Geodesic Dome Building, Part II

The dome actually worked! All three fourth grade classes rolled, measured, cut, marked, counted, and assembled two geodesic domes at the Integrated Arts Academy. A quality assurance team was established in order to ensure the newspaper rolls were strong and tight. Partner work was important, so students had one person tape while another person held newspaper rolls in place. Math was happening all around. The domes initially worked great, but then started to droop and fall after a few days. Students fixed them up and brainstormed ways to make them stronger.

This project was shared during an all-school assembly. Three of the fourth graders presented the work with a slideshow created by their class. More fourth graders sat inside one of the domes (to everyone’s delight!) in order to hold it up if it started to droop during the presentation. It didn’t need any support but it was really fun to have them sitting in there. The presentation touched on the math, art, and engineering in this project. Students also explained Buckminster Fuller's humanitarian vision for the geodesic dome.

I loved collaborating with Ada Leaphart, Judy Klima, and the fourth graders at IAA. I hope to do it again soon. There are so many wonderful opportunities to connect math and art in meaningful ways.

Geodesic Dome Building, Part I

Ada Leaphart, Integrated Arts Academy Art Teacher Extraordinaire, and I have embarked on an adventure. We’ve got all the fourth graders at IAA building geodesic domes out of newspaper.

I really don’t know how this is going to end up, so that is why I have named this Part I. I hope to report back with more news as the project progresses.

Ada and I decided to keep things loose. We didn’t want to figure everything out for the students by creating our own dome first, learning all the lessons, and then presenting a tidy scenario.

Instead, we have never attempted to create a geodesic dome out of newspaper or anything else, for that matter. Sometimes STEM+Art (I, unlike others, am not wanting to call that STEAM) should be messy and students should have the fun of making mistakes and doing all the figuring.

Before the students got started building, Ada showed a photo of a geodesic dome and asked students what they noticed. We got some math+art conversation going from that, as students noticed many geometric shapes, like triangles, pentagons, hexagons, and trapezoids. Then we talked about old Bucky Fuller (every class asked if he was still living) and how he really wanted to make the world a better place for everyone by using an efficient structure like a dome for shelter.

Kids couldn’t wait to get started. Here are the instructions we are using from PBS.

It turns out, you can roll newspaper in a loose, floppy, weak way or you can roll it in a very tight, very strong roll. Students shared successful and unsuccessful techniques. Among the successful techniques invented by students are 1) Asking someone else to help you tape the roll, 2) asking someone else for help, period, 3) twisting the roll when it is finished to make it even tighter, and 4) using a pencil to act as the center of the roll, then shaking it loose once the roll is finished.

We ended up with enough rolls to make one or two domes. 65 usable rolls are needed. Next time we will need to establish a Quality Control group to assess, select, and count the rolls we’ve got. Ada and I aren’t sure how the whole thing is going to go. At the end of it all I would like to set the dome on fire in the playground. I am not sure we will get permission for that. Oh well, we’re going to roll with it.

Geometry Daily

http://geometrydaily.tumblr.com/

I love the images on this website. A new one is created daily and generously shared with the world. I would like to use these with students. The only prompt would be, simply, “What do you see?”

Hexaflexagons

Alex Reutter, C.P. Smith Math Night Parent Extraordinaire, got me thinking about hexaflexagons. The other day, he mentioned that he thought kids would enjoy making them at Math Night. Hexaflexagons are folded paper hexagons that do a special flip. I decided I’d better try to figure these out ahead of time on a nice calm weekend at home.

I began by watching Vi Hart’s videos about hexaflexagons. Of course, Vi is fond of speeding things up, but I still thought I should be able to fold a strip of paper into equilateral triangles and make a hexaflexagon. Vi didn’t seem to be doing any measuring, like other websites recommend, so I was resistant to using a ruler. But after a bunch of mangled paper strips, I knew I needed a different strategy.

I found some pre-made, printable PDFs of hexaflexagon patterns. Some of the best are on a website called Aunt Annie’s crafts, on her Flexagons page. Print them, preferably in color. My brother and I were going to drive all the way down to Thetford, so I packed up some flexagon patterns, a scissor, and some double-sided tape for the trip.

I had plenty of time in the car to cut, tape, and fold several hexaflexagons, but I still didn’t know how to get them to do their special flip. I handed one to my brother while we stood around watching the Thetford cross country races, and he was able to figure it out.

