Sunday, April 28, 2013

The Shadow Knows

I believe this is by the great cartoonist and puzzler A.W. Nugent (about whom we will be hearing more).

I like this for a few reasons.

First, as a creativity exercise it brings in new and unusual shapes and gives the students open-ended instructions in how to deal with them.

Second, it helps build intuition about geometry (particularly projective geometry).

Third, it looks like fun.

The one change I would make would be to get different shapes from the same crumpled piece of paper by moving the light source.

Sunday, April 21, 2013

The greatest board game series ever?

I was never entirely clear on why 3M decided to get into the board game business, but for more than a dozen years they put out 3M's Bookshelf Games (so called because the boxes were designed to look like large hardcover books when placed in their slip covers). The line-up was a mixture of traditional games like chess and go and new games designed by freelancers like the incomparable Sid Sackson (Sackson's classic Acquire was a 3M game). The weakest of the series were still pretty good while the best have become, as mentioned before, classics.

Software developer Dennis Matheson has a detailed and affectionate website devoted to the series, Wikipedia has a good write-up as well, and, if your bookshelf has more space than mine, you can buy most of the games on EBay.

[Originally ran in West Coast Stat Views]

Sunday, April 14, 2013

Bookshelf -- The Hinged Square & Other Puzzles by Ivan Moscovich

I haven't seen the rest of the series but based on this book and Moscovitch's reputation, I'd certainly recommend seeking them out. The puzzles are beautifully illustrated and, in some cases, accompanied by a explanation of  the underlying mathematics.

The book also features the extraordinary pencil and paper game racetrack.

Sunday, April 7, 2013

Make your own Platonic Solids -- let the conspiracy theories commence

(Via Google, I found these at the Philalethes Society site, so active members of the Anti-Masonic Party might want to skip to the next post)

Here's another chapter in the ongoing playing with paper series. There are any number of interesting lessons you can build around the five Platonic Solids (as usual, Martin Gardner has some clever suggestions), but the best place to start is probably by building intuition by letting the kids make and manipulate them.

Depending on the age and sophistication level of the class, try one or more of the following:

1. Decorate then assemble these patterns;

2. Use these patterns to make dice. Try playing familiar games (chutes and ladders, Parcheesi, etc.) with the new dice;

3. Make mobiles using Platonic solids and paper tubes;

4. Make sculptures with the condition that attached sides have to match (this gives you three types of sculptures -- cube-based, dodecahedron-based and everything else);

5. Measure the surface area of each solid;

5b. Use fine Styrofoam pellets to estimate and compare the volumes of the different solids.

6. Using clear plastic for the outer shell, create dual polyhedron.

Wednesday, April 3, 2013

Another Captain Marvel paper plane -- this one slightly creepy

Given the fact that V-1 flying bombs had only recently been raining death on our allies in England when this toy came still it's an interesting design (check out the curve of the wings) and it makes a nice companion to this previous post.

You can print out the plane as a word document or PDF.

Let me know how it flies.

Paper bridges

As part of the ongoing paper engineering series and as a follow-up to the posts on paper platforms and paper chains, here's a suggestion for another design and construction project.

The objective is to build a center-load-bearing bridge between two platforms with fifty sheets of paper and a roll of tape, either optimizing weight supported with the condition that the platforms be at least two feet apart or optimizing distance between platforms with the condition that the bridge most support at least five pounds. You might also want to try a variant where a long piece of string is included allowing for suspension designs.

Like the platform project, this is one of those assignments that increases in complexity as the students advance. You can give the same instructions to a fourth grade class and to a group of freshman engineers with equally challenging results. You could even make this an annual event and watch the designs grow more complex and the approaches more sophisticated as the years passed.

Captain Marvel paper airplanes from 1945

More in the ongoing series on paper-based manipulative and projects.

I came across these online and I have no idea how well they actually fly, but given that we're talking about paper airplanes in the shape of cartoon characters, they should be a fairly easy sell.

Here are some thoughts on how to build a lesson plan around these toys. (I'd use the heaviest paper your photocopier can handle).

Since these actually WWII era toys, there's an obvious opportunity for teaching across the curriculum.

Try a basic statistics exercise by doing multiple tests of all three, recording distance and glide time and plotting the results.

Have kids come up with their own designs along the basic lines of these planes but with different themes and characters.

Tie this in with other paper airplanes and models.

From Just a Pile of Old Comics