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Puzzle: Random Blocks

Posted on by Denise Gaskins

Red block puzzle

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?

Continue reading Puzzle: Random Blocks

Quotations XIII: Mathematics Education Is Much More Complicated than You Expected

Posted on by Denise Gaskins

Registrations have been rolling in for our homeschool co-op, and the most popular classes are full already. Math doesn’t seem to be a “most popular” class. I can’t imagine why! Still, many of my students from last year are coming back for another go, and I am getting spill-over from the science class waiting list.

Anyway, I have started planning in earnest for our fall session. As usual, I look to those wiser than myself for inspiration…

Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.

— Paul Halmos

Continue reading Quotations XIII: Mathematics Education Is Much More Complicated than You Expected

The Thief in the Night

Posted on by Denise Gaskins

Alexandria Jones and her faithful dog Ramus slipped out of the tent when the talking started. One of Dad’s assistants had made the long drive into town to bring back pizza for supper. But now, all the adults would be working past midnight to finish the final site report.

Paperwork was necessary, she knew, but so-o-o boring.

Alex and Rammy wandered around the nearly-dark camp. Many of the tents were down. Crates stood near the road. All the artifacts had been carefully cleaned and labeled, and some were already shipped to the museum lab.

She ran a hand over the edge of a crate, then jerked back, wincing at the splinter that dug into her palm.

Continue reading The Thief in the Night

Math Jokes

Posted on by Denise Gaskins

Blame it on MathNotations and his Corny Math Jokes (which actually included one I hadn’t heard before) — or maybe I have been reading too many of Chickenfoot’s strange tales — but anyway, I’m in a mood for humor.

So here are a couple of old favorites:

— Eric W. Weisstein
from MathWorld–A Wolfram Web Resource

Hat tip: These had gotten lost in the dustbunnies of my memory until I saw the Frivolous Theorem mentioned recently at Art of Problem Solving.

Edited to add: Scott at Grey Matters recently updated his Mathematical Humor post, which may be where I had originally read these. He links to several more great MathWorld jokes, including the ever-tasty Pizza Theorem.

Welcome, Princess Kitten!

Posted on by Denise Gaskins

Not to be outdone by her older brother, Princess Kitten insisted on starting a blog of her own:

Kitten’s Purring

I have given them a section of my blogroll. If you are interested, they would both love to have you drop by and read their stories. Chickenfoot is writing in the “fractured fairytale” vein, at least for now, while Kitten’s tales tend toward animal adventures.

This teacher’s opinion: It certainly beats those dreaded “Pretend you’re a pencil” essays!

Game: Tens Concentration

Posted on by Denise Gaskins

Math concepts: addition, number bonds for 10, visual memory
Number of players: any number, mixed ages
Equipment: math cards, one deck

Set Up

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.

Continue reading Game: Tens Concentration

Quotations XII: Mathematicians at Play

Posted on by Denise Gaskins

This week’s quotes for teachers:

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

— Paul Halmos

There are many things you can do with problems besides solving them. First you must define them, pose them. But then, of course, you can also refine them, depose them, or expose them, even dissolve them! A given problem may send you looking for analogies, and some of these may lead you astray, suggesting new and different problems, related or not to the original. Ends and means can get reversed. You had a goal, but the means you found didn’t lead to it, so you found new goal they do lead to. It’s called play.

Creative mathematicians play a lot; around any problem really interesting they develop a whole cluster of analogies, of playthings.

— David Hawkins
The Spirit of Play [pdf, 1.4MB]
quoted by Rosemary Schmalz, Out of the Mouths of Mathematicians

Top 10 Reasons To Homeschool

Posted on by Denise Gaskins

This week’s Carnival of Homeschooling highlights the Department of Education’s (yes, the federal government agency) list of top reasons to homeschool your children. Janine Cate of Why Homeschool, the carnival’s home blog, says:

I’ve noticed that these reasons for homeschooling are phrased with the assumption that there must be something wrong with the school, wrong with the child or wrong with the family to motivate homeschooling. This is not surprising considering the list came from the Department of Education. Thus, I’ve added my own commentary in parenthesis.

It is an interesting read, as are the many homeschooling blog articles in the carnival. Check it out!

As I write, there is still time to send in your submissions for this week’s Carnival of Education, which should be up sometime tomorrow at The Education Wonks. I will come back then to put up a specific link.

Edited to add: The Carnival Of Education—Week 127 is now posted.

How to Make Math Cards

Posted on by Denise Gaskins

Many of the games on this blog call for Math Cards. You do not need to look for these in stores or in your school supply catalog. Math cards are simply a modified deck of normal, poker-style playing cards. Remove all face cards and jokers from the deck, leaving the ace through ten of each suit. Or use a set of Rook cards, without the bird.

Using the ace as a one, this gives you four sets of numbers 1-10, and you will be ready to play your way to fluency in almost any arithmetical topic: addition, subtraction, multiplication, division, greater-than/less-than, fractions, negative numbers, and more.

Card Holder for Young Hands

Math card holder

Little hands often have trouble holding more than a few cards at a time. Your child may enjoy making and using a card holder.

Save the plastic lids from two large margarine tubs or similar containers. Place the lids together, top to top. Line up the edges, then staple them together, putting two or three staples near the center of the lids. Let your child decorate the card holder with stickers, if desired.

To use the card holder, slip playing cards between the two lids and fan them out. The lids will hold the cards upright, so the child can easily see them all.

 
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“How to Make Math Cards” copyright © 2007 by Denise Gaskins.