Topicme258ff22ae862c65_1528449000663_0Topic

The properties of the quadrangles

Levelme258ff22ae862c65_1528449084556_0Level

Second

Core curriculumme258ff22ae862c65_1528449076687_0Core curriculum

IX. Polygons and circles. The student:

4) recognises and identifies: the square, the rectangle, the rhombusrhombusrhombus, the parallelogramparallelogramparallelogram and the trapeziumtrapeziumtrapezium;

5) is familiar with the most important properties of the square, the rectangle, the rhombusrhombusrhombus, the parallelogramparallelogramparallelogram and the trapezium; recognises the figures symmetrical about the axis and indicates the symmetry axes of figures.

Timingme258ff22ae862c65_1528449068082_0Timing

45 minutes

General objectiveme258ff22ae862c65_1528449523725_0General objective

Creating and interpreting mathematical texts, presenting data graphically.

Specific objectivesme258ff22ae862c65_1528449552113_0Specific objectives

1. Recognising the type of the quadranglequadranglequadrangle on the basis of its basic properties.

2. Calculating the perimeterperimeterperimeter of the quadrangle.

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

Learning outcomesme258ff22ae862c65_1528450430307_0Learning outcomes

The student:

- identifies the type of the quadranglequadranglequadrangle on the basis of its basic properties,

- calculates the perimeterperimeterperimeter of the quadrangle.

Methodsme258ff22ae862c65_1528449534267_0Methods

1. Situational analysis.

2. Flipped classroom.

Forms of workme258ff22ae862c65_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionme258ff22ae862c65_1528450127855_0Introduction

Students cut out paper models of the rectangle, the square, the rhombusrhombusrhombus, the parallelogramparallelogramparallelogram, the isosceles trapezium, the right trapezium the scalene trapeziumtrapeziumtrapezium and bring for the lesson.

Students are going to work using the flipped classroom method.

At home they familiarise themselves with the material included in the e‑book:

http://www.epodreczniki.pl/reader/c/114190/v/21/t/student-canon/m/iA1QepTWvL

Task

The students identify the type of the quadranglequadranglequadrangle depending on the properties of its diagonals:

a) the quadrangle with the diagonals of equal length,

b) the quadranglequadranglequadrangle with the diagonals which divide into halves and,

c) the quadrangle whose diagonals are perpendicular to each other.

Procedureme258ff22ae862c65_1528446435040_0Procedure

Students and the teacher revise the basic properties of the quadrangles.

Using the material the students have learned at home they are going to compete for the title of a quadranglequadranglequadrangle expert.

Task

The students place the quadrangles they prepared on the desk.

The teacher names one of the properties of the quadrangles and the students’ task is to pick up the appropriate quadranglequadranglequadrangle. The student who is the fastest in pointing at the appropriate quadrangles and does not make any mistakes becomes an expert.

The properties of quadrangles:

- The quadrangle with at least one pair of parallel sides.
- The diagonals of this quadrangle intersect at the right angle.
- One of the diagonals of this quadrangle divides the other into half.
- This quadrangle has got two pairs of equal adjacent sides.
- This quadrangle has got two pairs of parallel sides.
- The quadrangle has got all equal sides.
- One of the diagonal is the axis of symmetry of this quadrangle.
- The parallel sides are of equal length.
- The diagonals of the quadrangle intersect at the point which divides them into halves.
- The opposite sides of the quadrangle are of equal length.
- The quadrangle has at least one arm perpendicular to the base.
me258ff22ae862c65_1527752263647_0- The quadrangle with at least one pair of parallel sides.
- The diagonals of this quadrangle intersect at the right angle.
- One of the diagonals of this quadrangle divides the other into half.
- This quadrangle has got two pairs of equal adjacent sides.
- This quadrangle has got two pairs of parallel sides.
- The quadrangle has got all equal sides.
- One of the diagonal is the axis of symmetry of this quadrangle.
- The parallel sides are of equal length.
- The diagonals of the quadrangle intersect at the point which divides them into halves.
- The opposite sides of the quadrangle are of equal length.
- The quadrangle has at least one arm perpendicular to the base.

Task

Students work individually, using their computers. They are going to observe how the perimeterperimeterperimeter of the quadranglequadranglequadrangle changes depending on the lengths of its sides and angles.

[Geogebra applet]

After completing the task, the students complete the following sentence.

The perimeterperimeterperimeter of the trapeziumtrapeziumtrapezium is the sumsumsum of …….. sides. (all its)

Task

The students calculate the perimeterperimeterperimeter of the trapezium.

In your notebook draw the isosceles trapeziumtrapeziumtrapezium whose one base is 8 cm. The other base is 2 cm shorter and the arms are twice as short as the bottom base. Calculate its perimeterperimeterperimeter.

Selected students summarise the material they have learned by answering the following questions:

What types of quadrangles do you know?

How can we calculate the perimeterperimeterperimeter of the quadranglequadranglequadrangle?

Self‑study task

Find on the Internet the information about the dimensions of the Santiago Bernabeu stadium which is situated in Spain. Next, calculate the perimeterperimeterperimeter of the quadrangle‑shaped pitch.

Lesson summaryme258ff22ae862c65_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

Then, they write down properties of the quadrangles which they memorised:

-Each quadrangle has got two diagonals.
-The perimeter of the quadrangle is the sum of all its sides.
me258ff22ae862c65_1527752256679_0-Each quadrangle has got two diagonals.
-The perimeter of the quadrangle is the sum of all its sides.

Selected words and expressions used in the lesson plan

angleangleangle

axis of symmetryaxis of symmetryaxis of symmetry

diagonaldiagonaldiagonal

parallelogramparallelogramparallelogram

perimeterperimeterperimeter

quadranglequadranglequadrangle

rhombusrhombusrhombus

right angleright angleright angle

sumsumsum

trapeziumtrapeziumtrapezium

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rhombus1
rhombus

romb – równoległobok, który ma wszystkie boki równe

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wymowa w języku angielskim: rhombus
parallelogram1
parallelogram

równoległobok

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wymowa w języku angielskim: parallelogram
trapezium1
trapezium

trapez

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wymowa w języku angielskim: trapezium
quadrangle1
quadrangle

czworokąt

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wymowa w języku angielskim: quadrangle
perimeter1
perimeter

obwód

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wymowa w języku angielskim: perimeter
sum1
sum

suma

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wymowa w języku angielskim: sum
angle1
angle

kąt

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wymowa w języku angielskim: angle
axis of symmetry1
axis of symmetry

oś symetrii

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diagonal 1
diagonal

przekątna

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right angle1
right angle

kąt prosty – ma 90 stopni

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wymowa w języku angielskim: right angle