Topicm5956df55c77a5349_1528449000663_0Topic

Calculating areas and perimeters of polygons in the coordinate systemcoordinate systemcoordinate system

Levelm5956df55c77a5349_1528449084556_0Level

Second

Core curriculumm5956df55c77a5349_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

Timingm5956df55c77a5349_1528449068082_0Timing

45 minutes

General objectivem5956df55c77a5349_1528449523725_0General objective

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

Specific objectivesm5956df55c77a5349_1528449552113_0Specific objectives

1. Calculating areas and perimeters of polygons in the coordinate systemcoordinate systemcoordinate system.

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

Learning outcomesm5956df55c77a5349_1528450430307_0Learning outcomes

The student:

- calculates areas and perimeters of polygons in the coordinate systemcoordinate systemcoordinate system.

Methodsm5956df55c77a5349_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm5956df55c77a5349_1528449514617_0Forms of work

1. Individual work.

2. Work in pairs.

Lesson stages

Introductionm5956df55c77a5349_1528450127855_0Introduction

The teacher introduces the subject of the lesson - calculating areas and perimeters of polygons in the coordinate systemcoordinate systemcoordinate system.

Quick thematical contest.

The teacher asks 10 questions about formulas for areas and perimeters of polygons. A person that answers the most questions correctly gets two pluses.

Procedurem5956df55c77a5349_1528446435040_0Procedure

Students work individually, using computers. Their task is to mark polygons of given areas in the coordinate systemcoordinate systemcoordinate system.

[Geogebra applet]

Students’ conclusions

- If there is the same unit on both axes of the coordinate system, then as a unit of area we assume a square whose side is equal to the unit of each axis.m5956df55c77a5349_1527752263647_0If there is the same unit on both axes of the coordinate system, then as a unit of area we assume a square whose side is equal to the unit of each axis.

Contest in pairs.

Task 1
Draw six rectangles whose area is 24 in the coordinate systemcoordinate systemcoordinate system.

Task 2
Calculate the area of a trapezoid ABCD whose vertices are A (-2; -1), B (4; 1), C (1; 2), D (-1; 2).

Task 3
Points A (2; -2), B (5; -2), C (5; 1), are following vertices of a square. Give coordinates of the point D. Calculate the area of the ABCD square.

Task 4
One of the persons marks vertices of the rectanglerectanglerectangle in the coordinate systemcoordinate systemcoordinate system, in such a way that coordinates are integers. The second person calculates the area and the perimeter of this rectanglerectanglerectangle. Then they change roles.

Task 5
The line segment AB where A (-1; 1) and B (5; 1) is the base of the triangle ABC, whose area is equal to 18. Give coordinates of the vertex C if the triangle ABC is:

a. right‑angled,

b. isosceless.

The teacher sums‑up students’ work.

The teacher rewards pairs who gave the best solutions with highest marks.

An extra task:
Mark a tetragon ABCD whose coordinates are A (1; 2), B (5; 2), C (6; 3), D (2; 3) in the coordinate systemcoordinate systemcoordinate system. Then mark the tetragon A’B’C’D’ whose vertices are coordinates that are opposite numbers to coordinates of the ABCD tetragon. Calculate areas and perimeters of both tetragons. What do you notice?

Lesson summarym5956df55c77a5349_1528450119332_0Lesson summary

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

- If there is the same unit on both axes of the coordinate systemcoordinate systemcoordinate system, then as a unit of area we assume a square whose side is equal to the unit of each axis.

Selected words and expressions used in the lesson plan

area of the polygonarea of the polygonarea of the polygon

coordinate systemcoordinate systemcoordinate system

parallelogramparallelogramparallelogram

perimeter of the polygonperimeter of the polygonperimeter of the polygon

point coordinatespoint coordinatespoint coordinates

polygonpolygonpolygon

rectanglerectanglerectangle