Topicm358e60ca6f0b634b_1528449000663_0Topic

Axial symmetryaxial symmetryAxial symmetry II

Levelm358e60ca6f0b634b_1528449084556_0Level

Second

Core curriculumm358e60ca6f0b634b_1528449076687_0Core curriculum

XV. Symmetries. The student:

3) identifies axially symmetrical figures, marks their axes of symmetry and completes the figurefigurefigure which is axially symmetrical having the axis of symmetryaxis of symmetryaxis of symmetry and a part of figurefigurefigure given.

Timingm358e60ca6f0b634b_1528449068082_0Timing

45 minutes

General objectivem358e60ca6f0b634b_1528449523725_0General objective

Noticing regularities, similarities and analogies and formulating relevant conclusions.

Specific objectivesm358e60ca6f0b634b_1528449552113_0Specific objectives

1. Learning to formulate conclusions.

2. Identifying examples of axial symmetryaxial symmetryaxial symmetry in architecture, nature, etc.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm358e60ca6f0b634b_1528450430307_0Learning outcomes

The student:

- constructs figures symmetrical with respect to an axis,

- identifies examples of axial symmetryaxial symmetryaxial symmetry in architecture, nature, etc.

Methodsm358e60ca6f0b634b_1528449534267_0Methods

1. Flipped classroom.

2. Learning through observation.

Forms of workm358e60ca6f0b634b_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm358e60ca6f0b634b_1528450127855_0Introduction

The teacher asks students to revise the definition of axial symmetryaxial symmetryaxial symmetry and the construction of points symmetrical with respect to an axis.

Procedurem358e60ca6f0b634b_1528446435040_0Procedure

Task

The image of the polygonimage of the polygonimage of the polygon in axial symmetryaxial symmetryaxial symmetry.

Students work individually using computers.

Their task is to find the image of the polygonimage of the polygonimage of the polygon in axial symmetryaxial symmetryaxial symmetry. Students can create various polygons by changing the location of the vertices.

[Geogebra applet]

Students answer the following questions.

- What is the image of the polygonimage of the polygonimage of the polygon in axial symmetryaxial symmetryaxial symmetry?

Task

Students draw a right‑angled triangletriangletriangle ABC whose catheti are |AC| = 5 cm and |BC| = 12 cm. Find the imageimageimage of the triangle in axial symmetryaxial symmetryaxial symmetry with the axis equal to the hypotenuse of the triangletriangletriangle. The obtained triangle creates a polygonpolygonpolygon with the ABC triangletriangletriangle. Students calculate the perimeter of the obtained polygonpolygonpolygon.

The summary of the exercises is the discussion in which students should draw the following conclusions.

In axial symmetry the image:
- of the point is a point,
- of the line segment is a line segment of the same length,
- of the polygon is a polygon of the same area and perimeter,
- of the circle is a circle of the same radius.m358e60ca6f0b634b_1527752263647_0In axial symmetry the image:
- of the point is a point,
- of the line segment is a line segment of the same length,
- of the polygon is a polygon of the same area and perimeter,
- of the circle is a circle of the same radius.

Axial symmetry on the coordinate system.

The teacher explains that the students can read out the coordinates of symmetrical pointssymmetrical pointssymmetrical points on the coordinate system. The axis of symmetryaxis of symmetryaxis of symmetry can be axis X or Y.

Students think about the properties of the coordinates of te points symmetrical with respect to axis X.

The drawing shows the points on the coordinate system that are symmetrical with respect to axis X.

[Illustration 1]

By transforming point A(x, y) in symmetry with respect to axis X we obtain a point A'(x, -y).m358e60ca6f0b634b_1527752256679_0By transforming point A(x, y) in symmetry with respect to axis X we obtain a point A'(x, -y).

Task

Students think what the coordinates of the pointcoordinates of the pointcoordinates of the point symmetrical to point A (4, 3) will be in the symmetry with respect to axis Y.

Task

Students give the coordinates of the pointcoordinates of the pointcoordinates of the point symmetrical to point A (x, y) in the symmetry with respect to axis Y.

By transforming point A (x, y) in a symmetry with respect to axis Y we obtain the point A' (-x, y).

The teacher points out that symmetry can also be noticed in architecture, nature, etc. However, usually it is the symmetry with respect to a plane, not an axis.

Task

Students watch the pictures. Together they think whether it is possible to identify the axis of symmetryaxis of symmetryaxis of symmetry on them.

[Illustration 2]

Lesson summarym358e60ca6f0b634b_1528450119332_0Lesson summary

Students do the revision exercises.

Then, together they sum‑up the classes, by formulating the conclusions to memorise.

- The coordinates of symmetric points can be given on the coordinate system. The axis of symmetryaxis of symmetryaxis of symmetry can be axis X or Y.

- By transforming the point A (x, y) in the symmetry with respect to axis X we obtain the point A' (x, -y).

- By transforming the point A (x, y) in the symmetry with respect to axis Y we obtain the point A' (-x, y).

In axial symmetry the image:
- of the point is a point,
- of the line segment is a line segment of the same length,
- of the polygon is a polygon of the same area and perimeter,
- of the circle is a circle of the same radius.m358e60ca6f0b634b_1527752263647_0In axial symmetry the image:
- of the point is a point,
- of the line segment is a line segment of the same length,
- of the polygon is a polygon of the same area and perimeter,
- of the circle is a circle of the same radius.

Selected words and expressions used in the lesson plan

axial symmetryaxial symmetryaxial symmetry

axis of symmetryaxis of symmetryaxis of symmetry

circlecirclecircle

coordinates of the pointcoordinates of the pointcoordinates of the point

figurefigurefigure

imageimageimage

image of the polygonimage of the polygonimage of the polygon

polygonpolygonpolygon

symmetrical pointssymmetrical pointssymmetrical points

triangletriangletriangle