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.
Alex’s & Leon’s Homeschool Puzzle
While checking out the book table after a homeschool group meeting, Maria Jones glanced up to see her children laughing with some kids she did not recognize. Driving home, she asked about the new family, but Alex and Leon had been too busy exchanging silly stories to even ask the strangers’ names.
“Well,” Leon said, “the boy told me he has twice as many sisters as brothers.”
No way!” said Alex. “The girl told me that she has the same number of brothers and sisters.”
How can that be?
Leonhard’s Block Puzzles
Leonhard Jones is Alexandria Jones’s younger brother. He enjoys woodworking, and he cut a wooden cube into 8 smaller blocks to make himself a puzzle.
Puzzle #1
Leon painted the 8 blocks with his two favorite colors: red and forest green. When he was finished, Leon could put the blocks together into a red cube, or he could switch them around to make a green cube.
How did Leon paint his blocks?
Planning Ahead: St. Patrick’s Day
Photo by Brittany G.
I found this cute lesson on Meeyauw’s blog:
And that sent me searching for more St. Patrick’s Day math:
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…
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.
Nim Revisited
Photo by Sister72.
Dave at MathNotations offers another version of Nim that will give your students something to think about:
[1,2]-3-[4,5]-6-[7,8]…21 Helping Children Devise and Understand Winning Strategies
Way To Go, Boys!
Photo by ccarlstead.
Congratulations, math team! All your hard work paid off, and I hope you enjoyed yourselves thoroughly. Of course, as C. S. Lewis wrote:
…if you do one good deed, your reward usually is to be set to do another and harder and better one.
Now it’s time to practice for the state level in March. You can find practice problems online at:
Preparation Drills for MATHCOUNTS
or
The “Go Figure!” math challenge
[ACK! MathCounts has re-written their website. The old link is no longer any good, but I haven’t yet found the new location for this game.]
And give the new interactive Countdown Round game a try:
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:
Right-click and choose “Save” to download:
- The secret of Egyptian fractions (pdf 364KB)
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.
The Game of Algebra
My pre-algebra class hit the topic of equations just as the NFL season moved into the playoffs. The result was this series of class notes called “The Game of Algebra.”
We used the Singapore Math NEM 1 textbook, which is full of example problems and quality exercises. These notes simply introduce or review the main concepts and vocabulary in a less-textbooky way.
I hope you find them useful.
2008 Mathematics Game
Are you ready for a challenge? Join us for the 2008 Mathematics Game. Here are the rules:
Use the digits in the year 2008 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial) — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.
- All four digits must be used in each expression.
- Only the digits 2, 0, 0, 8 may be used.
- Multi-digit numbers such as 20, 208, or .02 MAY be used this year.
- The square function may NOT be used.
- The integer function may NOT be used.
By definition:
[See Dr. Math’s Why does 0 factorial equal 1?]
For this game we will accept the value:
[See the Dr. Math FAQ 0 to the 0 power.]
Denise Gaskins' Let's Play Math 