MamaSquirrel has posted some great ideas for doing elementary math without a formal math program.
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Hints and Solutions: Patty Paper Trisection
No peeking! This post is for those of you who have given the trisection proof a good workout on your own. If you have a question about the proof or a solution you would like to share, please post a comment here.
But if you haven’t yet worked at the puzzle, go back and give it a try. When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.
Continue reading Hints and Solutions: Patty Paper Trisection
Puzzle: Patty Paper Trisection
[Feature photo above by Michael Cory via Flickr (CC BY 2.0).]
One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.
One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why.
ABC’s of Mathematics
The ninth Carnival of Mathematics at JD2718 takes us on an alphabetical romp through the world of math blogging.
There is plenty for everyone this week, from elementary and secondary math education to logic and recreational puzzles—too many good articles to list individually, so click over there and read them for yourself!
Historical Tidbits: Alexandria Jones Answers
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 afterwards. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. Figure it out for yourself — and then check the answer just to prove that you got it right.
Continue reading Historical Tidbits: Alexandria Jones Answers
Historical Tidbits: Alexandria Jones
Test Yourself: Logic
Can you solve the Wason Selection Task puzzle at Text Savvy blog? [Blog has disappeared.]
Here is an interactive version of the Wason Selection Task, and you can find out more information about it on the Wikipedia page.
Warning: Don’t read the comments Wikipedia page until you have tried the puzzle for yourself. Why ruin your fun?
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.
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](https://s0.wp.com/latex.php?latex=x+-+%5Cleft%5B%5Cfrac%7B1%7D%7B4%7Dx+%2B+0.6%5Cleft%28%5Cfrac%7B3%7D%7B4%7D+%5Cright%29x++%5Cright%5D++%3D+48&bg=ffffff&fg=303030&s=0&c=20201002)
…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.
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.
Denise Gaskins' Let's Play Math 