Topicm1545b60d14f29b05_1528449000663_0Topic

Rational numbersrational numbersRational numbers

Levelm1545b60d14f29b05_1528449084556_0Level

Second

Core curriculumm1545b60d14f29b05_1528449076687_0Core curriculum

V. Calculations on common and decimal fractionsfractionsfractions. The student:

1) calculates values of arithmetic expression that require arithmetic calculations on integersintegersintegers or numbers written as common fractionsfractionsfractions, mixed numbers and decimal fractions, also rational negative, not more difficult than:
$-\frac{1}{2}:025+5,25:0,05-7\frac{1}{2}\cdot (2,5-3\frac{2}{3})+1,25$.

Timingm1545b60d14f29b05_1528449068082_0Timing

45 minutes

General objectivem1545b60d14f29b05_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm1545b60d14f29b05_1528449552113_0Specific objectives

1. Writing the number in the form of reduced fraction.

2. Identifying natural numbersnatural numbersnatural numbers, integersintegersintegers, rational numbersrational numbersrational numbers, multiplicative reverses, additive inversesadditive inversesadditive inverses and marking them on the number line.

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

Learning outcomesm1545b60d14f29b05_1528450430307_0Learning outcomes

The student:

- writes the number in the form of reduced fraction,

- identifies natural numbersnatural numbersnatural numbers, integersintegersintegers, rational numbersrational numbersrational numbers, multiplicative reverses, additive inversesadditive inversesadditive inverses and marks them on the number line.

Methodsm1545b60d14f29b05_1528449534267_0Methods

1. Discussion.

2. Chain of associations.

Forms of workm1545b60d14f29b05_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm1545b60d14f29b05_1528450127855_0Introduction

The teacher introduces the subject of the lesson – writing numbers in the form of reduced common fraction and identifying natural numbersnatural numbersnatural numbers, integersintegersintegers and rational numbersrational numbersrational numbers and marking them on the number line.

Students revise what numbers are called natural numbersnatural numbersnatural numbers, integersintegersintegers and rational numbersrational numbersrational numbers and what are the characteristics of fraction. They give examples of such numbers.

Procedurem1545b60d14f29b05_1528446435040_0Procedure

Discussion 
– What number is called rational? Students look for information in available sources of knowledge.

Definition of the rational number.
A rational number is a number that can be written in the form of a reduced fraction $\frac{a}{b}$, where a and b are integers and $b\ne 0$.
Rational numbers are natural numbers, integers and fractions.m1545b60d14f29b05_1527752263647_0Definition of the rational number.
A rational number is a number that can be written in the form of a reduced fraction $\frac{a}{b}$, where a and b are integers and $b\ne 0$.
Rational numbers are natural numbers, integers and fractions.

Students work using the method of the chain of associations. They obtain a big cardboard with a chain made of empty links on it. They fill in the links with names of number sets and their most important properties.

Students present their chains and discuss most important links. Then, they used obtained information in exercises.

Task
Prove that the following numbers are rational.

a) -4,7

b) $5\frac{4}{7}$

c) 0,(8)

d) -3,(9)

Task
Mark the following numbers on the number line. Remember about choosing the right unit.

a) $-\frac{1}{4};1,5$

b) -4,2; -2,8

c) $-\frac{2}{7};-\frac{8}{7}$

d) $\frac{7}{4};2,75$

Task
Read what numbers correspond to points marked on the number line.

Students work individually, using computers. Their task is to place a point on the number line so that it has the given coordinate.

Discussion 
– What rational numbersrational numbersrational numbers are called additive inversesadditive inversesadditive inverses and what are multiplicative inversesmultiplicative inversesmultiplicative inverses? Students discuss and make theories. They can verify their theories using available sources of information, for example the Internet.

[Geogebra applet]

Conclusions:
- The multiplicative inverse for the number a, for $a\ne 0$ is the number $\frac{1}{a}$.
- Inverses are number that are located on the opposite sides of 0 on the number line and whose distance from 0 is the same.
Students use obtained information by doing exercises.m1545b60d14f29b05_1527752256679_0- The multiplicative inverse for the number a, for $a\ne 0$ is the number $\frac{1}{a}$.
- Inverses are number that are located on the opposite sides of 0 on the number line and whose distance from 0 is the same.
Students use obtained information by doing exercises.

Task
Find the multiplicative inverse for each number.

$2,3;3\frac{1}{7};-5,625;0,\left(4\right);-4\frac{2}{11}$

Task
From the following pairs choose those that are pairs of additive inversesadditive inversesadditive inverses and those that are pairs of multiplicative inversesmultiplicative inversesmultiplicative inverses.

$\frac{4}{3}and-\frac{3}{4}$

$\frac{1}{5}and5$

$2,8and8,2$

$0,625and\frac{8}{5}$

$1\frac{2}{7}and1\frac{7}{2}$

$2,2and\frac{5}{11}$

$-4,4and\frac{22}{5}$

$-4,5and\frac{9}{2}$

An extra task:
Identify all integersintegersintegers whose distance from zero on the number line is smaller than 4,(9).

Lesson summarym1545b60d14f29b05_1528450119332_0Lesson summary

Students do the revision exercises.

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

- A rational number is a number that can be written in the form of a reduced fraction  $\frac{a}{b}$, where a and b are integersintegersintegers and $b\ne 0$.

- The multiplicative inverse for the number a, for $a\ne 0$ is the number $\frac{1}{a}$.

- Inverses are number that are located on the opposite sides of 0 on the number line and whose distance from 0 is the same.

Selected words and expressions used in the lesson plan

additive inversesadditive inversesadditive inverses

fractionsfractionsfractions

integersintegersintegers

multiplicative inversesmultiplicative inversesmultiplicative inverses

natural numbersnatural numbersnatural numbers

rational numbersrational numbersrational numbers