Tan gram :
2.1 Introduction
Tan gram is a useful manipulated material to teach geometry teaching specilly in school level which can we make by using plastic, plywood and card paper . The tan gram is a dissection puzzle consisting of seven flat shapes , called tans , which are put together to form shapes . The objective of the puzzle is to form a specific shape (given only in outline or silhouette ) using all seven pieces, which may not overlap . Tan gram is a one kind of geometrical shape which are as follows:
The invention of the tan gram puzzle is unrecorded in history . The earliest known chinese book is dated 1813 but the puzzle was very old by then . one reason for this could be that in china , its country of origin , at the time it was considered a game for women and children . This would have made it unworthy of "serious " study and unlikely to be written about . Different times , different ways of thinking.
The roots of the word Tan gram are also shrouded in time , with a number of possible explanations . The one I like best involves the Tanka people. These river people of china wree great traders who were involved in the opium trade . The western sailors they traded opium with likely played with the puzzle when they visited their Tanka girlfriends .The story I believe is that it comes from the obsolete English word "tramgram " meaning puzzle or trinket .
Tan grams enjoyed a surge of interst during the 19th century in Europe and America . This , no doubt , was due to the opening up of trade with china and the aforemantioned sailors bringing home new found amusements . "The chinese puzzle " spawned a flood of books and picture card sets. Some quite elaborate chinese examples exist with pieces carved from and / or inlaid with ivory , jade and other fine materials . others were cheap , locally made copies in wood or fired clay . some books blindly reproduced previous mistakes in the patterns . some things never change.
In 1903, sam Loyd wrote his great spoof of Tan gram history , the Eighth book of Tan . He had many people convinced that the game was invented 4000years ago by the god Tan . According to Loyd , the first 7 Books of tan were linked with many famous people and historical events . All very convincing and it made sam a lot of money . Later examination showed it to be a colossal joke . The book did catalog over 600 patterns , many by Loyd himself . He also introduced (along with H.F .Dudeney ) the idea of paradoxes.
Fu Tsiang wang and chuan – chin Hsiung mathematically proved in 1942 the existence of a finite set of patterns feferred to as " convex" . In this context, it means that there are no indentations along the outside edge. There are only 13 silhouettes that qualify . other finte sets may exist.
Tan grams continue to entertain and frustrate now days . The puzzle attracts people on a number of levels . it's simplicity makes it accessible to a broad spectrum of people . The figures spark visually inclined people though their form , liveliness and striking simplicity .Many of the designs are adaptable to quilting , applique and many other artistic or craft projects . story tellers can weave a tale with many characters and objects using only the seven tans . it interests the math inclined with the geometry and ratios of the pieces .you find them used in classrooms around the world to teach basic math ideas in an intersting way.
2.3 construction of Tan gram
Materials
· A rectangular pieces of paper of suitable for folding
· A pare of scissors
· A pair of scissors a ruler (optional )
Activities
A complete set of tangrams consists of seven pieces ;
· A small square
· Two small congruent triangles
· Two large congruent triangles
· A medium – size triangle
· A parallelogram
You can make your own set of tan grams from a single piec of paper . just follow thes simple steps ;]
2.4 Making of Tan gram pieces
Probably the tan gram pieces are developed from cutting a 4 X4 – square in pieces-
You use it to make tangram pieces . you draw a 4X4 –square with some diagonals on plywood or on cardboard . then you saw or but the pieces as shown at the drawing .
Creating a set of tan grams from written instructions is a great exercise in geometry vocabulary and following directions . you can do this to have your students make tan grams and use them with some of the other activities. Here are the instuctions I use with you students . with younger students , you "ll want to lead the class in this constructions ; with older students , you may wish to supply written instructions and have them work on construction in groups .
1. Start with a square pieces of construction paper .
2. Fold in half along the diagonal and cut along the resulting crase .
3. 3.Fold one of the resultant n half and cut .set these two pieces aside (1&2).
4. Find the midpoint of the hypotenuse of the remaining large triangle by folding and lightly creasing .
5. Fold the triangle so that the vertex of the right angle touches the midpoint of the
6. Hypotense .cut along the resulting crease , and set aside the small triangle (3).
7. Fold the ramaining trapezoid in half along its line of symmetry and cut into two smaller trapezoids.
8. Fold one trapezoid so that the vertices at the ends of the longest edge meet. Cut along the crease to make a small triangle and a square (4&5).
9. Fold the other trapezoid so that the obtuse angle meets the right angle at the opposite
Vertex. Cut along the crease to make another small triangle and a parallelogram (6&7).
2.5 Use of Tan gram:
This is used in geometrical teaching for geometrical shaped their relation. This is more useful in teaching geometry for started steps students. We make different kinds geometrical shapes by using tan gram some modes are as
We can to teach concept of congruent triangles and area of parallelograms using pieces 6 and 7 of Tan gram as well as concept of similarity of triangles using pieces 3 and 6.
We use Tan gram to teach different convex figures
Reference:
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