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.

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!

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.