Topicm939c3555d00a13c7_1528449000663_0Topic

AreaareaArea of the figurefigurefigure. Units of area

Levelm939c3555d00a13c7_1528449084556_0Level

Second

Core curriculumm939c3555d00a13c7_1528449076687_0Core curriculum

XI. Calculations in geometry. The student:

3) uses the units of the areaunits of the areaunits of the area: mmIndeks górny 2², cmIndeks górny 2², dmIndeks górny 2², mIndeks górny 2², kmIndeks górny 2², ar, hectare (without the conversion of units).

Timingm939c3555d00a13c7_1528449068082_0Timing

45 minutes

General objectivem939c3555d00a13c7_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm939c3555d00a13c7_1528449552113_0Specific objectives

1. Measuring the area of the figurethe area of the figurethe area of the figure with unconventional methods.

2. Conversion of the units of the areaunits of the areaunits of the area.

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

Learning outcomesm939c3555d00a13c7_1528450430307_0Learning outcomes

The student:

- measures the area of the figurethe area of the figurethe area of the figure with unconventional methods,

- converts the units of the areaunits of the areaunits of the area.

Methodsm939c3555d00a13c7_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm939c3555d00a13c7_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm939c3555d00a13c7_1528450127855_0Introduction

The teacher introduces the subject of the lesson: measuring the areas of polygons with unconventional methods and the conversion of the units of the areaareaarea.

Students revise the units of the areaunits of the areaunits of the area they learnt before. They establish which ones areareare the most useful ones to calculate the areaareaarea of objects of various sizes, e.g. a piece of paper, the floor in the classroom or a lawn in a park.

Procedurem939c3555d00a13c7_1528446435040_0Procedure

Task
Students work individually, using computers.

Their task is to calculate the areaareaarea of the drawn polygonpolygonpolygon, assuming that the length of the side of one squaresquaresquare is 1.

[Geogebra applet]

Task
Students measure  the area of the figure, assuming that one unit is the polygon presented below.m939c3555d00a13c7_1527752263647_0measure  the area of the figure, assuming that one unit is the polygon presented below.

[Illustration 1]

Discussion:

If we assume another figurefigurefigure as the unit of the area, will the areaareaarea of the given polygonpolygonpolygon be expressed with the same number?

The conclusion of the discussion should be that while determining the area of the figurethe area of the figurethe area of the figure, it is important to give the unit in which it is expressed.

Units of the areaunits of the areaUnits of the area of figures.

Task
Students recall that 1mIndeks górny 2² is the squaresquaresquare whose side is 1 m.

Then they write the relations between the units of the areaunits of the areaunits of the area.

Note that:

1 cmIndeks górny 2² = 100 mmIndeks górny 2².
1 dmIndeks górny 2² = 100 cmIndeks górny 2² = 10000 mmIndeks górny 2².
1 mIndeks górny 2² = 100 dmIndeks górny 2² = 10000 cmIndeks górny 2².
1 kmIndeks górny 2² = 1000000 mIndeks górny 2².

Task
Students express the area of the carpet, which is 8.4 mIndeks górny 2² in dmIndeks górny 2² and in cmIndeks górny 2².m939c3555d00a13c7_1527752256679_0Students express the area of the carpet, which is 8.4 mIndeks górny 2² in dmIndeks górny 2² and in cmIndeks górny 2².

Units of area of lands.

Task
Students search the Internet for information concerning the units of the areaunits of the areaunits of the area of lands, used in farming, forestry and geodesy. Together they order the information. They establish the relations between the units.

Note that:

The units of the area used to determine the size of fields and other agriculture areas.
1 ar (1 a) is the square whose side is equal to 10 m.
1 a = 10 m ⋅ 10 m = 100 mIndeks górny 2².
1 hectare (1 ha) is the square whose side is equal to 100 m.
1 ha = 100 m ⋅ 100 m = 10000 mIndeks górny 2².

Students use the acquired skills in the following exercises:

Task
The pitch has the dimensions 110 m and 65 m. How many hectares does this amount to? How many ares does it have?

Lesson summarym939c3555d00a13c7_1528450119332_0Lesson summary

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

Units of areaareaarea.

The basic unit of the area is 1 square metresquare metresquare metre.

1mIndeks górny 2² is the squaresquaresquare whose side is equal to 1 m.

The relations between the units of the areaunits of the areaunits of the area:

1 cmIndeks górny 2² = 100 mmIndeks górny 2².

1 dmIndeks górny 2² = 100 cmIndeks górny 2² = 10000 mmIndeks górny 2².

1 mIndeks górny 2  Indeks górny koniec² = 100 dmIndeks górny 2² = 10000 cmIndeks górny 2².

1 kmIndeks górny 2² = 1000000 mIndeks górny 2².

The units of the areaunits of the areaunits of the area used to determine the size of fields and other agriculture areas.

1 ar (1 a) is the square whose side is equal to 10 m.

1 a = 10 m ⋅ 10 m = 100 mIndeks górny 2².

1 hectare (1 ha) is the squaresquaresquare whose side is equal to 100 m.

1 ha = 100 m ⋅ 100 m = 10000 mIndeks górny 2².

Selected words and expressions used in the lesson plan

areareare

areaareaarea

figurefigurefigure

hectarehectarehectare

measuremeasuremeasure

polygonpolygonpolygon

squaresquaresquare

square metresquare metresquare metre

the area of the figurethe area of the figurethe area of the figure

units of the areaunits of the areaunits of the area