TANGRAMS - An Introduction
The concept of TANGRAM PUZZLES is believed to be originated in
These 7 components of can be obtained by following the following steps:
Step 1: Cut out a square piece of a thin card board of suitable size, say 8cm. or any other multiple of 4 units so that it may be easily split in to a 4X4 Grid as shown below:
Step 2: In the 4X4 grid obtained in step1 draw the lines indicted by red lines in the figure drawn on the right.
Step3: By moving a cutter (may be a pair of scissors along the red lines to get the 7 components of the Tangrams Puzzles. These components will be of following shapes:
1 2 3
4 5 6 7
These 7 pieces are the basis of all tangram puzzles.
For each puzzle a shape is given, and you have to find how to make that shape using
ALL 7 PIECES.
Here is an example of a puzzle and its solution -
Puzzle Solution
Here are 3 puzzles for you to try
1.
2. 3.
Now, see if you can fit all the pieces together to make a rectangle:
You can put the 7 pieces together in different ways to make other pictures shown below:
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| Bridge | Pipe | Rabbit | Runner |
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| Candle | Another Candle | Cat | Bird |
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| Hexagon | Another Hexagon | Another Bird | One More Bird |
Educational value of the 7 components of ‘TANGRAMS’
These components can be used for learning the concept of:
· Geometric Shapes
· Congruency of triangles
· Fractional numbers and equivalent fractions
· Areas
etc.
For example: By placing the second cut out of the 7 pieces of the ‘Tangram Puzzles’ obtained above on the first cut out, you may observe that the two components These components can be used for learning the concept of of same shape and size and hence that of congruency.
Again placing the same cut outs in an adjacent position as shown below, we may observe that the diagonal of a rectangle divides the rectangle into two congruent triangles.
Each of the two triangles is ½ of the whole rectangle.
Therefore area of one of the two triangles is ½ times the area of a rectangle.----------(1)
By placing the same cut outs on a 10X10 grid in the position of forming a rectangle and counting the number of squares being covered by the rectangle thus formed, we may deduce the formula:
Area of a rectangle = length X breadth square units ---- (2)
Results (1) and (2) imply that
Area of a triangle = ½ Base X Height square units
etc.
Jigsaw puzzle with four parts
My learned colleague Professor Götz directed my attention to the following problem. The four coloured areas are moved, their shape remains exactly the same ... but look what happens:
Solution
Both polygones are not triangles but (different) quadrilaterals. Figure 1 shows (in an exaggerated way) the deviation of these quadrilaterals from a triangle. The lower quadrilateral is convex, the upper one is not.
Figure 1
Figure 2 shows the exact representation of both near-triangular quadrilaterals. As all vertices of both quadrilaterals coincide with a lattice point (see the grey crosses) their areas are easily calculated to 32 and 33 square units.
Figure 2
Nets for Solid Shapes
Cube
To make a net of a cube, first look at one, such as a dice.
How many sides does it have?
Six, so make sure that your net has 6 squares.
Now you must work out a way to arrange six squares so that on folding them you may get a cube.
The easiest way is to think of a cube as a combination of six identical faces- four sides, a top and a bottom.
Arrange four squares in a line to get you the side faces.
Now put the top square on one side of this line and the bottom on the other.
There are 6 possible arrangements (apart from rotations and reflections).
Now, see if you can find all the nets for a cube by looking at the following nets:.
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After selecting a correct net design, we need to draw it out.
Here is one of them as an example.
See if you can work out which nets will make a tetrahedron. There are two correct nets
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In fact there are two correct nets in the above picture.
See if you can find all the nets for an octahedron below.
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| There are eleven correct nets in this picture. |
Tetrahedrons are not very common. They do have one useful property:
They are very stable.
Normally, tetrahedron packaging are used for storing liquids, such as fruit juice.
These are made in a very tactful manner, which we can try for ourselves.
Make a cylinder of paper and glue its edge down.
Pinch one end, and glue that.
Now pinch the other end in the opposite direction, and glue that.
It will naturally form a tetrahedron.
For doing so, might have to play around with the dimensions of the cylinder to get a regular tetrahedron.
