Topicm0f9c63b8453cb3f2_1528449000663_0Topic

Examples of applying direct proportionality

Levelm0f9c63b8453cb3f2_1528449084556_0Level

Third

Core curriculumm0f9c63b8453cb3f2_1528449076687_0Core curriculum

V. Functions. The student:

1) identifies functions as clear assignment using word description, table, graph, formula (including formula on different sets);

2) calculates values of function given by an algebraic formula;

5) interprets coefficients in the formula of a linear function;

6) identifies the formula of a linear function based on information about its plot of its properties.

Timingm0f9c63b8453cb3f2_1528449068082_0Timing

45 minutes

General objectivem0f9c63b8453cb3f2_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm0f9c63b8453cb3f2_1528449552113_0Specific objectives

1. Applying direct proportionalitydirect proportionalitydirect proportionality in exercises.

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

Learning outcomesm0f9c63b8453cb3f2_1528450430307_0Learning outcomes

The student:

- applies direct proportionality in exercises.

Methodsm0f9c63b8453cb3f2_1528449534267_0Methods

1. Discussion.

2. Mathematical quiz.

Forms of workm0f9c63b8453cb3f2_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionm0f9c63b8453cb3f2_1528450127855_0Introduction

Students revise the definition of direct proportionalitydirect proportionalitydirect proportionality.

Definition of direct proportionality.

- Direct proportionality is a relation between two variables x and y, defined by the formula y = a · x. The number a, different from zero, is called the coefficient of proportionality.

Discussion – where in everyday situations we can find directly proportional values?

The teacher announces quick the mathematical quiz. The person that answers 3 questions correctly is the champion.

1. A worker makes 16 details in an hour. How many details will he make in 1,5 hours?

2. In 8 hours a pump pumps 72 litres of water. How many litres will it pump in 2 hours?

3. A car uses on average 4 litres of gasoline on 55 km distance. How many kilometres can the car make if it uses on average 14,5 litres of gasoline?

Procedurem0f9c63b8453cb3f2_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to observe the relation between the length of the diagonal of a square and the length of its side.

[Interactive illustration]

In pairs, students identify the relation between the altitude of the equilateral triangle and the length of its side.

Then each person from the pair gives own example describing mathematical relation and the other person gives a formula for proper proportion.

Students use obtained information in the exercises.

Task
Five packages of cheese cost 17 zł. Will 27 zł be enough to buy eight packages of this cheese?

Task
1 l box of milk costs 2,80 zł. How does the cost of all shopping change depending on the bought amount of boxes of milk? Draw a table describing the amount of of bought boxes of milk (in the range {2, 3, 4, 5, 6, 7}) in relation to their price.m0f9c63b8453cb3f2_1527752263647_01 l box of milk costs 2,80 zł. How does the cost of all shopping change depending on the bought amount of boxes of milk? Draw a table describing the amount of of bought boxes of milk (in the range {2, 3, 4, 5, 6, 7}) in relation to their price.

Task
Let’s consider all rectangles whose one side is equal to 5. Is the area of this triangle directly proportional to the length of the other side? If yes, give the formula, coefficient of proportionality and draw a plot of this relation.m0f9c63b8453cb3f2_1527752256679_0Let’s consider all rectangles whose one side is equal to 5. Is the area of this triangle directly proportional to the length of the other side? If yes, give the formula, coefficient of proportionality and draw a plot of this relation.

Task
A train travelled 150 km in 2,5 hours. How many kilometres did it travel in 1,25 hours if it was going with the same speed?

The teacher evaluates students’ work. Together they verify obtained results.

An extra task:
Is a side of an equilateral triangle and a radius of a circle inscribed in this triangle directly proportional? If yes, give the formula and the coefficient of proportionality.

Lesson summarym0f9c63b8453cb3f2_1528450119332_0Lesson summary

Students do the revision exercises.

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

- Direct proportionalitydirect proportionalityDirect proportionality is a relations between two variables x and y, defined by the formula y = a · x. The number a, different from zero, is called the coefficient of proportionality.

Selected words and expressions used in the lesson plan

direct proportionalitydirect proportionalitydirect proportionality

formula of the functionformula of the functionformula of the function

linelineline

plot of the functionplot of the functionplot of the function

values directly proportionalvalues directly proportionalvalues directly proportional