More Fun with Hexa-Trex

Posted on by Denise Gaskins

Hexa-trex turtle logo

My elementary Math Club students had fun practicing their math facts and “out of the box” thinking with Hexa-Trex puzzles. The object of Hexa-Trex is to find a path through all the number and operation tiles to make a true equation. The “Easy” puzzles are just the right level for my 4th-5th grade students, although they get stumped whenever the equations require Order of Operations. One girl enjoyed the puzzles enough to take our extra pages home for her dad.

Hexa-Trex puzzles were featured in the October issue of Games magazine, and now you can enjoy Hexa-Trex away from the computer with Bogusia Gierus‘s new book, The First Book of Hexa-Trex Puzzles. If you are thinking ahead to Christmas (can it be that time already?!), and if you have a puzzle lover in the family, this little book would make a fun stocking-stuffer.

Egyptian Math: The Answers

Posted on by Denise Gaskins

Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original posts. Figure them out for yourself—and then check the answers just to prove that you got them right.

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Egyptian Geometry and Other Challenges

Posted on by Denise Gaskins

Rhind papyrus

Would you like to study “the knowledge of all existing things and all obscure secrets”? That is how Scribe Ahmose (also translated Ahmes) described his mathematical papyrus. Ahmose’s masterpiece is now called the Rhind Papyrus, after Alexander Henry Rhind, a Scotsman who was one of the first archaeologists to make meticulous records of his excavations (rather than simply hunting for treasures). Rhind purchased the papyrus from an antiquities dealer in Luxor, Egypt, in 1858.

Ahmose’s writing included a huge table of fractions as well as story problems, geometry, algebra, and accounting. Can you solve any of Scribe Ahmose’s problems?

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Another Egyptian Math Puzzle

Posted on by Denise Gaskins

Pyramids clip artI have one last puzzle for those of you who are following my Alexandria Jones series on hieroglyphic math and the Egyptian scribe’s method of multiplication by doubling. Here is the “teaser” problem from the cover of the Sept./Oct.1998 issue of my newsletter:

One more Egyptian math puzzle (pdf, 53KB)

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Egyptian Math Puzzles

Posted on by Denise Gaskins

What we know about ancient Egyptian mathematics comes primarily from two papyri, the first one written around 1850 BC. Moscow papyrus problem 14This is called the Moscow papyrus, because it now belongs to Moscow’s Pushkin Museum of Fine Arts. The scroll contains 25 problems, mostly practical examples of various calculations. Problem 14, which finds the volume of a frustrum (a pyramid with its top cut off), is often cited by mathematicians as the most impressive Egyptian pyramid of all.

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Trouble with Percents

Posted on by Denise Gaskins

Can your students solve this problem?

There are 20% more girls than boys in the senior class.
What percent of the seniors are girls?

This is from a discussion of the semantics of percent problems and why students have trouble with them, going on over at MathNotations. (Follow-up post here.)

Our pre-algebra class just finished a chapter on percents, so I thought Chickenfoot might have a chance at this one. Nope! He leapt without thought to the conclusion that 60% of the class must be girls.

After I explained the significance of the word “than”, he solved the follow-up problem just fine.

Puzzle: Random Blocks

Posted on by Denise Gaskins

Red block puzzle

In the first section of George Lenchner’s Creative Problem Solving in School Mathematics, right after his obligatory obeisance to George Polya (see the third quote here), Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.

A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown above. How many of the 1-cm cubes do not have red paint on any face?

And then he challenges us as teachers:

Do you have any ideas for extending the problem?
If so, then jot them down.

This is strategically placed at the end of a right-hand page, and I was able to resist turning to read on. I came up with a list of 15 other questions that could have been asked — some of which will be used in future Alexandria Jones stories. Lechner wrote only seven elementary-level problems, and yet his list had at least two questions that I had not considered. How many can you come up with?

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Solution: The Cat’s Lasagna

Posted on by Denise Gaskins

The puzzle (from The mysterious temporal freeze) was:

A certain famous cat snarfs down an 11″x13″ pan of lasagna in 3 seconds flat. Assuming the fat feline has a bottomless pit for a stomach and continues to eat at the same rate, how long will it take him to devour a pasta the size of the state of Illinois?

Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterwards. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. Figure it out for yourself — and then check the answer just to prove that you got it right.

Continue reading Solution: The Cat’s Lasagna

The Mysterious Temporal Freeze

Posted on by Denise Gaskins

Pyramids clip artAlexandria Jones stepped into the huge tent that protected her father’s excavation site from the desert winds. She laughed to herself. It was like walking into a circus.

She knelt down to whisper in the ear of her faithful dog Ramus. “In this ring, grad students carefully brush away another layer of sand. In the next ring, the artist sketches every piece as it is found.” She waved her arm. “And over there, our flashiest attraction — drum roll, please — the photographers shoot each shard of pottery from every possible angle. But where is the Master of Ceremonies?”

Alex and Rammy found Professor Jones near the back of the tent, talking to another student. While she waited for her dad, she looked through an assortment of numbered artifacts that were ready to be packed and sent to the museum.

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Puzzle: Patty Paper Trisection

Posted on by Denise Gaskins

[Feature photo above by Michael Cory via Flickr (CC BY 2.0).]

trisection

One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.

One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why.

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