Topicm55b29b884c19ac45_1528449000663_0Topic

The concept of function, functional dependency

Levelm55b29b884c19ac45_1528449084556_0Level

Third

Core curriculumm55b29b884c19ac45_1528449076687_0Core curriculum

V. Functions. The student:

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

Timingm55b29b884c19ac45_1528449068082_0Timing

45 minutes

General objectivem55b29b884c19ac45_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm55b29b884c19ac45_1528449552113_0Specific objectives

1. Identifying correspondences that are functions.

2. Describing functional dependencies.

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

Learning outcomesm55b29b884c19ac45_1528450430307_0Learning outcomes

The student:

- identifies correspondenes that are functions,

- describes functional dependencies.

Methodsm55b29b884c19ac45_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm55b29b884c19ac45_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson plan

Introductionm55b29b884c19ac45_1528450127855_0Introduction

During this class, students will be describing functional dependencies and will get to know the concept of functionfunctionfunction.

Procedurem55b29b884c19ac45_1528446435040_0Procedure

Students assign proper capital to a proper country.

[Illustration 1]

They notice that it is bijective correspondencecorrespondencecorrespondence. They illustrate the solution in the form of a graph.

[Illustration 2]

Each country has exactly one capital assigned to it.

Group work – students do similar exercises.

Task

In the beginning of the school year, the nurse made measurements of height of all students. In one of the groups she obtained the following results:

[Table 1]

Analyse the data in the table. Draw conclusions.

Do the graph of proper correspondences.

Students should notice that the association is not bijective – 3 persons have the same height.

An exemplary graph made by students:

[Illustration 3]

Each student has its height assigned.

Task
Students observe how the distance made by car is changing in constant time units.

They compare considered examples, try to define the function as bijective correspondencecorrespondencecorrespondence.

[Geogebra applet]

Definition of functionfunctionfunction.

Function $f$ from the set $X$ into set $Y$ is called correspondence in which each element of the set $X$ corresponds to exactly one element of the set $Y$. We write down function f defined in the set $X$ with values in the set $Y$ in the form of:m55b29b884c19ac45_1527752256679_0Function $f$ from the set $X$ into set $Y$ is called correspondence in which each element of the set $X$ corresponds to exactly one element of the set $Y$. We write down function f defined in the set $X$ with values in the set $Y$ in the form of:

Students use shaped abilities in exercises.

Task

Fill in the dotted spaces in such a way that the correspondencecorrespondencecorrespondence is a functionfunctionfunction.

a) Each triangle corresponds to  ...
b) Each natural number corresponds to ...
c) Each cube corresponds to ...

Task

Determine sets $X$ and $Y$ in such a way that the correspondence $f:X\to Y$ illustrates a function.
Use the following data:
a) A set of dates of birth, a set of people.
b) A set of numbers expressing the area of a city, a set of cities.
c) A set of names, a set of number of letters occurring in the name.m55b29b884c19ac45_1527752263647_0Determine sets $X$ and $Y$ in such a way that the correspondence $f:X\to Y$ illustrates a function.
Use the following data:
a) A set of dates of birth, a set of people.
b) A set of numbers expressing the area of a city, a set of cities.
c) A set of names, a set of number of letters occurring in the name.

Task

Give examples of such two sets X and $Y$, that the created correspondence $f:X\to Y$ and $g:Y\to X$ are functions.

An extra task:

Give two examples of correspondencecorrespondencecorrespondence being functions, using data from your school ID.

Lesson summarym55b29b884c19ac45_1528450119332_0Lesson summary

Students do the revision exercises.

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

Function $f$ from the setsetset $X$ into set $Y$ is called correspondencecorrespondencecorrespondence in which each element of the setelement of the setelement of the set $X$ corresponds to exactly one element of the setelement of the setelement of the set $Y$. We write down function f defined in the setsetset $X$ with valuesvaluesvalues in the set $Y$ in the form of:

Selected words and expressions used in the lesson plan

functionfunctionfunction

functional dependencefunctional dependencefunctional dependence

correspondencecorrespondencecorrespondence

setsetset

element of the setelement of the setelement of the set

valuesvaluesvalues