# Tangram Challenge

## Who can be the first to make ...

... a triangle from 2 pieces?

... a parallelogram from 2 pieces?

... a rectangle from 2 pieces?

... a trapezium from 2 pieces?

... a pentagon from 2 pieces?

... a parallelogram from 3 pieces?

... a rectangle from 3 pieces?

... a triangle from 3 pieces?

... a trapezium from 3 pieces?

... a pentagon from 3 pieces?

... a parallelogram from 4 pieces?

... a triangle from 4 pieces?

... a trapezium from 4 pieces?

... a rectangle from 4 pieces?

... a pentagon from 4 pieces?

... a triangle from 5 pieces?

... a rectangle from 5 pieces?

... a rectangle from 6 pieces?

... a parallelogram from 5 pieces?

... a parallelogram from 6 pieces?

... a pentagon from 5 pieces?

... a pentagon from 6 pieces?

... a triangle from 7 pieces?

... a rectangle from 7 pieces?

... a trapezium from 5 pieces?

... a trapezium from 6 pieces?

... a trapezium from 7 pieces?

... a parallelogram from 7 pieces?

... a pentagon from 7 pieces?

... a star from 7 pieces?

This is a test of speed designed as a fun, whole-class activity. Pupils can use a paper tangram (see instructions below) or, if they have access to computers, could use the click-and-drag tangram below. Hold down the shift key [or shift] while you drag to rotate the pieces.

Here are the instructions for creating your own trangram from a square piece of card.

## 1

Using a pencil and ruler draw a diagonal line from the top right to bottom left corners of your square.

Take your time and be as accurate as possible.

## 2

Measure the lengths of a side of your square to the nearest milimetre.

Halve this measurement to find the mid points of the right and bottom sides.

Join these two points with a straingt line.

## 3

Place you ruler on the square as if you are going to draw the other diagonal.

Draw the line along your ruler from the top left point of the square until you reach the line you drew in instruction 2.

## 4

Draw a line parallel to the line you drew in instruction 2 that passes through the midpoint of the right side of the square as shown in the diagram.

You clould use a set square to help you draw parallel lines.

## 5

Draw a line parallel to the bottom of the square as shown to complete the tangram.

More Tangram Maths, Transum

Friday, March 16, 2018

"Write down the mathematical shape names for each of the 7 pieces.
Place the pieces in order of size, with the smallest first.
If a tangram puzzle makes an 8cm by 8cm square, what would be the areas of each of the pieces?
What would be the perimeters of each of the pieces?
What are the angles in each of the pieces?"

Henry Ernest Dudeney, Amusements In Mathematics

Friday, March 16, 2018

"The late Mr. Sam Loyd, of New York, who published a small book of very ingenious designs, possessed the manuscripts of the late Mr. Challenor, who made a long and close study of Tangrams. This gentleman, it is said, records that there were originally seven books of Tangrams, compiled in China two thousand years before the Christian era. These books are so rare that, after forty years' residence in the country, he only succeeded in seeing perfect copies of the first and seventh volumes with fragments of the second. Portions of one of the books, printed in gold leaf upon parchment, were found in Peking by an English soldier and sold for three hundred pounds. A few years ago a little book came into my possession, from the library of the late Lewis Carroll, entitled The Fashionable Chinese Puzzle. It contains three hundred and twenty-three Tangram designs, mostly nondescript geometrical figures, to be constructed from the seven pieces."

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There are solutions with diagrams to this puzzle but they are only available to those who have a Transum Subscription.

Don't forget to try Tangram Template and Tangram Table.

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