Topicm3be11e90db17ff16_1528449000663_0Topic

Cartesian coordinate system on a plane

Levelm3be11e90db17ff16_1528449084556_0Level

Second

Core curriculumm3be11e90db17ff16_1528449076687_0Core curriculum

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

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

Timingm3be11e90db17ff16_1528449068082_0Timing

45 minutes

General objectivem3be11e90db17ff16_1528449523725_0General objective

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

Specific objectivesm3be11e90db17ff16_1528449552113_0Specific objectives

1. Learning the construction of the cartesian coordinate system on a planecartesian coordinate system on a planecartesian coordinate system on a plane.

2. Marking points on the coordinate system.

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

Learning outcomesm3be11e90db17ff16_1528450430307_0Learning outcomes

The Student:

- learns the construction of the cartesian coordinate system on a plane,

- marks points on the coordinate system.

Methodsm3be11e90db17ff16_1528449534267_0Methods

1. Discussion.

2. Flipped classroom.

Forms of workm3be11e90db17ff16_1528449514617_0Forms of work

1. Work in pairs.

2. Group work

Lesson stages

Introductionm3be11e90db17ff16_1528450127855_0Introduction

At home, students search available knowledge sources (films, animations, educational materials) for information about the cartesian coordinate system on a planecartesian coordinate system on a planecartesian coordinate system on a plane. Then, they make notes to systemize obtained knowledge.

The teacher introduces the subject of the lesson – expanding knowledge about the coordinate system. They will also mark points in the coordinate system.

Procedurem3be11e90db17ff16_1528446435040_0Procedure

Students chosen by the teacher shortly discuss results of their research and answer teacher’s questions.

1. How else is the axis X called?
2. How do we call the axis Y?
3. What is the point of intersection of axes X and Y?

Task
Students verify their answers based on the multimedia illustration.

[Interactive illustration]

Students’ conclusions:

- The cartesian coordinate system is created by two perpendicular number lines.
- The point of intersections of axes is called the beginning of the coordinate system.
- The horizontal axis X is called the abscissa.
- The vertical axis Y is called the ordinate.m3be11e90db17ff16_1527752263647_0- The cartesian coordinate system is created by two perpendicular number lines.
- The point of intersections of axes is called the beginning of the coordinate system.
- The horizontal axis X is called the abscissa.
- The vertical axis Y is called the ordinate.

The teacher divides students into groups.

Each group gets a set of exercises to do. A group that correctly solved the first task, can proceed to the next task.

Task
Mark points of given coordinates in the coordinate system.

a) A (3; 1), B (3; 4), C (-2; 1)

b) A (2; 1), B (4; 5), C (-3; 5), D (-5; 1)

What figure will you obtain after connecting consecutive points and first point with last point using line segments?

Task 
Which point will be located on the abscissa of the coordinate system?

a) A (4; 0)

b) B (0; -5)

c) C (0; 0)

d) D (8; 0)

Check your assumptions by making a proper drawing. Write a conclusion.

Conclusion:

- Second coordinate of a point located on the abscissa is equal to 0.

Task 
Which point will be located on the ordinate of the coordinate system?

a) A (2; 0)

b) B (0; -4)

c) C (0; 0)

d) D (0; 10)

Check your assumptions by making a proper drawing. Write a conclusion.

Conclusion:

- First coordinate of a point located on the ordinate is equal to 0.

Task
Mark such point Z on the coordinate system whose

a) both coordinates are greater than 6.

b) first coordinate is smaller by three than second.

c) second coordinate is twice greater than first.

How many solutions does this task have?

Task
Mark five points on the coordinate system, whose second coordinate is greater by 3 than first coordinate. What figure will you obtain by connecting these points?m3be11e90db17ff16_1527752256679_0Mark five points on the coordinate system, whose second coordinate is greater by 3 than first coordinate. What figure will you obtain by connecting these points?

The teacher evaluates students’ work. Two groups that did all obligatory tasks and the extra task the fastest obtain highest marks.

An extra task:
Find the number m knowing that.

a) The point D (m + 4; 7) is located on the X axis.

b) The point G (-3; 3m - 1) is located on the Y axis.

Lesson summarym3be11e90db17ff16_1528450119332_0Lesson summary

Students do the revision exercises.

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

- The cartesian coordinate system is created by two perpendicular number lines.

- The point of intersections of axes is called the beginning of the coordinate systembeginning of the coordinate systembeginning of the coordinate system.

- The horizontal axis X is called the abscissa.

- The vertical axis Y is called the ordinate.

- Second coordinate of a point located on the abscissa is equal to 0.

- First coordinate of a point located on the ordinate is equal to 0.

Selected words and expressions used in the lesson plan

axis of abscissasaxis of abscissasaxis of abscissas

axis of ordinatesaxis of ordinatesaxis of ordinates

beginning of the coordinate systembeginning of the coordinate systembeginning of the coordinate system

cartesian coordinate system on a planecartesian coordinate system on a planecartesian coordinate system on a plane

coordinates of a pointcoordinates of a pointcoordinates of a point