Topicm5d218001753b8b5e_1528449000663_0Topic

The sum, the product and the difference of the number intervalnumber intervalnumber interval

Levelm5d218001753b8b5e_1528449084556_0Level

Third

Core curriculumm5d218001753b8b5e_1528449076687_0Core curriculum

I. Real numbersreal numbersReal numbers. The student:

6) uses the concept of the number intervalnumber intervalnumber interval, marks the intervals on the number linenumber linenumber line.

Timingm5d218001753b8b5e_1528449068082_0Timing

45 minutes

General objectivem5d218001753b8b5e_1528449523725_0General objective

Interpretation and the use of information presented both in a mathematical and popular science texts also using graphs, diagrams and tables.

Specific objectivesm5d218001753b8b5e_1528449552113_0Specific objectives

1. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2. Getting to know the definitions of the sum, the product and the difference of the number intervals.

3. Marking the sum, the product and the difference of the number intervals on the number linenumber linenumber line.

Learning outcomesm5d218001753b8b5e_1528450430307_0Learning outcomes

The student:

- knows the definitions of the sum, the product and the difference of the number intervals,

- marks the sum, the product and the difference of the number intervals on the number line.

Methodsm5d218001753b8b5e_1528449534267_0Methods

1. Wandering posters.

2. Situational analysis.

Forms of workm5d218001753b8b5e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm5d218001753b8b5e_1528450127855_0Introduction

The students are divided into groups. Every group gets a sweet of paper with one question referring to the number intervals. The students write down their answer and pass the poster to another group. There are as many rounds as there are groups. Having finished work, the representative of each group reads the answers from the posters. The posters are placed on the board. The teacher and the students analyse the content of the posters and explain the doubts.

Procedurem5d218001753b8b5e_1528446435040_0Procedure

The teacher informs the students that the aim of the class is getting to know the sum, the product and the difference of the number intervals as well as presenting them on a number linenumber linenumber line.

Discussion – what is the sum, the product and the difference of the number intervals. The students find the answers in the available sources.

Definition

- A set of elements that belong to set A or set B is called the sum of sets A and B (represented as A ∪ B).

- A set of elements that belong to set A, but don’t belong to set B is called the difference of sets A and B (represented as A – B or A \ B).

A set of elements that belong to set A and at the same time to set B is called the intersection (product) of sets A and B (represented as A ∩ B).

Task
Make a graphic representation of the sum, the product and the difference of the number intervals.
Discussion – can the same operations be performed on the number intervals as on sets? The students formulate their hypotheses, check them and formulate the conclusion. The analysis of the interactive diagram will help the students.m5d218001753b8b5e_1527752256679_0Make a graphic representation of the sum, the product and the difference of the number intervals.
Discussion – can the same operations be performed on the number intervals as on sets? The students formulate their hypotheses, check them and formulate the conclusion. The analysis of the interactive diagram will help the students.

[Interactive illustration]

The conclusion that should be formulated by the students:

- Operations can be performed on number intervals because they are sets.

Using the definitions the students solve the tasks individually.

Task
Find sets:m5d218001753b8b5e_1527752263647_0Find sets: A ∪ B, A ∩ B, A \ B, B \ A.

a) $A=(-5,0),B=<-3,5)$

b) $A=(-6,3),B=<-2,4)$

c) $A=(-\infty ,7),B=<-2,\infty )$

Task
Mark set X on the number linenumber linenumber line.

a) $X=(-3,1)\cup (3,5)$

b) $X=<-4,1>\cup <2,3>\cup <5,7>$

Task
Let A = (-6, 4), B = (-8, 6). How many integers belong to set.

a) A ∪ B

b) A ∩ B

c) A \ B

d) B \ A

Task
How many elements belong to set X? Make an appropriate illustration.

a) $X=<-4,7>\cap \mathrm{\mathbb{N}}$

b) $X=(0,8)\cap \mathrm{\mathbb{N}}$

c) $X=<-\sqrt{6},\sqrt{6}>\cap \mathrm{ℂ}$

Having solved all the tasks, the students present their results. The teacher assesses their work and explains the doubts.

An extra task:
Which of the sets: A ∪ B, A ∩ B, A \ B, B \ A is an empty set?

a) $A=(0,6),B=<0,6>$

b) $A=<2,5>,B=(5,8>$

Lesson summarym5d218001753b8b5e_1528450119332_0Lesson summary

The students do the consolidation tasks.

They formulate the conclusions to memorize.

- Operations can be performed on number intervals because they are sets.

Selected words and expressions used in the lesson plan

natural numbersnatural numbersnatural numbers

number intervalnumber intervalnumber interval

number linenumber linenumber line

product of intervalsproduct of intervalsproduct of intervals

real numbersreal numbersreal numbers

subset of the set of real numberssubset of the set of real numberssubset of the set of real numbers

sum of intervalssum of intervalssum of intervals