[In the last episode, Alexandria Jones received a letter from archaeologist Sofia Theano, asking for help with a Pythagorean puzzle.]
The Mosaic Tile Mystery
Dear Alexandria Jones,
We continue to excavate the ancient building complex, which I believe may have been Pythagoras’s school. Yesterday, one of our digging crews uncovered a mosaic tile floor in the courtyard. The pattern of the tiles alternates between two square designs. (See enclosed sketches.)
During your family’s recent visit, you expressed an interest in the mathematical ideas of Pythagoras. Could you or your father offer us any insight into what these tile designs may represent?
I look forward to your response.
Sincerely,
Sofia Theano, Ph.D.
Crotone, Italy
Answers to Leon’s Figurate Number Puzzles
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 post. Figure them out for yourself — and then check the answers just to prove that you got them right.
Puzzle: Figuring Out Figurate Numbers
Photo by frumbert.
Alexandria Jones‘s parents decided that the family needed to relax after the excitement of tracking Simon Skulk, so they spent the next day at a beach on the Mediterranean coast. Leon collected pebbles and tried to build up figurate numbers — numbers that make a figure, or shape — the way Dr. Theano had shown them.
April Fool’s Day: Fun with Math Fallacies
Photo by RBerteig. Take a break from “serious” math and have a little fun today with some classics of recreational mathematics. Do you have a favorite math or logic fallacy? Please share it in the Comments below. Continue reading April Fool’s Day: Fun with Math Fallacies
Answers to Alex’s and Leon’s Puzzles
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.
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?
Happy Pi Day II
[Feature photo above by pauladamsmith.]
Now there is an ancient Greek letter,
And I think no other is better.
It isn’t too tall,
It might look very small,
But its digits, they go on forever.— Scott
Mrs. Mitchell’s Virtual School
Time to Celebrate
Are your students doing anything special for 
If you need ideas, here are some great
Math Contest Tip Sheets
Most of our math contest preparation consists of working lots and lots of old test problems. Occasionally, however, I put together a tip sheet summarizing a topic that my students have trouble remembering.
The Christmas Present Quandary
Alexandria Jones hated using store-bought wrapping paper at Christmas. She tried to wrap each present as a hand-crafted work of art.
Last year, she did mini-scenes with plastic figures building cotton snowmen or skating on aluminum-foil ponds — and, for her brother Leonhard’s gift, her favorite creation: toy dinosaurs having a snowball fight. But those 3-D scenes got knocked about under the Christmas tree.
This year, she decided, she would wrap the packages flat. But then, how could she make them special?
Denise Gaskins' Let's Play Math 