More Math Resources

My math resources page continues to grow, with new discoveries and with pages I had simply overlooked. (Shame on me!) As I add new entries, I will occasionally post them on the blog as well. Like this:

1000 Problems to Enjoy
A large collection of challenge problems for grades 7-9, or for anyone who wants to play around with math and logic. Answers are in the Doc files, but don’t peek. Figure it out for yourself, and use the file only to check your work. It’s no fun when someone just gives you the answer!

Hexa-Trex Puzzle of the Day
“Object of the game: Find a path through all the tiles to make a math equation.” Difficulty ranges from easy to quite challenging.

Continue reading More Math Resources

Solving Complex Story Problems

[Dragon photo above by monkeywingand treasure chest by Tom Praison via flickr.]


Let’s play around with a middle-school/junior high word problem:

Cimorene spent an afternoon cleaning and organizing the dragon’s treasure. One fourth of the items she sorted was jewelry. 60% of the remainder were potions, and the rest were magic swords. If there were 48 magic swords, how many pieces of treasure did she sort in all?

[Problem set in the world of Patricia Wrede’s Enchanted Forest Chronicles. Modified from a story problem in Singapore Primary Math 6B. Think about how you would solve it before reading further.]

How can we teach our students to solve complex, multi-step story problems? Depending on how one counts, the above problem would take four or five steps to solve, and it is relatively easy for a Singapore math word problem. One might approach it with algebra, writing an equation like:

x - \left[\frac{1}{4}x + 0.6\left(\frac{3}{4} \right)x  \right]  = 48

…or something of that sort. But this problem is for students who have not learned algebra yet. Instead, Singapore math teaches students to draw pictures (called bar models or math models or bar diagrams) that make the solution appear almost like magic. It is a trick well worth learning, no matter what math program you use.

Continue reading Solving Complex Story Problems

Free (Mostly) Math Resources on the Internet

Please take a few minutes to look at my handy new math resource page (in the “For Your Information” box at the top of my sidebar). I moved all the math resource links from my sidebar onto a page of their own, where I could add descriptions and comments.

Whew! That was a lot of work. I hope you find it useful. If you know of any other great math pages I should add to the list, please tell me.

How Can We Teach Problem Solving?

We continue to plan our co-op courses for next fall. Some of the classes I had hoped for will not happen, and my children are going to have to make some tough choices between the remaining topics. Unfortunately, they have not yet mastered the ability to be in two classrooms at once.

I have three math courses to plan, and I think I will focus as much as I can on teaching math through problems, even at the elementary level. These are once-a-week enrichment classes for homeschooled students, so I assume they have a “normal” math program at home. I want to introduce a few topics they might not otherwise see, to deepen their understanding of the topics they have studied, and to give them a taste of that “Aha!” feeling that comes from conquering a challenging problem. Has anybody done something like this, and can you recommend some good resources?

Continue reading How Can We Teach Problem Solving?

Historical Tidbits: The Pharaoh’s Treasure

[Read the story of the pharaoh’s treasure here: Part 1, Part 2, and Part 3.]

I confess: I lied — or rather, I helped to propagate a legend. Scholars tell us that the Egyptian rope stretchers did not use a 3-4-5 triangle for right-angled corners. They say it is a myth, like the corny old story of George Washington and the cherry tree, which bounces from one storyteller to the next — as I got it from a book I bought as a library discard.

None of the Egyptian papyri that have been found show any indication that the Egyptians knew of the Pythagorean Theorem, one of the great theorems of mathematics, which is the basis for the 3-4-5 triangle. Unless a real archaeologist finds a rope like Alexandria Jones discovered in my story, or a papyrus describing how to use one, we must assume the 3-4-5 rope triangle is an unfounded rumor.

Continue reading Historical Tidbits: The Pharaoh’s Treasure

Carnival, Carnival, Carnival

The 120th Carnival of Education is now up and running at I Thought a Think. As always, a wide variety of interesting articles to browse. Enjoy!

Carnival of MathematicsEdited to add: Oops! I missed the 8th Carnival of Mathematics last week.
My favorite posts mostly came in pairs.

Two puzzles from MathNotations:
When Curves Collide
Going off on Tangents

Two brainteasers from SharpBrains:
The Unkindest Cut of All
The Really, Really, Really Big Number

Two mind-blowing infinity puzzles that were fun to read, even though I didn’t really understand the answers:
Cats in a Tree
Dogs in a Mineshaft

And the odd-one-out is a history post:
Calculators: Past, Present and Future

My Favorite Unpopular Posts

I get a bit tired of the various memes [definition: things to blog about when you have no ideas of your own, a state with which I can easily identify!] that float around the blogsphere—songs from A’s iPod, irrelevant things that nobody knew about B, or C’s favorite TV commercials… But Dana at Principled Discovery has a new meme that actually looks interesting.

Objective: Share ten of your favorite posts, although they went largely unnoticed in the broader blogosphere.

Continue reading My Favorite Unpopular Posts

The Secret of the Pharaoh’s Treasure, Part 3

[In the last episode, Alexandria Jones discovered a mysterious treasure: three wooden sticks, like tent pegs, and a long loop of rope with 12 evenly spaced knots. Her father explained that it was an ancient Egyptian surveyor’s tool, used to mark right angles.]

Back at the camp, Fibonacci Jones stacked multi-layer sandwiches while Alexandria poured milk and set the table for supper.

“Geometry,” Fibonacci said.


Geo means earth, and metry means to measure. So geometry means to measure the earth. That is what the Egyptian rope stretches did.”

Alex thought for a moment. “So in the beginning, math was just surveying?”

“And taxes…”

Continue reading The Secret of the Pharaoh’s Treasure, Part 3