Topicmc29f4368a5b1704f_1528449000663_0Topic

Polygons in the coordinate systemcoordinate systemcoordinate system

Levelmc29f4368a5b1704f_1528449084556_0Level

Second

Core curriculummc29f4368a5b1704f_1528449076687_0Core curriculum

X. The number line. The coordinate systemcoordinate systemcoordinate system on a plane.

The student:

2) finds coordinates of points (in the drawing) marked in the coordinate systemcoordinate systemcoordinate system on a plane;

3) draws points of given, integer coordinates (of any sign) in the coordinate systemcoordinate systemcoordinate system

Timingmc29f4368a5b1704f_1528449068082_0Timing

45 minutes

General objectivemc29f4368a5b1704f_1528449523725_0General objective

Interpreting and creating texts with mathematical context and presenting data graphically.

Specific objectivesmc29f4368a5b1704f_1528449552113_0Specific objectives

1. Marking polygons in the coordinate systemcoordinate systemcoordinate system.

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

Learning outcomesmc29f4368a5b1704f_1528450430307_0Learning outcomes

The student:

- marks polygons in the coordinate systemcoordinate systemcoordinate system.

Methodsmc29f4368a5b1704f_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workmc29f4368a5b1704f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc29f4368a5b1704f_1528450127855_0Introduction

The teacher introduces the subject of the lesson – marking polygons in the coordinate systemcoordinate systemcoordinate system and using their properties.

The class starts with a short contest in pairs. Each student gives coordinates of three noncollinear points. The second person from the pair marks these points in the coordinate systemcoordinate systemcoordinate system and connects them with line segment. Then they identify the type of the obtained triangletriangletriangle.

Proceduremc29f4368a5b1704f_1528446435040_0Procedure

[Geogebra applet 1]

Students work individually, using computers. Their task is to mark the fourth vertex in such a way that the obtained tetragon ABCD is a parallelogram.
Discussion – how to calculate lengths of sides of the rectangle ABCD whose vertices are A (2; 3), B (5; 3), C (5; -2), D (2; -2).

Students mark vertices of a rectanglerectanglerectangle in the coordinate systemcoordinate systemcoordinate system and try to calculate how many line segment units do sides of the figure have.

Students’ conclusions

- In order to calculate lengths of sides of a polygonpolygonpolygon, it is convenient to place it in such a way in the coordinate systemcoordinate systemcoordinate system that its vertices are on points of integer coordinates.

- If the side AB of a polygonpolygonpolygon is parallel to the X axis of the coordinate systemcoordinate systemcoordinate system, the length of the side is equal to the absolute value of the difference of first coordinates of points A and B.

- If the side CD of a polygonpolygonpolygon is parallel to the Y axis of the coordinate systemcoordinate systemcoordinate system, the length of the side is equal to the absolute value of the difference of second coordinates of points C and D.

Students use obtained information by participating in the individual task contest. Three first students that do all exercises correctly, get highest marks.

Task 1
There are points in the coordinate systemcoordinate systemcoordinate system A (-1; 0), B (5; 0), C (3; 2). Find such point D that the polygonpolygonpolygon ABCD is an isosceles trapezoid. Calculate lengths of bases of this trapezoid.

Task 2
There is the parallelogram ABCD in the coordinate systemcoordinate systemcoordinate system.

[Geogebra applet 1]

[Illsutration 1]

a. Are abscissas of points C and D the same?

b. How many points with both positive coordinates are inside the parallelogramparallelogramparallelogram ABCD?

c. Give the difference between the ordinate and the abscissa of the point B.

d. Calculate the length of the shorter side of the parallelogram ABCD.

Task 3
There are points A (3; 2) and B (-3; 2). Find such points C and D that the centre of symmetry of the rectanglerectanglerectangle ABCD is the beginning of the coordinate systemcoordinate systemcoordinate system. Calculate lengths of sides of this rectanglerectanglerectangle.

Task 4
Mark points in the coordinate systemcoordinate systemcoordinate system A (-1; -1), B (2; 2), C (0; 4).

Give coordinates of such point D that the obtained tetragon is:

a. a rectanglerectanglerectangle that is not a square,

b. a square,

c. a right‑angled trapezoid that is not a rectanglerectanglerectangle,

d. a deltoid. Is there a solution for each case?

The teacher sums‑up and evaluates students’ work.

An extra task:
Calculate the length of the longest side of the ABC triangle whose vertices are A (-3; -1), B (2; -1), C (2; 4).

Lesson summarymc29f4368a5b1704f_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

- In order to calculate lengths of sides of a polygon, it is convenient to place it in such a way in the coordinate system that its vertices are on points of integer coordinates.mc29f4368a5b1704f_1527752256679_0In order to calculate lengths of sides of a polygon, it is convenient to place it in such a way in the coordinate system that its vertices are on points of integer coordinates.

- If the side AB of a polygon is parallel to the X axis of the coordinate system, the length of the side is equal to the absolute value of the difference of first coordinates of points A and B.mc29f4368a5b1704f_1527752263647_0If the side AB of a polygon is parallel to the X axis of the coordinate system, the length of the side is equal to the absolute value of the difference of first coordinates of points A and B.

- If the side CD of a polygon is parallel to the Y axis of the coordinate systemcoordinate systemcoordinate system, the length of the side is equal to the absolute value of the difference of second coordinates of points C and D.

Selected words and expressions used in the lesson plan

coordinate systemcoordinate systemcoordinate system

deltoiddeltoiddeltoid

isosceles trapezoidisosceles trapezoidisosceles trapezoid

parallelogramparallelogramparallelogram

polygonpolygonpolygon

rectanglerectanglerectangle

tetragontetragontetragon

triangletriangletriangle