Topicm1dccc9b8e4806dc4_1528449000663_0Topic

The classification of the quadrangles

Levelm1dccc9b8e4806dc4_1528449084556_0Level

Second

Core curriculumm1dccc9b8e4806dc4_1528449076687_0Core curriculum

IX. Polygons and circles. The student:

4) recognises and identifies: the square, the rectangle, the rhombus, the parallelogram and the trapezium,

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

Timingm1dccc9b8e4806dc4_1528449068082_0Timing

45 minutes

General objectivem1dccc9b8e4806dc4_1528449523725_0General objective

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

Specific objectivesm1dccc9b8e4806dc4_1528449552113_0Specific objectives

1. Recognising and identifying the quadrangles.

2. Describing the dependences among the quadrangles.

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

Learning outcomesm1dccc9b8e4806dc4_1528450430307_0Learning outcomes

The student:

- recognises and identifies the quadrangles: the square, the rectangle, the parallelogram, the rhombus, the trapezium.

- describes the dependences among the quadrangles.

Methodsm1dccc9b8e4806dc4_1528449534267_0Methods

1. Flipped classroom.

2. Situational analysis.

Forms of workm1dccc9b8e4806dc4_1528449514617_0Forms of work

1. Pair work.

2. Class work.

Lesson stages

Introductionm1dccc9b8e4806dc4_1528450127855_0Introduction

The flipped classroom will be used during the lesson. To realise such method the student revise the material about the quadrangles.

They can use the information on the website epodreczniki.pl.

They are obliged to bring paper models of the rectangles, the squares, the parallelograms, the rhombuses and the trapeziums.

Procedurem1dccc9b8e4806dc4_1528446435040_0Procedure

Task

Students work individually using their computers. They are going to change the position of the vertices of the polygon to make the particular quadrangle.

[Geogebra applet]

After completing the task the students answer the following questions:
Is the square a parallelogram?
Is the rectangle a square?
Is the parallelogram a rhombus?
Is it possible to draw a quadrangle which is not a trapezium?

Students should put the quadrangles they know into appropriate groups: for example the group of the parallelograms should include the square, the rhombus, the parallelogram.

Task
The students work in pairs. Among the paper models one person chooses the rectangle, the other one the parallelogram.

They describe chosen quadrangle to each other.

After completing the task the student should notice the differences between the rectangle and the parallelogram:
1. The diagonals of the rectangle are equal, the diagonals of the parallelogram are of different length.
2. The angles of rectangle are equal and they are 90°, the opposite angles of parallelogram are equal.

In similar way the students indicate the similarities between the square and the rhombus.

They should notice that:
1. The sides of both figures are of the equal length.
2. The diagonals intersect at the right angle and divide into halves.
3. The sum of the interior angles is 360°.

An extra task

Cut out of paper the equilateral triangle. Then, cut the other isosceles triangle with the same base but different length of the arms. Join the triangles with their bases. You will get the quadrangle in a shape of the kite. Such quadrangle is called a deltoid.m1dccc9b8e4806dc4_1527752263647_0Cut out of paper the equilateral triangle. Then, cut the other isosceles triangle with the same base but different length of the arms. Join the triangles with their bases. You will get the quadrangle in a shape of the kite. Such quadrangle is called a deltoid.

Answer the following questions:m1dccc9b8e4806dc4_1527752256679_0Answer the following questions:
1. What can you say about the length of its sides?
2. What can you say about its angles?
3. How many diagonals does the deltoid have?
4. How many degrees are the angles between the diagonals?
5. What other properties do the diagonals have?
6. What figures is the quadrangle divided into by the diagonals?

Lesson summarym1dccc9b8e4806dc4_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

Then, together they sum up the classes, drawing the conclusions to memorize:
1. The rectangle is a trapezium.
2. The square is a rhombus.
3. The rectangle is a trapezium.

Homework:
Design the tessellation by choosing the quadrangles it is made of. Use the A4 size paper sheet.m1dccc9b8e4806dc4_1527712094602_0Design the tessellation by choosing the quadrangles it is made of. Use the A4 size paper sheet.

Selected words and expressions used in the lesson plan

angles of the quadrangleangles of the quadrangleangles of the quadrangle

diagonaldiagonaldiagonal

parallelogramparallelogramparallelogram

quadranglequadranglequadrangle

rectanglerectanglerectangle

rhombusrhombusrhombus

sidesideside

squaresquaresquare

trapeziumtrapeziumtrapezium

vertex of a quadranglevertex of a quadranglevertex of a quadrangle