Topicm9e688cc896eeba51_1528449000663_0Topic

The areaareaarea of the rectanglerectanglerectangle and the squaresquaresquare

Levelm9e688cc896eeba51_1528449084556_0Level

Second

Core curriculumm9e688cc896eeba51_1528449076687_0Core curriculum

XI. Calculation in geometry. The student:

2) calculates the areaareaarea of: triangle, squaresquaresquare, rectanglerectanglerectangle, rhombus, parallelogram and trapezium, presented in the figurefigurefigure and in practical situations, including data which require the conversion of units and in situations in which the dimensions are not typical, e.g. the areaareaarea of a triangle with sidesideside 1 km and the altitude of 1 mm;

3) uses the units of the areaareaarea: mmIndeks górny 2², cmIndeks górny 2², dmIndeks górny 2², mIndeks górny 2², kmIndeks górny 2², are, hectare (without the conversion of the units in calculation).

Timingm9e688cc896eeba51_1528449068082_0Timing

45 minutes

General objectivem9e688cc896eeba51_1528449523725_0General objective

Matching the mathematical model to a simple situation and using it in various contexts.

Specific objectivesm9e688cc896eeba51_1528449552113_0Specific objectives

1. CalculatingcalculatingCalculating the areaareaarea of the rectangle and the squaresquaresquare.

2. Measuring the area of the rectanglerectanglerectangle using the unit squares.

3. Communicating in English; developing mathematical and basic scientific; technical and digital competences; developing learning skills.

Learning outcomesm9e688cc896eeba51_1528450430307_0Learning outcomes

1. Calculates the areaareaarea of a rectanglerectanglerectangle the square when the sidesideside lengths are known.

2. Uses the letter symbols for calculatingcalculatingcalculating the area of the rectangle/squaresquaresquare.

Methodsm9e688cc896eeba51_1528449534267_0Methods

1. Practical exercises.

2. Situation analysis.

Forms of workm9e688cc896eeba51_1528449514617_0Forms of work

1. Individual work.

2. Whole‑class work.

Lesson stages

Introductionm9e688cc896eeba51_1528450127855_0Introduction

Revision of the definition of the rectanglerectanglerectangle and the squaresquaresquare.

The rectangle is a quadrangle with all right angles.

The squaresquaresquare is a rectanglerectanglerectangle with all equal sides.

The teacher informs the students about the topic of the lesson. They are going to learn how to calculate the rectangle areaareaarea and how to use this knowledge in solving the tasks.

Procedurem9e688cc896eeba51_1528446435040_0Procedure

The teacher gives each pair of students two cardboard models of rectangles (the bigger red one and the smaller yellow one). They decide how to determine which rectanglerectanglerectangle has a bigger areaareaarea. Using tracing paper with squares on it, students decide how many unit squares each rectangle is made of.

Then the teacher gives the students tracing paper with bigger sides of the unit squares with which they measured the rectangle area previously.

The students should notice that the red rectangle areaareaarea is bigger in each case. However, the numbers defining the rectanglerectanglerectangle areas are different.

In order to calculate the areaareaarea of the figurefigurefigure we can divide it into identical unit squares. The number of the identical squares indicates how large the area of the figure is. If we use squares with sidesideside length 1 to measuremeasuremeasure the area of a figure , we find out how many units squares the area of the figurefigurefigure is made of.

In the case of large figures it is very hard to count the squares, so we calculate the areaareaarea of the rectanglerectanglerectangle on the basis of its dimensions.

Task:

Open the applet and by moving the orange vertices change the dimensions of the rectanglerectanglerectangle. Notice how much its areaareaarea changes.

[Geogebra applet]

The teacher advises the students to describe what they observed in the applet. The students and the teacher draw conclusion:

In order to calculate the area of a rectanglerectanglerectangle we multiply its adjacent sides. If the side lengths are expressed in cm, the areaareaarea is expressed in cmIndeks górny 2².

[Illustration 1]

Using the applet the students observe the change of the squaresquaresquare area by changing its sides length.Having completed the exercise the students should draw the following conclusion: In order to calculate the areaareaarea of a square we should square the length of its sides.

[Illustration 2]

Task:

Calculate the area of the rectangle with the dimensions 5 x 6.

Task:

Calculate the areaareaarea of a squaresquaresquare with the sidesideside lengths of 4.

Task:

Calculate the area of a rectanglerectanglerectangle with sides of a, b :

a) a = 3 cm, b = 10 cm,

b) a = 8 cm, b = 2 cm,

c) a = 6 cm, b = 6 cm.

Task:

Calculate the areaareaarea of a rectangle if one of the sides is 5 centimetres long and the other is:

a) twice as long;

b) four times shorter.

An extra task:

Calculate the sidesideside length of the rectanglerectanglerectangle knowing that its areaareaarea is 64 cm2, and its width equals 4 cm.

Lesson summarym9e688cc896eeba51_1528450119332_0Lesson summary

The students complete the summary exercises .

Then they summarise the lesson, drawing conclusions to be memorised:

- In order to calculate the area of the rectangle you should multiply its length by its width.m9e688cc896eeba51_1527752263647_0- In order to calculate the area of the rectangle you should multiply its length by its width.

- The area of a square equals the square of its sides length.m9e688cc896eeba51_1527752263647_0- The area of a square equals the square of its sides length.

Homework:

Look for the dimensions of the football pitch in the Internet and calculate its areaareaarea.

Selected words and expressions used in the lesson plan

areaareaarea

calculatingcalculatingcalculating

dimensiondimensiondimension

figurefigurefigure

measuremeasuremeasure

rectanglerectanglerectangle

sidesideside

squaresquaresquare

unit squareunit squareunit square