Tangram

The tangram (Chinese: 七巧板; pinyin: qīqiǎobǎn; literally: 'seven boards of skill') 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 an outline or silhouette) using all seven pieces, which can not overlap.

How to Play?

To move the pieces, drag on the centre of each piece.

To rotate, drag on the vertice of the piece with the curved arrow sign.

Piece 4 is special and has the ability to flip, due to its unique shape.

The combobox has several options and starts by default a square.

Currently, there are house and cat but more can be added if requested by teachers.

The hint when selected will place all the pieces into the respective outlines

The show Length when mouse over will show the length of the outline which is the perimeter when added together

The reset button will set the original states into the simulation.

Area and Length

piece 1, medium right triangle,$$ area = \frac{1}{2} *base*height = \frac{1}{2}*6*6= 18 $$ $$length of sides = 6,6,6 \sqrt{2}$$

piece 2, small right triangle,$$ area = \frac{1}{2} *base*height = \frac{1}{2}*6*3= 9 $$ $$length of sides = 6,3\sqrt{2},3\sqrt{2}$$

piece 3, square,$$ area = length*height = 3\sqrt{2}*3\sqrt{2}= 18 $$ $$length of sides = 3\sqrt{2},3\sqrt{2},3\sqrt{2},3\sqrt{2}$$

piece 4, parallelogram,$$ area = *base*height = 6*3= 18 $$ $$length of sides = 6,3\sqrt{2},6,3\sqrt{2}$$

piece 5, small right triangle,$$ area = \frac{1}{2} *base*height = \frac{1}{2}*6*3= 9 $$ $$length of sides = 6,3\sqrt{2},3\sqrt{2}$$

piece 6, large right triangle,$$ area = \frac{1}{2} *base*height = \frac{1}{2}*12*6= 36 $$ $$length of sides = 12,6\sqrt{2},6\sqrt{2}$$

piece 7, large right triangle,$$ area = \frac{1}{2} *base*height = \frac{1}{2}*12*6= 36 $$ $$length of sides = 12,6\sqrt{2},6\sqrt{2}$$

Special Feature

This tangram is designed for aligning to Mathematics learning of area and perimeter, see bottom right corner text box in yellow.

The objectives are to get students to be problem solving (laying the pieces into the different shapes while having a easy way to understand the area of the tangram is a constant while the perimeter is not constant and depends on the outline of the shape.

Lesson Flow

Teacher will instruct students to calculate the area of the square, which simply is 12*12 = 144 m^2

Teacher to demonstrate basic interactions using the simulation such as drag on numbers to move pieces, drag on pointed vertice to rotate pieces.

Students are asked to calculate the area of the 7 pieces individually and sum up the total.

With the aid of the combobox option -house, teacher to demonstrate how to move and rotate the pieces to form a house.

Teacher will instruct students to do this same task on their phones via the mobile browser chrome or equivalent

Notice the students should think and struggle to complete the house, problem solving.

For challenge, students can also form shape of a cat.

Synthesizing together,what can the students conclude about the the area of the square = 144 m^2, the house and the cat?

Discuss why the area is a constant? What are the observable data that suggests the total area is a constant?

Similarly, do the same for perimeter

The check box show Length can be used on computer on entering the outline that reveals the length, students that can simply add all the numbers on the outline to find out the perimeter.

Synthesizing together,what can the students conclude about the the perimeter of the square = 48 m , the house = 61 m and the cat = 81 m approximately?

Discuss why the perimeter is not constant? What are the observable data that suggests the perimeter is not constant?