Topicm811140c72578dc3e_1528449000663_0Topic

Direct proportionalitydirect proportionalityDirect proportionality

Levelm811140c72578dc3e_1528449084556_0Level

Third

Core curriculumm811140c72578dc3e_1528449076687_0Core curriculum

V. Functions. The student:

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

Timingm811140c72578dc3e_1528449068082_0Timing

45 minutes

General objectivem811140c72578dc3e_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm811140c72578dc3e_1528449552113_0Specific objectives

1. Applying properties of direct proportionality.

2. Making a plot of a function f(x) = ax.

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

Learning outcomesm811140c72578dc3e_1528450430307_0Learning outcomes

The student:

- applies properties of direct proportionality,

- makes a plot of a function f(x) = ax.

Methodsm811140c72578dc3e_1528449534267_0Methods

1. Discussion.

2. Talking cards.

Forms of workm811140c72578dc3e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm811140c72578dc3e_1528450127855_0Introduction

At home students revise the relation between directly proportional values.

Procedurem811140c72578dc3e_1528446435040_0Procedure

The teacher asks students to write examples of directly proportional values on the ‘talking cards’. Values can be given in different forms – description, tabletabletable, formula, etc.

The teacher collects cards and reads propositions. Based on them, students define direct proportionalitydirect proportionalitydirect proportionality.

Definition of direct proportionality.
Direct proportionality is a relations between two variables x and y, whose quotient is constant.

Therefore y = ax. The number a, different from zero, is called the coefficient of proportionalitycoefficient of proportionalitycoefficient of proportionality.

Task
Students work individually, using computers. Their task is to observe plots of the function y = ax and methods of calculating coordinates of points that belong to the plot of the functionplot of the functionplot of the function.

[Geogebra applet]

Conclusions:

- The plot of the function f(x) = ax, where a ≠ 0, is a linelineline whose equation is y = ax.

- The plot of the function f(x) = ax , for $x\in ℝ$ goes through the beginning of the coordinate system and through each point (x, ax).

Students use obtained information to do the exercises.

Task
Draw the plot of the function f(x) = -3x. Give four exemplary points that the plot goes through. What is the minimum amount of points whose coordinates we need to calculate to draw the plot?m811140c72578dc3e_1527752263647_0Draw the plot of the function f(x) = -3x. Give four exemplary points that the plot goes through. What is the minimum amount of points whose coordinates we need to calculate to draw the plot?

Task
Draw the plot of the functionplot of the functionplot of the function $f\left(x\right)=\frac{1}{3}x$.

Task
Give the formula of the functionformula of the functionformula of the function f(x) = ax, if the point A (2, -4) belongs to its plot.

Task
In the picture there is the plot of the function f(x) = ax. Calculate a.

[Illustration 1]

An extra task:
The plot of the functionplot of the functionplot of the function f(x) = -x was translated two units up along the axis Y, and as a result plot of the function g was obtained. Give formula of the functionformula of the functionformula of the function g.

Lesson summarym811140c72578dc3e_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, whose quotient is constant.

Therefore y = ax. The number a, different from zero, is called the coefficient of proportionalitycoefficient of proportionalitycoefficient of proportionality.

- The plot of the function f(x) = ax, where a ≠ 0, is a line whose equation is y = ax.
- The plot of the function f(x) = ax, for $x\in R$ goes through the beginning of the coordinate system and through each point (x, ax).m811140c72578dc3e_1527752256679_0- The plot of the function f(x) = ax, where a ≠ 0, is a line whose equation is y = ax.
- The plot of the function f(x) = ax, for $x\in R$ goes through the beginning of the coordinate system and through each point (x, ax).

Selected words and expressions used in the lesson plan

coefficient of proportionalitycoefficient of proportionalitycoefficient of proportionality

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

tabletabletable

values directly proportionalvalues directly proportionalvalues directly proportional