Topicmef4f89afd81f4c11_1528449000663_0Topic

The length of the circumference

Levelmef4f89afd81f4c11_1528449084556_0Level

Second

Core curriculummef4f89afd81f4c11_1528449076687_0Core curriculum

XIV. The length of the circumference and the area of the circle. The student:

1) calculates the length of the circumference of the given radius or diameter;

2) calculates the radius or diameter of a circumference while having the length of the circumference give.

Timingmef4f89afd81f4c11_1528449068082_0Timing

45 minutes

General objectivemef4f89afd81f4c11_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmef4f89afd81f4c11_1528449552113_0Specific objectives

1. Calculating the length of the circumferencecircumferencecircumference of the given radiusradiusradius or diameterdiameterdiameter.

2. Calculating the radius or diameter of a circumference while having the length of the circumference give.

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

Learning outcomesmef4f89afd81f4c11_1528450430307_0Learning outcomes

The student:

- calculates the length of the circumference of the given radiusradiusradius or diameter,

- calculates the radius or diameter of a circumference while having the length of the circumference give.

Methodsmef4f89afd81f4c11_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workmef4f89afd81f4c11_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmef4f89afd81f4c11_1528450127855_0Introduction

The teacher introduces the subject of the lesson - calculating the length of the circumferencecircumferencecircumference of the given radius or diameterdiameterdiameter or calculating the radius or diameter of a circumference while having the length of the circumference give.

Proceduremef4f89afd81f4c11_1528446435040_0Procedure

A few days before the class, the teacher asks one of the students to prepare information about the circle and the circumferencecircumferencecircumference at home. This students presents the prepared material in the beginning of the class. The other colleagues ask him/her questions about the concepts related with the circle.

Task
Students work individually, using computers. Their task is to observe how the relation between the length of the circumference and the diameterdiameterdiameter changes depending on the change of the length of the radius.

[Geogebra applet]

The conclusion students should draw:

- The relation between the length of the circumferencecircumferencecircumference and the diameter is a constant independent of the length of the radius.

Students are divided into groups and search for information about number $\mathrm{\pi }$ in available sources. They make a note about its origin, its name and experiments of the ancient Egyptians and other mathematicians regarding giving the most accurate approximation of the number $\mathrm{\pi }$.

Chosen students present their information.

Conclusion:

- The length $L$ of the circumference whose radius is r is expressed with the formula $L=2·\pi ·r$.

Students use obtained information in the exercises.

Task
Calculate the length of the circumference whose radius is:

a) r = 7,

b) r = 1,

c) r = 0,2.

Task
Calculate the approximate length of the circumference whose radius is 2 cm. Assume the approximation of number $\mathrm{\pi }$ with the accuracy of:

a) units,

b) decimal parts,

c) hundredths parts,

d) thousandths parts.

Task
Calculate how many times the length of the circumferencecircumferencecircumference whose radius is 4 is greater than the length of the circumference whose diameterdiameterdiameter is 1.

Task
Give the radiusradiusradius of the circumferencecircumferencecircumference whose length is:

a) $\mathrm{\pi }$,

b) $10\mathrm{\pi }$,

c) $5$.

Task
The diameter of the wheel of a car is equal to 45 cm. Calculate how many times the wheel will rotate on the road that is 3 m long. Assume $\mathrm{\pi }=\frac{22}{7}.$mef4f89afd81f4c11_1527752263647_0The diameter of the wheel of a car is equal to 45 cm. Calculate how many times the wheel will rotate on the road that is 3 m long. Assume $\mathrm{\pi }=\frac{22}{7}.$

Task
Calculate the radius of the wheel of a bike that rotates 20 times on the road that is 50 m long. Assume $\mathrm{\pi }=3,14.$mef4f89afd81f4c11_1527752256679_0Calculate the radius of the wheel of a bike that rotates 20 times on the road that is 50 m long. Assume $\mathrm{\pi }=3,14.$

An extra task:
Calculate the length of a circle circumscribed about the equilateral triangle whose side is equal to 4.

Lesson summarymef4f89afd81f4c11_1528450119332_0Lesson summary

Students do the revision exercises.

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

- The relation between the length of the circumferencecircumferencecircumference and the diameter is a constant independent of the length of the radius. This relation is marked with the Greek letter $\mathrm{\pi }$.

- The length $L$ of the circumference whose radius is r is expressed with the formula $L=2·\pi ·r$.

Selected words and expressions used in the lesson plan

centre of the circlecentre of the circlecentre of the circle

circumferencecircumferencecircumference

diameterdiameterdiameter

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 $\mathrm{\pi }$

radiusradiusradius