Topicmc813976363c03f53_1528449000663_0Topic

Identifying properties and location of a point in the coordinate system

Levelmc813976363c03f53_1528449084556_0Level

Second

Core curriculummc813976363c03f53_1528449076687_0Core curriculum

X. The number line. The coordinate system on a plane. The student:

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

3) draws points of given, integer coordinates (of any sign) on the coordinate system.

Timingmc813976363c03f53_1528449068082_0Timing

45 minutes

General objectivemc813976363c03f53_1528449523725_0General objective

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

Specific objectivesmc813976363c03f53_1528449552113_0Specific objectives

1. Identifying properties and location of a point in the coordinate system.

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

Learning outcomesmc813976363c03f53_1528450430307_0Learning outcomes

The student:

- identifies properties and location of a point in the coordinate system.

Methodsmc813976363c03f53_1528449534267_0Methods

1. Discussion.

2. Task tables.

Forms of workmc813976363c03f53_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionmc813976363c03f53_1528450127855_0Introduction

The teacher introduces the subject of the lesson - identifying properties and location of a point in the coordinate system.

Proceduremc813976363c03f53_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to observe signs of the first and the second coordinate of a point in each quadrants of the coordinate systemquadrants of the coordinate systemquadrants of the coordinate system.

[Geogebra applet]

Students’ conclusions:

- Axes of the coordinate system divide the plane into four parts, called quadrants.mc813976363c03f53_1527752263647_0Axes of the coordinate system divide the plane into four parts, called quadrants.

- Quadrants have numbers I, II, III, IV, anti‑clockwise, starting from the top right corner.mc813976363c03f53_1527752256679_0Quadrants have numbers I, II, III, IV, anti‑clockwise, starting from the top right corner.

- Points located on the axes of the coordinate system do not belong to any quadrants of the coordinate systemquadrants of the coordinate systemquadrants of the coordinate system.

- If the point P (x; y) belongs to:

• I quadrant of the coordinate system, then both coordinates of the point are positive numbers.

• II quadrant of the coordinate system, then the first coordinate is a negative number and the second is a positive number.

• III quadrant of the coordinate system, then both coordinates of the point are negative numbers.

• IV quadrant of the coordinate system, then the first coordinate is a positive number and the second is a negative number.

Students work in groups using the method of task tables and do exercises.

Task - Table 1
Write three exemplary points belonging to II and IV quadrant of the coordinate system. What is the sign of the abscissasign of the abscissasign of the abscissa and the ordinate of II and IV quadrans of the coordinate system?

Task - Table 2 
In the coordinate system, mark three pairs of points whose abscissas are positive and ordinates are opposite numbers. In which quadrants of the coordinate systemquadrants of the coordinate systemquadrants of the coordinate system will such pairs of points be located?

Task - Table 3 
Identify the location of the point and put it in the right place of the table.

$A(-3;4),B(2;5),C(-23;-33),D(\frac{1}{2};0,3),E(0;-2),F(\frac{2}{7};-7),$

$G(-1;\frac{3}{8}),H(0;0),I(-4;-10),J(0,3;-4),K(-3;3)$

[Table]

Task - Table 4 
In the coordinate system, mark 10 points whose first coordinate is greater than the second one. In which quadrants are these points located? The teacher sums‑up groups’ work. The teacher rewards the group that worked the fastest with highest marks.

An extra task:
A points whose coordinates are (-2; -3) was translated 5 units to the right along the X axis and then obtained point was translated 2 units up along the Y axis. In which quadrant of the coordinate system is the obtained point? Give its coordinates.

Lesson summarymc813976363c03f53_1528450119332_0Lesson summary

Students do the revision exercises.

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

- Axes of the coordinate system divide the plane into four parts, called quadrants.

- Quadrants have numbers I, II, III, IV, anti‑clockwise, starting from the top right corner.

- Points located on the axes of the coordinate system do not belong to any quadrants of the coordinate systemquadrants of the coordinate systemquadrants of the coordinate system.

- If the point P (x; y) belongs to:

• I quadrant of the coordinate system, then both coordinates of the point are positive numbers.

• II quadrant of the coordinate system, then the first coordinate is a negative number and the second is a positive number.

• III quadrant of the coordinate system, then both coordinates of the point are negative numbers.

• IV quadrant of the coordinate system, then the first coordinate is a positive number and the second is a negative number.

Selected words and expressions used in the lesson plan

coordinates of a pointcoordinates of a pointcoordinates of a point

negative coordinatenegative coordinatenegative coordinate

positive coordinatepositive coordinatepositive coordinate

property of a pointproperty of a pointproperty of a point

quadrants of the coordinate systemquadrants of the coordinate systemquadrants of the coordinate system

sign of the abscissasign of the abscissasign of the abscissa

sign of the ordinatesign of the ordinatesign of the ordinate