Here is the simplest puzzle from the November/December 1998 issue of Alexandria Jones stories. The answer (and more puzzles) will follow.
Christmas gift for Leon (pdf, 68KB)
More puzzles are now here:
Answers are also posted:
Read all the posts from the November/December 1998 issue of my Mathematical Adventures of Alexandria Jones newsletter.
UPDATE: Some of the links below have gone missing, as internet sites tend to do. Check out my *huge* new blog post:
We interrupt our regularly scheduled math program to bring you the following Christmas links…
First, A to Z Home’s Cool offers some fun for older students and teachers:
Also check out the annual Price of Christmas Index to see what the “12 Days of Christmas” gifts would cost you this year. Or explore the Nrich Advent Math Calendars to play with a new math activity every day until Christmas.
You can find just the song here: http://vihart.com/music/gauss12days.mp3.
Maria at Homeschool Math Blog has posted a fun set of worksheets:
Pan balance problems to teach algebraic reasoning.
Princess Kitten, at nearly 9yo, keeps telling me, “I hate math, but I like algebra.” So I printed all four pages for her to try. These get pretty complicated, and the 2-variable problems had her flummoxed for awhile. But after an explanation and bit of pouting (I think she hates math because she’s such a perfectionist that she can’t bear to get something wrong, even the first time), she came back and conquered the toughest ones.
Photo by Håkan Dahlström via flickr.
Math concepts: addition and subtraction within 100, logical strategy
Number of players: 2 or 3
Equipment: printed hundred chart (also called a hundred board) and beans, pennies, or other tokens with which to mark numbers — or use this online hundred chart
Place the hundred chart and a small pile of tokens where both players can reach them.
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.
Have you considered experimenting with writing in your math class this year? It seems that math journals are a growing fad, and for good reason:
Writing is how we think our way into a subject and make it our own.
Math journal entries can be as simple as class notes, or they can be research projects that take hours of experimentation and pondering. Students may use the journal to store their thoughts as they work several days to solve a challenge problem of the week, or they might jot down quick reflections about what they learned in today’s math class.
This post has been revised to incorporate all the suggestions in the comments below, plus many more activities. Please update your bookmarks:
Or continue reading the original article…
In the first section of George Lenchner’s Creative Problem Solving in School Mathematics, right after his obligatory obeisance to George Polya (see the third quote here), Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.
A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown above. How many of the 1-cm cubes do not have red paint on any face?
And then he challenges us as teachers:
Do you have any ideas for extending the problem?
If so, then jot them down.
This is strategically placed at the end of a right-hand page, and I was able to resist turning to read on. I came up with a list of 15 other questions that could have been asked — some of which will be used in future Alexandria Jones stories. Lechner wrote only seven elementary-level problems, and yet his list had at least two questions that I had not considered. How many can you come up with?
Photo by Windell Oskay via Flickr (CC BY 2.0).
Math concepts: logic, patterns, divisibility
Number of players: 2
Equipment: 10 tokens, any sort, mix or match
Place the pile of tokens (pebbles, toothpicks, beans, pennies, dry cereal, etc.) on the table between the players.
Math concepts: addition, number bonds for 10, visual memory
Number of players: any number, mixed ages
Equipment: math cards, one deck
Each player draws a card, and whoever choses the highest number will go first. Then shuffle the cards and lay them all face down on the table, spread out so no card covers any other card. There are 40 cards in a deck, so you can make a neat array with five rows of eight cards each, or you may scatter them at random.
Denise Gaskins' Let's Play Math 