# Tangram Christmas Tree

## Accurately construct a tangram puzzle then use it to make a Christmas tree and answer a short quiz.

You will need a square piece of paper. Thick Christmas wrapping paper is perfect!

Follow the instructions to make a tangram and then use it to create a Christmas tree.

 You can decide whether or not overlapping pieces are allowed. Your tree must be symmetrical.

When you have finished there will be a short quiz about your tangram tree.

## 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 straight 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.

 How many of your tangram pieces are polygons? How many of the pieces have at least one line of symmetry? The largest triangles are similar to the smallest triangle. How many times bigger are the sides of the larger triangles than the corresponding sides of the small triangle? How many times bigger is the area of one of the larger triangles than the area of the small triangle? How many of the pieces have an interior angle sum of 360°?
Check

Use your tangram pieces to do the activity called Tangram Table.

Race against your classmates with Tangram Challenge.

You could also try some other Christmaths Activities.

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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#### Tower of Hanoi

Move the pieces of the tower from one place to another in the minimum number of moves. This puzzle was invented in 1883 but is still as captivating today as it was all those years ago.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

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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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