## Math Puzzle from the Ancient Kingdom of Cats

It may look like Cimorene has lain down on the job, but don’t be fooled! She’s hard at work, creating a math investigation for your students to explore.

Cats know how important it can be for students to experiment with math and try new things. Playing with ideas is how kittens (and humans!) learn.

Cimorene wants you to know that the Make 100 Math Rebels Kickstarter offers a great way for human children to learn math through play. She encourages you to go watch the video and read all about the project:

Too often, school math can seem stiff and rigid. To children, it can feel like “Do what I say, whether it makes sense or not.” But cats know that kids are like kittens — they can make sense of ideas just fine if we give them time to play around.

Continue reading Math Puzzle from the Ancient Kingdom of Cats

## Fractions: 1/5 = 1/10 = 1/80 = 1?

[Feature photo is a screen shot from the video “the sausages sharing episode,” see below.]

How in the world can 1/5 be the same as 1/10? Or 1/80 be the same as one whole thing? Such nonsense!

No, not nonsense. This is real-world common sense from a couple of boys faced with a problem just inside the edge of their ability — a problem that stretches them, but that they successfully solve, with a bit of gentle help on vocabulary.

Here’s the problem:

• How can you divide eight sausages evenly among five people?

Think for a moment about how you (or your child) might solve this puzzle, and then watch the video below.

## Egyptian Math: Fractions

I have been enjoying James Tanton’s website. In this video, Tanton explains a foolproof method for creating Egyptian fractions:

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

## Egyptian Fractions: The Answer Sheet

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 (relatively) 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 post. Figure them out for yourself — and then check the answers just to prove that you got them right.

## The Secret of Egyptian Fractions

Alex made a poster of Egyptian-style fractions, from 1/2 to 9/10. Many of the fractions were easy. She knew that…

$\frac{5}{10} = \frac{4}{8} = \frac{3}{6} = \frac{2}{4} = \frac{1}{2}$

Therefore, as soon as she figured out one fraction, she had the answer to all of its equivalents.

She had the most trouble with the 7ths and 9ths. She tried converting these to other fractions that were easier to work with. For example, 28 has more factors than 7, making 28ths easier to break up into other fractions with one in the numerator.

## The Secret of Egyptian Fractions

Photo from Library of Congress via pingnews.

Archaeology professor Dr. Fibonacci Jones came home from a long day of lecturing and office work. Stepping inside the front door, he held up a shiny silver disk.

“Ta-da!” he said.

“All right!” said his daughter Alexandria. “The photos are here.”

They had to chase Alex’s brother Leon off the computer so they could view the images on the CD, but that wasn’t hard. He wanted to see the artifacts, too. Alex recognized several of the items they had dug up from the Egyptian scribe’s burial plot: the wooden palette, some clay pots, and of course the embalmed body.

Then came several close-up pictures of writing on papyrus.

Photo from MathsNet.net.

## How to Write Egyptian Fractions

“I remember how to read the Egyptian numbers,” Alex said, “but what are these marks above them?”

Dr. Jones nodded. “I thought you would catch that. Those are fractions. The scribe places an open mouth, which is the hieroglyph ‘r’, over a number to make its reciprocal.”

“I know that word,” Leon said. “It means one over the number. Like, the reciprocal of 12 is 1/12, right?”

“That is right. 1/12 would be written as…”

## The Rest of the Story

As I transcribed this article from my old math newsletter, I realized that it would require more graphics than I was willing to construct. LaTex does not handle Egyptian hieroglyphs — or at least, I don’t know how to make it do so. Instead, I decided to scan the newsletter pages and give them to you as a pdf file:

The file includes a student worksheet for Egyptian fractions from 1/2 to 9/10.

## Egyptian Fractions: The Answer Sheet

The answers are now posted.

## To Be Continued…

Read all the posts from the January/February 1999 issue of my Mathematical Adventures of Alexandria Jones newsletter.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

## Egyptian Math: The Answers

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.

## Egyptian Geometry and Other Challenges

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?

## Egyptian Math Puzzles

What we know about ancient Egyptian mathematics comes primarily from two papyri, the first one written around 1850 BC. This 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.