An Ancient Mathematical Crisis

Posted on by Denise Gaskins

PythagoreanCat

[When Alexandria Jones and her family visited an excavation in southern Italy, they learned several tidbits about the ancient school of mathematics and philosophy founded by Pythagoras. Here is Alex’s favorite story.]

It hit the Pythagorean Brotherhood like an earthquake, a crisis of faith which shook the foundations of their universe. Some say Pythagoras himself made the dread discovery, others blame Hippasus of Metapontum.

Something certainly did happen with Hippasus. The Brotherhood sent him into exile for insubordination, or for breaking the rule of secrecy — or was it for proving the unthinkable? According to legend, Hippasus drowned at sea, but was it a mere shipwreck or the wrath of the gods? Some say the irate Pythagoreans threw him overboard…

Continue reading An Ancient Mathematical Crisis

Answers to Leon’s Figurate Number Puzzles

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

Continue reading Answers to Leon’s Figurate Number Puzzles

Puzzle: Figuring Out Figurate Numbers

Posted on by Denise Gaskins


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.

Continue reading Puzzle: Figuring Out Figurate Numbers

April Fool’s Day: Fun with Math Fallacies

Posted on by Denise Gaskins

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

Quotations XIX: How Do We Learn Math?

Posted on by Denise Gaskins

He doesn’t learn algebra
in the algebra course;
he learns it in calculus.

I have been catching up on my Bloglines reading [procrastinating blogger at work — I should be going over the MathCounts lesson for Friday’s homeschool co-op class], and found the following quotation at Mathematics under the Microscope [old blog posts are no longer archived].

Continue reading Quotations XIX: How Do We Learn Math?

The Game of Algebra

Posted on by Denise Gaskins

NFL football
Photo by velo_city.

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.

Continue reading The Game of Algebra

Puzzles for the New Year

Posted on by Denise Gaskins
by Koshyk via flickr

As we all head back to school, here are some interesting calendar puzzles:

  • 2008 is a leap year. Why do leap years happen? If we didn’t add a leap day every so often, would January eventually come in the summer?
  • Today is Thursday. What day of the week will it be exactly one year from today?
  • January 1, 2008, came on a Tuesday. When will be the next year that begins on Tuesday?
  • My birthday (in March) lands on a Monday this year. When is the next year my birthday will come on a Monday? How about YOUR birthday — when is the next time it will happen on the same day of the week as this year?
  • Can you find a pattern in the way dates move from one day of the week to another, year after year?

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The Golden Christmas Tree

Posted on by Denise Gaskins

Last time, Alexandria Jones and her family were on their way to Uncle William’s tree farm to find the perfect Christmas tree, and Dr. Jones taught us about the Golden Section:

The \; Golden \; Section \; ratio

|———————A———————|————B————|

A \; is \; to \; B \; as \; \left(A + B \right) \; is \; to \; A, \; or . . .

\frac{A}{B} = \frac{A + B}{A} = \: ?

I gave you three algebra puzzles to solve. Did you try them?

  • What is the exact value of the Golden Section ratio?
  • If a 7-foot tree will fit in the Jones family’s living room, allowing for the tree stand and for a star on top, how wide will the tree be?
  • Approximately how much surface area will Alex and Leon have to fill with lights and ornaments?

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 have not 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.

Continue reading The Golden Christmas Tree

A-Hunting They Will Go

Posted on by Denise Gaskins

Alexandria Jones and her family piled into the car for a drive in the country. This year, they were determined to find an absolutely perfect Christmas tree at Uncle William Jones’s tree farm.

“I want the tallest tree in Uncle Will’s field,” Alex said.

“Hold it,” said her mother. “I refuse to cut a hole in the roof.”

“But, Mom!” Leon whined. “The Peterkin Papers…”

“Too bad. Our ceiling will stay a comfortable 8 feet high.”

Continue reading A-Hunting They Will Go

Ben Franklin Math: Elementary Problem Solving 3rd Grade

Posted on by Denise Gaskins

The ability to solve word problems ranks high on any math teacher’s list of goals. How can I teach my students to solve math problems? I must help them develop the ability to translate “real world” situations into mathematical language.

In two previous posts, I introduced the problem-solving tools algebra and bar diagrams. These tools help our students organize the information in a word problem and translate it into a mathematical calculation.

Working Math Problems with Poor Richard

This time I will demonstrate these problem-solving tools in action with a series of 3rd-grade problems based on the Singapore Primary Math series, level 3A. For your reading pleasure, I have translated the problems into the life of Ben Franklin, inspired by the biography Poor Richard by James Daugherty.

Continue reading Ben Franklin Math: Elementary Problem Solving 3rd Grade