These hexaflexagons are really cool. It’s worth trying one yourself. They were discovered by Arthur H. Stone in 1939, then popularized by Martin Gardner in his Scientific American column called “Mathematical Games” in 1956. Try pre-made patterns at first. I think starting students this way, then asking them how they might create their own if given a blank piece of paper, pencil, ruler, glue, and scissors, would be an excellent math activity, perfect for differentiation. We'll see how it goes at Math Night!

Making Math More

Woman sewing quilt : New York World's Fair, 1939-1940. NYPL

Did you know there is a new museum in New York City called the Museum of Mathematics (or MoMath for short)? They say the grand opening will be in 2012 at 11 East 26th Street in Manhattan. I am hoping to visit it over April vacation.

For now, we've got MoMath guru George Hart's Math Monday column in MAKE Magazine. Here's a nice piece on quilting and geometry. Check it out. You and your students could try building octiamonds with pattern blocks if you aren't a big quilter.

Hyperbolic Space

Poincaré disc model of hyperbolic space from fractalsciencekit.com

Margaret Wertheim gave this interesting lecture called "The Beautiful Math of Coral".

  

She does a thorough job of explaining the math of hyperbolic space here on her website, the Institute for Figuring. There are photos of the gorgeous crocheted coral reefs, too.

In her words...

The Crochet Reef Project was inspired by the technique of hyperbolic crochet originally developed by Dr Daina Taimina, a mathematician at Cornell. In 1997 Dr Taimina discovered how to make models of the geometry known as "hyperbolic space" using the art of crochet. Until that time many mathematicians believed it was impossible to construct physical models of hyperbolic forms; yet nature had been doing just that for hundreds of millions of years. It turns out that many marine organisms embody hyperbolic geometry in their anatomies - among them kelps, corals, sponges, sea slugs and nudibranchs. Thus the Crochet Reef not only looks like a coral reef, it draws on the same underlying geometry endemic in the oceanic realm.

There are very good reasons why marine organisms take on hyperbolic forms: this geometry is a marvelous way to maximize surface area in a limited volume, thereby providing greater opportunity for filter feeding by stationary organisms.

An unidentified folded coral in Flynn Reef, part of the Great Barrier Reef, near Cairns, Queensland, Australia. By Toby Hudson.

Crochet works because it is an easy way to increase stitches in each row to produce ruffling. I haven’t crocheted since childhood, but I do remember increasing stitches when I wasn’t supposed to. Maybe I should try a coral reef. 

Math and the iPad

 

I have a new iPad and I’m looking for good math apps.

Lee Orlando has a new iPad, too. She loves trying new things and is already way ahead of me on using the iPad in math class. This is from a recent email:

This weekend I bought an adapter for my iPad so I can hook it up to the LCD projector, and I also got a wireless keyboard.  Today, I went into school to try it out.  It was so cool to see the iPad screen projected and to sit at the back of the room (or any place in the room for that matter) and see the text appear.

This was soon followed by another email:

I just found some awesome free apps for the iPad.  All are from "Mathtappers" and the three that I downloaded involve placing numbers (including rational numbers) on a number line and finding equivalent fractions.  All games are designed for three levels of play.  I've been trying them out at each of the levels, and they get pretty challenging at the highest level.  However, the easiest level is well within the ability of fifth graders.

...these apps look like a great way to engage students in a whole-class warm-up activity/discussion.   I had made up my own number line activity using a sketching app that I have... the kids' attention level goes WAY high when they get to come up and draw on the iPad!  Getting that adapter for the LCD projector may have been the best investment I have made in a long time.

Later, I ran into Lee at school and she showed me how she’d photographed a piece of graph paper to use as the background of her sketching app, so that students could draw arrays and fractions with the aid of the grid. What a great idea!

I hunted around a bit and found some other useful apps. My favorite so far is Sketchpad Explorer. If it’s been awhile since you contemplated the Pythagorean theorem, you’ll enjoy the Getting Started screen, which allows you to drag right and non-right triangles around to see the theorem in action.

The real fun, though, comes when you touch the little book icon in the lower left corner of the screen. Choose “Elementary Mathematics” and Sketchpad Explorer presents you with a suite of eight activities involving symmetry, triangles, fractions, decimals, multiples, and volume. There is even a logic game which gives less than and greater than clues to find an unknown number. Sketchpad Explorer’s creativity and nice, clean graphics are appealing. At first glance, there seems to be a wealth of resources and lesson ideas for teachers on the website. I can’t wait to try these with students.