Topicm657f585f82572fd7_1528449000663_0Topic

The tangrams

Levelm657f585f82572fd7_1528449084556_0Level

Second

Core curriculumm657f585f82572fd7_1528449076687_0Core curriculum

XI. Calculations in geometry. The student:

4) Calculates the areaareaarea of the polygons using the method for dividing into smaller polygons or completing to the larger ones as in the following situations:

[Illustration 1]

VI. The elements of algebra. The student:

2) uses letter marking of unknown numerical values and writes down simple algebraic expressions on the basis by the information in a practical context, for example writes the perimeterperimeterperimeter of the triangle with the sides of: a, a+2, b.

Timingm657f585f82572fd7_1528449068082_0Timing

45 minutes

General objectivem657f585f82572fd7_1528449523725_0General objective

Matching a mathematical model to the simple situations and using it in various contexts.

Specific objectivesm657f585f82572fd7_1528449552113_0Specific objectives

1. Calculating the areaareaarea of the polygonpolygonpolygon using the method for dividing into smaller polygons.

2. Writing simple algebraic expressions describing the perimeterperimeterperimeter of the figurefigurefigure.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competencies; developing learning skills.

Learning outcomesm657f585f82572fd7_1528450430307_0Learning outcomes

The student:

- calculates the areaareaarea of the polygons using the method for dividing into smaller polygons,

- writes down the simple algebraic expressions to describe the perimeterperimeterperimeter of the figurefigurefigure.

Methodsm657f585f82572fd7_1528449534267_0Methods

1. Practical exercises.

2. Situational analysis.

Forms of workm657f585f82572fd7_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm657f585f82572fd7_1528450127855_0Introduction

The student brings the tangramtangramtangram to the class.

The teacher introduces the topic of the lesson: learning about the tangram and the properties of its elements.

Procedurem657f585f82572fd7_1528446435040_0Procedure

The teacher introduces the tangramtangramtangram:

The tangram is a puzzle. It comes from China and it has been known for 3000 years. The first European mentions about tangram come from the 18th century.m657f585f82572fd7_1527752263647_0The tangram is a puzzle. It comes from China and it has been known for 3000 years. The first European mentions about tangram come from the 18th century.

The tangram is the square divided into 7 parts: 2 large right triangles, 1 middle right triangle, 2 small right triangles, 1 square, 1 parallelogram. Each of the parts is called the tan.m657f585f82572fd7_1527752256679_0The tangram is the square divided into 7 parts: 2 large right triangles, 1 middle right triangle, 2 small right triangles, 1 square, 1 parallelogram. Each of the parts is called the tan.

[Illustration 2]

Task

The students look closer at the construction of the tangramtangramtangram, then, they answer the following questions:

Which tans have the equal areas?

How many times the area of the largest triangle larger than the areaareaarea of the smallest one?

How many times the areaareaarea of the smaller triangle less than the area of the squaresquaresquare?

The students should come up with the following conclusions:

- the areaareaarea of the middle triangle equals the area of the parallelogramparallelogramparallelogram and the square,

- the area of the large triangle is four times bigger than the area of the small triangle,

- the area of the squaresquaresquare is twice as big as the areaareaarea of the small triangle.

Task

The students work individually using their computers. They are going to create the green polygonpolygonpolygon using all the seven tans.

[Geogebra applet]

After completing the task the students answer the questions:

Do the arranged polygons have the same area?

How can we calculate the areaareaarea of the complex shaped polygonpolygonpolygon?

Do the arranged polygons have the same perimeterperimeterperimeter?

The students are supposed to draw the following conclusions:

- the arranged polygons have the same areas because the identical figures were used to make them,

- the area of the complex – shaped polygons can be calculated by dividing it into the polygons whose areaareaarea we are able to calculate,

- the arranged polygons have different perimeters.

The students prepare the tangrams they have brought to the class.

Task

a) Use the tangramtangramtangram to arrange the figures presented below. Use all the tans.

b) Assume that the lengths of the sides of the smallest tantantan are d, d, s. Write the algebraic expressions which describe the perimeters of the arranged figures.

[Illustration 3]

An extra task

Use the tangramtangramtangram to arrange the following figures. Use all the tans.

[Illustration 4]

Lesson summarym657f585f82572fd7_1528450119332_0Lesson summary

Students do the exercises summerising the class.

Then, together they sum up the classes, drawing the conclusions to memorize:

- the tangram is a puzzle, the square divided into 7 parts (tans): 2 large right triangles, 1 middle right triangle, 2 small right triangles, 1 square, 1 parallelogram,
- the area of the figures made of all tans equals the area of the whole tangram. Their perimeters may differ.m657f585f82572fd7_1527712094602_0- the tangram is a puzzle, the square divided into 7 parts (tans): 2 large right triangles, 1 middle right triangle, 2 small right triangles, 1 square, 1 parallelogram,
- the area of the figures made of all tans equals the area of the whole tangram. Their perimeters may differ.

Selected words and expressions used in the lesson plan

areaareaarea

figurefigurefigure

parallelogramparallelogramparallelogram

perimeterperimeterperimeter

polygonpolygonpolygon

right triangleright triangleright triangle

shapeshapeshape

squaresquaresquare

tantantan

tangramtangramtangram