Topicmb0758175cd39020a_1528449000663_0Topic

Point symmetrypoint symmetryPoint symmetry II

Levelmb0758175cd39020a_1528449084556_0Level

Second

Core curriculummb0758175cd39020a_1528449076687_0Core curriculum

XV. Symmetries. The student:

4) identifies figures symmetric about a pointpointpoint and marks their points of symmetry.

Timingmb0758175cd39020a_1528449068082_0Timing

45 minutes

General objectivemb0758175cd39020a_1528449523725_0General objective

Noticing regularities, similarities and analogies and formulating relevant conclusions.

Specific objectivesmb0758175cd39020a_1528449552113_0Specific objectives

1. Constructing figures symmetric about a pointpointpoint.

2. Noticing examples of point symmetrypoint symmetrypoint symmetry in architecture, nature etc.

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

Learning outcomesmb0758175cd39020a_1528450430307_0Learning outcomes

The student:

- constructs figures symmetric about a pointpointpoint,

- notices examples of the point symmetrypoint symmetrypoint symmetry in architecture, nature etc.

Methodsmb0758175cd39020a_1528449534267_0Methods

1. Flipped classroom method.

2. Learning through observation.

Forms of workmb0758175cd39020a_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmb0758175cd39020a_1528450127855_0Introduction

The teacher asks the students to prepare for the class and revise the definition of point symmetrypoint symmetrypoint symmetry and the ways to construct points symmetric about a pointpointpoint.

Proceduremb0758175cd39020a_1528446435040_0Procedure

Task

The ImageimageImage of the line segment, the polygonpolygonpolygon and the circlecirclecircle in point symmetrypoint symmetrypoint symmetry.

Students work individually using computers. Their task is to find the imageimageimage of the line segment, the polygon and the circlecirclecircle in point symmetrypoint symmetrypoint symmetry.

[Geogebra applet]

Students answer the following question.

- What is the imageimageimage of the line segment, the polygonpolygonpolygon and the circlecirclecircle in the point symmetrypoint symmetrypoint symmetry?

Task

Students draw a right‑angled triangleright‑angled triangleright‑angled triangle ABC whose cathetuses are |AC| = 5 cm and |BC| = 12 cm. Then they find the imageimageimage of the triangletriangletriangle in symmetry about pointpointpoint C. The obtained triangletriangletriangle creates a polygonpolygonpolygon with the triangletriangletriangle ABC. Students calculate the perimeter of this polygon.

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

In point symmetry the image:
- of a point is a point,
- of a line segment is a line segment of the same length,
- of a circle is a circle of the same radius,
- of a polygon is a polygon of the same shape, perimeter and area.mb0758175cd39020a_1527752263647_0In point symmetry the image:
- of a point is a point,
- of a line segment is a line segment of the same length,
- of a circle is a circle of the same radius,
- of a polygon is a polygon of the same shape, perimeter and area.

Point symmetrypoint symmetryPoint symmetry on the coordinate system.

The teacher tells the students that point symmetry can also be considered on the coordinate system. The point of symmetry can be the origin of the coordinate system.mb0758175cd39020a_1527752256679_0point symmetry can also be considered on the coordinate system. The point of symmetry can be the origin of the coordinate system.

Task

Students together think about the properties of the coordinates of the points of symmetry with respect to the origin of the coordinate system.

The drawing shows points on the coordinate system which are symmetric with respect to the origin of the coordinate system.

[Illustration 1]

By transforming any point A (x, y) in symmetry about the pointpointpoint (0, 0) we obtain point A’ (-x, -y).

Task

What will be the coordinates of a point symmetric to pointpointpoint A(3, -7) in symmetry about the origin of the coordinate system?

The teacher points out that examples of point symmetrypoint symmetrypoint symmetry can also be noticed in architecture, nature etc.

Task

Students decide if this is a figure in which you can notice point symmetrypoint symmetrypoint symmetry. If so, where is the point of symmetry of this figure?

Lesson summarymb0758175cd39020a_1528450119332_0Lesson summary

Students do the revision exercises.

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

In point symmetry the image:
- of a point is a point,
- of a line segment is a line segment of the same length,
- of a circle is a circle of the same radius,
- of a polygon is a polygon of the same shape, perimeter and area.mb0758175cd39020a_1527752263647_0In point symmetry the image:
- of a point is a point,
- of a line segment is a line segment of the same length,
- of a circle is a circle of the same radius,
- of a polygon is a polygon of the same shape, perimeter and area.

We can also consider point symmetrypoint symmetrypoint symmetry on the coordinate system. The point of symmetry can be the origin of the coordinate system.

By transforming point A (x, y) in symmetry about the origin we obtain pointpointpoint A’ (-x, -y).

Examples of point symmetrypoint symmetrypoint symmetry can also be noticed in architecture, nature etc.

Selected words and expressions used in the lesson plan

circlecirclecircle

figurefigurefigure

imageimageimage

image of a line segmentimage of a line segmentimage of a line segment

pointpointpoint

point symmetrypoint symmetrypoint symmetry

polygonpolygonpolygon

right‑angled trianright‑angled triangleright‑angled trian

symmetrical pointssymmetrical pointssymmetrical points

triangletriangletriangle