Topicmf55d8ff325e63ab9_1528449000663_0Topic

Values directly proportional

Levelmf55d8ff325e63ab9_1528449084556_0Level

Second

Core curriculummf55d8ff325e63ab9_1528449076687_0Core curriculum

VII. Direct proportionality. The student:

1) gives examples of directly proportional values;

2) determines the value directly proportional in case of specific proportional relations, for example value of bought goods in relation to the number of goods, the amount of used fuel in relation to the amount of drive kilometres, the number of read pages depending on the time of reading.

Timingmf55d8ff325e63ab9_1528449068082_0Timing

45 minutes

General objectivemf55d8ff325e63ab9_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmf55d8ff325e63ab9_1528449552113_0Specific objectives

1. Identifying and applying directly proportional values.

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

Learning outcomesmf55d8ff325e63ab9_1528450430307_0Learning outcomes

The student:

- identifies and applies directly proportional values,

- applies directly proportional values to solve tasks set in real context.

Methodsmf55d8ff325e63ab9_1528449534267_0Methods

1. Discussion.

2. Talking cards.

Forms of workmf55d8ff325e63ab9_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmf55d8ff325e63ab9_1528450127855_0Introduction

The teacher asks if students met with proportions before. If yes, in what context. Maybe they know what are directly proportional values? If yes, they will verify their knowledge during the class. If not, they will get to learn it.

Proceduremf55d8ff325e63ab9_1528446435040_0Procedure

Task
Students work individually using computers. Their task is to observe how we create directly proportional values.

[Geogebra applet]

Students work using the method of a talking card.

Each student gets a paper card where they write down examples from everyday life that describes directly proportional values. The student chosen by the teacher collects cards and reads examples. Interesting propositions are being discussed and as a result students draw proper conclusions.

Conclusion:
- Two values are directly proportional if one of them increases and the other increases at the same rate.
- The quotient of values directly proportional is constant and is called a proportionality coefficient.mf55d8ff325e63ab9_1527752263647_0Conclusion:
- Two values are directly proportional if one of them increases and the other increases at the same rate.
- The quotient of values directly proportional is constant and is called a proportionality coefficient.

Students work in pairs. Each student from the pair gives two examples of directly proportional values presented in the table. The other person verifies examples and calculates the proportionality coefficient.

Students use obtained information to do the exercises.

Task
Decide if the following values are directly proportional.
a) The length of a side of a rectangle and its area.
b) The amount of animals in the household and the amount of legs of these animals.
c) The amount of dogs at the farm and the number of legs of these dogs.
d) Persons’ age and their height.mf55d8ff325e63ab9_1527752256679_0Decide if the following values are directly proportional.
a) The length of a side of a rectangle and its area.
b) The amount of animals in the household and the amount of legs of these animals.
c) The amount of dogs at the farm and the number of legs of these dogs.
d) Persons’ age and their height.

Task
Decide if the values presented in the table are directly proportional.

If yes, calculate the proportionality coefficient.

[Table 1]

Task
A car drove 10 km in 15 min. How many kilometres will it drive in 20 minutes in the same conditions?mf55d8ff325e63ab9_1527712094602_0A car drove 10 km in 15 min. How many kilometres will it drive in 20 minutes in the same conditions?

Task
In order to drive 25 km in the car, you need on average 2 litres of gas. How many litres of gas do you need to buy extra to drive 80 km?

An extra task:
In the Internet look for information about how much human voice travels in 1 second in air. Calculate how much time is needed for the voice to travel 500 metres.

Lesson summarymf55d8ff325e63ab9_1528450119332_0Lesson summary

Students do the revision exercises.

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

- Two values are directly proportional if one of them increases and the other increases at the same rate.

- The quotientquotientquotient of values directly proportionalvalues directly proportionalvalues directly proportional is constant and is called a proportionality coefficient.

Selected words and expressions used in the lesson plan

coefficient of proportionalitycoefficient of proportionalitycoefficient of proportionality

proportionproportionproportion

quotientquotientquotient

values directly proportionalvalues directly proportionalvalues directly proportional