### The rectangle game.

I'm not going to tell you what this lesson plan is designed to teach.

See if you can guess

. But even if you can not guess the "official" name, it is perhaps less important than noticing the patterns.

If you

*do* work out the "subject", or think you have, please do not post the answer. Just PM me. The reason for this is that once you "see" the answer, the exercise becomes useless.

This is another exercise to encourage the investigation of the natural world.

O.K. As the teacher, you have some preparation to do. First the ingredients.

103 marble set. (assuming the marbles are 1cm in diameter)

Minimum requirement:

***2 cloth bags with a pull chord on the top...

***1 bag, say 7x7 cm, the other say, 10x10 cm

***103 marbles, all the same size. (they can be stored in the bags)

***1 large piece of thick card (the board) 54 cm x 54 cm (54 diameters)

***Pin holes should be drilled every 1 cm (or the diameter of the marbles)

***thick card strips (triple or more thickness) 2 x 54 cm and 2 x 27 cm

***(Pin holes should be drilled every 1 cm (or the diameter of the marbles))

***blunt pins that fit in the holes, so the strips can be held on the board.

***A printout with all the numbers from 1 to 103 down the side.

For a flashy set, you can have a wooden board and wooden strips, more bags, more marbles.

The game.

Rules.

On the first turn, children may choose any number from 22 to 66. (Subsequently, any number is OK). They put that number of marbles into a bag, and take the bag and card strips to the board (physically separated from the large bag of marbles.)

They must create as many rectangles as possible with these marbles. (eg 48 marbles = 12x4 and 6x8 etc)

They must make rectangles, not lines. Anything 1 x something is not allowed.

No spaces in the rectangle are allowed, and no left over marbles either.

They must note down on their print-out against the numbers in question, the rectangles they find.

Which numbers have the most rectangles?

Are there any numbers with no rectangles?

Â©Alexander Streater 2001

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