Transum Software

Tangram Christmas Tree

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

Holly Holly

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.

Tangram Christmas Tree

You can decide whether or not overlapping pieces are allowed.

Tangram Christmas Tree

Your tree must be symmetrical.

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



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.



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.



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.



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.



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

Your tangram is now ready to be cot out.

How many of your tangram pieces are polygons? Correct Wrong
How many of the pieces have at least one line of symmetry? Correct Wrong
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? Correct Wrong
How many times bigger is the area of one of the larger triangles than the area of the small triangle? Correct Wrong
How many of the pieces have an interior angle sum of 360°? Correct Wrong

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.


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.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

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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?

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Featured Activity

Great Expectation

Great Expectation

An interactive online activity requiring logical thinking and a certain amount of luck. Numbers 1 to 6 are presented randomly and are to be used to produce two 2-digit numbers. Can you ensure that the first number is greater than the second?


There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

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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.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


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Description of Levels



Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up