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.
The Puzzling Pythagorean Pebbles
Alexandria Jones and her family flew to Italy for spring break. Her father, the famous archaeologist, had to visit an excavation.
It was late when their plane landed in Crotone, a small coastal city near the instep of Italy’s boot. Dr. Jones had used the Internet to find a hotel that allowed pets, so Alex was able to snuggle down with her favorite pillow — her trusty dog, Ramus.
The Original School of Mathematics
The next day, Dr. Jones introduced his family to Sonya Theano, a former student of his and the director of this dig. “Come, let me show you around,” Dr. Theano said. “We’ve uncovered several buildings of a small compound, set apart from the city of Crotona, as it was called then. From the pottery and trade goods, we estimate these buildings were in use around 550-500 BCE.”
Math Games by Kids
Photo by Mike Licht, NotionsCapital.com.
The cold came back and knocked me flat, but there are compensations. The downtime gave me a chance to browse my overflowing bookmarks folder, and I found something to add to my resource page. Princess Kitten and I enjoyed exploring these games and quizzes from Ambleweb.
Backwards Math
Photo by Complicated.
Princess Kitten is recovering from her cold and getting some energy back. She came to me and said wistfully, “I wish I could do backwards math.”
I looked up from my keyboard. “Backwards math? What do you mean?”
“Umm. It’s kinda hard to explain, but I can show you.”
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
Retro-Dated Magic Square Puzzles
The hectic holidays kept me from finishing the Christmas stories of Alexandria Jones. I am finally getting them typed up, but I past-dated them to keep the seasonal connection. So if you want to read more, here are the newest posts:
In Between Sneezes… Multiplication Videos
Sitting at home with a cold, tired of watching TV and playing video games, stumbled upon…
A great theorem from math history
Subtracting Mixed Numbers: A Cry for Help
Photo by powerbooktrance.
Paraphrased from a homeschool math discussion forum:
“Help me teach fractions! My son can do long subtraction problems that involve borrowing, and he can handle basic fraction math, but problems like
give him a brain freeze. To me, this is an easy problem, but he can’t grasp the concept of borrowing from the whole number. It is even worse when the math book moves on to
.”
Several homeschooling parents replied to this question, offering advice about various fraction manipulatives that might be used to demonstrate the concept. I am not sure that manipulatives are needed or helpful in this case. The boy seems to have the basic concept of subtraction down, but he gets flustered and is unsure of what to do in the more complicated mixed-number problems.
The mother says, “To me, this is an easy problem” — and that itself is one source of trouble. Too often, we adults (homeschoolers and classroom teachers alike) don’t appreciate how very complicated an operation we are asking our students to perform. A mixed-number calculation like this is an intricate dance that can seem overwhelming to a beginner.
I will go through the calculation one bite at a time, so you can see just how much a student must remember. As you read through the steps, pay attention to your own emotional reaction. Are you starting to feel a bit of brain freeze, too?
Afterward, we’ll discuss how to make the problem simpler…
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.
Denise Gaskins' Let's Play Math 