## Kiss those Math Headaches GOODBYE!

### Summertime Geometry Scavenger Hunt

Here’s a nice summer-days math project …

I just happened to be looking at the NM Highway signs page online a couple of days ago when I saw this nice little list of signs, just below:

NM Highway Signs

I couldn’t help but notice that there are quite a few recognizable geometric figures on this page, and I thought, “This would be a cool thing to show to kids who either have studied, or are studying geometry.”

My suggestion: Show this to your children and ask them how many geometric figures they can recognize.

### Rubik’s Slide: play your way to geometric knowledge

A toy that educates … could it be a dream?

I recently found something that fits that category, educating students in concepts of GEOMETRY.

It’s called the Rubik’s Slide, created by Techno Source. I bought this Rubik’s Slide a few months ago because I needed another puzzle to keep my tutoring clients entertained while I grade their work, which I often do at the start of sessions.

Rubik's Slide Logo

### Times Tables, Learning the Threes

What’s more important for early math than knowing the times tables?

Not much, right?

Since the times table facts are so fundamental, and because many students struggle with them, I’d like to share a strategy I came up with today for
learning the 3s. This technique works particularly well with students
who struggle with memorizing apparently random facts. (We know these
facts are not random, but if learned with nothing more than flash cards,
they can appear random.)

The strategy involves three stages, each stage bringing the child closer
to being able to QUICKLY access the desired multiplication facts. Here are the stages, in order they should be taught.

STAGE ONE:  “Patty-Cake Threes”

What I do here amounts to a “patty-cake” approach to learning the threes, which works like this.

The student and I sit facing each other with our hands up. We hit our right hands together and say “one,” then hit our left hands together and say “two.” Then we
hit BOTH HANDS TOGETHER and say, “THREE.” When saying the “one” and “two,” we utter the numbers quietly. But when we say “THREE” and all successive multiples of three, we say these numbers loudly, almost (but
not quite) shouting.

After three, we continue:  “four, five, SIX … seven, eight, NINE, ten,
eleven, TWELVE … ” and so on. So this gives children a fun way to
hear — and get a feel in their body for — the multiples of three, in the proper
order.

Image by davie_the_amazing via Flickr

STAGE TWO:  “Finger-Drumming”.

After the child has the rhythm of the number three, from the “patty-cake” approach, we do “finger-drumming.” To “finger-drum” the multiples of 3, the child makes a fist with one hand, and shakes it, saying with each shake, “one, two, THREE!” And when saying “THREE,” the child extends one finger from the fist. The child continues: “four, five, SIX,” and at “SIX,” he extends another finger, so he has two fingers out.

Then you ask the child, for example, “What is three times two?” Answer: the number he just said, “six.”

In this way, the child can “finger-drum” out all of the multiples of three. To
reinforce the times tables as you go, ask questions like:  “What is 3 x 4? What is
3 x 5? etc.” Each time you ask, the child must “finger-drum” till s/he gets the
correct answer. This flows very nicely from the “patty-cake” approach as it
builds on the rhythmic feel for counting in threes.

STAGE THREE:   “Finger-Skip-Counting”   The third stage follows “finger-
drumming.” To begin finger-skip-counting, the child must have done enough “finger-drumming” so s/he is quite familiar with the multiples in the correct order.

To “finger-skip-count,” 3 x 4, for example, the child holds out a fist and
runs through the multiples of 3, like this:  “Three (extending one finger), Six (extending two fingers), Nine (extending three), Twelve (extending four fingers).”  You ask, “So what is 3 x 4?” And the child answers:  “3 x 4 equals 12.”

I found it helpful to first just challenge the child with the multiples from 3 x 1 through 3 x 5. Once s/he develops competence there, proceed to “finger-skip-counting” the multiples from 3 x 6 through 3 x 10. Finally do 3 x 11 and 3 x 12.

Put all together, these three stages offer a fun and rhythmic way for children
to learn their multiples of three. I’m curious to find out if I can use a similar
approach for the 4s, and I’ll find out soon.

I can’t be sure, but it seems like children could probably learn their 4s
by jumping rope, or doing other activities with a rhythmic nature.

If any of you have used an approach like this one for learning the times
tables, feel free to share it.

### Play a game, meet John Nash

This blog post falls into the category of “pure fun,” at least for people who enjoy board games.

Here’s a board game that is easy to learn, fun to play, enjoyed by people of all ages, and best of all — invented by two world-class mathematicians: Piet Hein and John Nash.

The game is generally called Hex*, and you can even play it online.

The rules of Hex are so easy that anyone can grasp them fast. They are: use game tokens to create an unbroken path that goes from one side of the game board to the other. You get to put down one token on every turn, and players alternate putting them down. Tokens, once put down, cannot be taken off the board. Tokens do not kill other tokens, jump or move in any other way. Their sole purpose is to be part of a path that traverses the board.

Of course, as one player tries to go from his side of the board to the other, the other player tries to do the same, but from her side of the board to the other. As you defend against the other player’s path, you start to make your own path. Very interesting.

The best thing to do with this game, though, is just play it. To that end, go to any site online that has the game. I recommend either of these sites:

This one allows you to play on a 7×7 board, and it has background info on the game and some strategy tips.

This one lets you play on a board that is 11 x 11, and it allows you to record your moves and get a record of your moves, for study.

I have brought Hex — along with checkers, go and chess — to various “Games Nights” that I have organized and run at local schools and rec centers. Invariably more people end up playing Hex than any of the other games. It has a sort of magnetic attraction quality to it.

Try it and see for yourself.

* One note about the name. The story goes that Nash invented the game one night while sitting on the “john” in a bathroom at Princeton. The floor of the bathroom, tiled in hexagons, gave Nash the idea for the game. So the game is sometimes affectionately called “John” in honor of both the inventor and place of discovery.

P.S.: For a good book about the game, check out Hex Strategy by Cameron Browne. I got my copy through Amazon. The book also has templates that allow you to create your own physical game boards. It also brings out many of the mathematical ways of looking at the game.