Topicme549de09b28105c8_1528449000663_0Topic

The area of the circle

Levelme549de09b28105c8_1528449084556_0Level

Second

Core curriculumme549de09b28105c8_1528449076687_0Core curriculum

XIV. The length of the circumferencecircumferencecircumference and the area of the circle:

3) calculates the area of the circlearea of the circlearea of the circle of the given radiusradiusradius or diameterdiameterdiameter;

4) calculates the radius or the diameter of a circle of the given area.

Timingme549de09b28105c8_1528449068082_0Timing

45 minutes

General objectiveme549de09b28105c8_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesme549de09b28105c8_1528449552113_0Specific objectives

1. Calculating the area of the circle of the given radius or diameter.

2. Calculating the radius or the diameter of a circle of the given area.

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

Learning outcomesme549de09b28105c8_1528450430307_0Learning outcomes

The student:

- calculates the area of the circle of the given radius or diameter,

- calculates the radius or the diameter of a circle of the given area.

Methodsme549de09b28105c8_1528449534267_0Methods

1. Discussion.

2. JIGSAW.

Forms of workme549de09b28105c8_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionme549de09b28105c8_1528450127855_0Introduction

The teacher introduces the subject of the lesson - calculating the area of the circlearea of the circlearea of the circle of the given radiusradiusradius or diameterdiameterdiameter and calculating the radius or the diameter of a circle of the given area.

Procedureme549de09b28105c8_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to observe the way of determining the approximate value of the area of the circle of the given radiusradiusradius.

[Geogebra applet]

Conclusion:

- The area of the circlearea of the circlearea of the circle whose radius is r is equal to the product of the number $\mathrm{\pi }$ and the square of the radius.

Students analyse the example.

Example:

How many circles can be cut out of a red, square piece of paper, whose side is equal to 40 cm if the area of one circle is equal to $16\pi$ cmIndeks górny 2²?

First we need to calculate the radiusradiusradius of the circle.

Therefore the diameterdiameterdiameter of the circle: $\mathrm{d}=8\mathrm{cm}.$

Along one side of the square we can put $40:8=5$ circles.

On one piece there can be: $5·5=25$ circles.

Therefore, we can cut out $25$ circles from one piece of red paper.

Students work with the JIGSAW method.

The teacher divides students into 4 persons groups. Each member of the group gets different task from the tasks below. After solving the tasks, students gather in groups that were doing the same task. They discuss the solutions and clarify any doubts. Then, they return to the initial groups and present the solutions to other members.

Task
The diameterdiameterdiameter of the coin is equal to 4 cm. Calculate the surface area of the coin.

Task
What is the area of a circle whose circumferencecircumferencecircumference is equal to $10\mathrm{\pi }?$

Task
How will the area of circle change if its diameter becomes twice greater?me549de09b28105c8_1527752256679_0How will the area of circle change if its diameter becomes twice greater?

Task
A circle has been inscribed in the square and circumscribed around the same square. Calculate the ratio of the area of the circle circumscribed around the square to the area of the circle inscribed in the square.me549de09b28105c8_1527752263647_0A circle has been inscribed in the square and circumscribed around the same square. Calculate the ratio of the area of the circle circumscribed around the square to the area of the circle inscribed in the square.

An extra task:
There are two circles that are externally tangent to each other. The distance between their centres is equal to 12 cm. Calculate the areas of this circles if their radiuses are in 3:1 ratio to each other.

Lesson summaryme549de09b28105c8_1528450119332_0Lesson summary

Students do the revision exercises.

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

- The area of the circlearea of the circlearea of the circle whose radiusradiusradius is r is equal to the product of the number $\mathrm{\pi }$ and the square of the radius.

Selected words and expressions used in the lesson plan

circumferencecircumferencecircumference

radiusradiusradius

diameterdiameterdiameter

centre of the circlecentre of the circlecentre of the circle

length of the circumference whose radius is rlength of the circumference whose radius is rlength of the circumference whose radius is r

number $\mathrm{\pi }$number $\mathrm{\pi }$number $\mathrm{\pi }$

area of the circlearea of the circlearea of the circle