspiggies, teachers forget how important these visualising exercises can be in the development of maths thinking skills.
So my little Sweeties, we’re going to use some of these maths skills to build up your maths brain.
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1. Rotating Tessellation
A tessellation is a repeating pattern with no gaps like floor tiles.
Look at the pattern. It involves equilateral triangles repeated.
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Oops! Not exactly perfect, but Mathspig was using paper and scissors!
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We aren’t going to write a computer program, but rather think what we might want the program to do. The Rotation Tessellation algorithm would go something like this. Take triangle shape, rotate around fixed point A until area tiled, stop. Take new fixed point, rotate new shape around this point until all area tiled, repeat, repeat, repeat.
2. Flip Tessellations
This time we will use mirror images, which we create by flipping an image.
As the Eurovision Song contest has just finsihed we’ll use an image of the Twin Brothers Jedward to create our flip tessellation. You can use any image to create a flip tessellation, even your own head!!!!!!!!! First I took one brother.
Then I flipped him horizontally.
Then I flipped him vertically
and then I just kept going.. unfortunately, I had to print and scan to get the wallpaper effect.
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We could create an algorithm, which tells the computer to do this: Take Jedward 1, flip horizontal, flip last pic vertical, flip last pic horizontal, copy new pic, flip horizontal, flip vertical, flip horizontal, repeat, repeat…………….
In fact, Mathspig had an JEDWARD algorithm in her head, copy, paste, copy, paste, copy, paste….. Arghhhhhhh! ….couldn’t stop…..
But you end up with a lovely set of JEDWARD floor tiles, or curtain fabric or maybe shirt material!!!!!! Nice! It depends on your taste, really.
As part of our Mid-year/ End of year madness here are some crazy things to do with Lego.
The idea with these projects is to challenge you, my pretties, by giving you the Lego, the time and the inspiration so you can go, go, go for it and, maybe even, surprise yourself.
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1. Going Loopy
Can you make something round from oblong Lego blocks?
Lego constructions can move. Here is The Blossoming Lotus built by the Brickengineer. If you click on this link you can see the Lotus blossom. Cool! Can you make a Lego flower bloom, mathspigs?
But if you really want to see some Lego flowers bloomin’ get yourself down to the Reiman Gardens @ Iowa State University. They have the Lego flowers, the Lego birds, the Lego butterflies, a Lego Zoo. Perhaps, mathspigs, your class could put your heads together and make a Lego garden or a Lego Zoo.
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3. Going Square
Lego artist Nathan Sawaya’s Lego sculptures are mind boggling. You can find the following sculptures @ sayhi-todesign blog spottoor @ Nathan’s own blog, The Art of the Brick. Maybe, mathspigs, you could build a geometric sculpture out of Lego blocks.
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Or get inspired by Nathan Sawaya’s other sculptures
Wow! That’s just how Mathspig feels when I’m waking up in the morning.
Another way to get your brain wrapped around the idea of symmetry, 2D patterns and 3D image rotations is by building a musical instrument and some of them even play music, um, sort of!
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1. Lego Harpsichord built by a kid
with ordinary Lego that works!!!
2. Lego Electric Guitar that really works
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3. Lego Flute that works
They say it works. Mathspig hasn’t heard it. The kid could be just spending time blowing on a Lego block.
Here is another art work by Lego artist Nathan Sawaya. The cello doesn’t play music, but this is such an awesome video of Nathan building the cello, it is a MUST see, mathspigs.
It doesn’t play music, but think about it mathspigs. It would look soooooo cool sitting in your bedroom. Besides, many a guitar sits in a bedroom without being played.
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6. Lego Saxaphone
Here is another work by Pat Dube. It doesn’t play music but it’s just cool, man. Put on those sunglasses, feel the vibe and chill.
Now mathspigs, let’s get mobile. There is a lot of symmetry and 3D rotations involved in building a Lego ca. You can go low -tech or high tech. Get ready mathspigs here we go:
1. Lego Balloon Car
I don’t think you’ll need instructions for this one. Maybe you could pimp that ride, mathspigs.
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