Topicm32e925d608ce61cf_1528449000663_0Topic

Comparing rational numbersrational numbersrational numbers

Levelm32e925d608ce61cf_1528449084556_0Level

Second

Core curriculumm32e925d608ce61cf_1528449076687_0Core curriculum

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

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

Timingm32e925d608ce61cf_1528449068082_0Timing

45 minutes

General objectivem32e925d608ce61cf_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm32e925d608ce61cf_1528449552113_0Specific objectives

1. Comparing rational numbersrational numbersrational numbers.

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

Learning outcomesm32e925d608ce61cf_1528450430307_0Learning outcomes

The studnet:

- compares rational numbersrational numbersrational numbers.

Methodsm32e925d608ce61cf_1528449534267_0Methods

1. Discussion.

2. Task tablestask tablesTask tables.

Forms of workm32e925d608ce61cf_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm32e925d608ce61cf_1528450127855_0Introduction

Students revise information about rational numbersrational numbersrational numbers, give examples of such numbers and assign them to various sets (for example natural sets or integers).

The teacher introduces the subject of the class – comparing natural numbers.

Procedurem32e925d608ce61cf_1528446435040_0Procedure

Brainstorming – how to compare two rational numbersrational numbersrational numbers? Students should notice that in order to do that we can investigate differences of those numbers, their quotient or location on the number linenumber linenumber line.

Task

Students work individually, using computers. Their task is to place points on the number line in such a way that they have given coordinate. Based on the position of the points on the number line they compare the numbers.

[Geogebra applet]

Conclusions students should draw:

- Each positive number is greater than the negative number.
- Out of two positive numbers the one located further from 0 on the number line is greater.
- Out of two negative numbers the one located closer to 0 on the number line is greater.m32e925d608ce61cf_1527752263647_0- Each positive number is greater than the negative number.
- Out of two positive numbers the one located further from 0 on the number line is greater.
- Out of two negative numbers the one located closer to 0 on the number line is greater.

Students work in groups using the task table method. They are supposed to do exercises.

Table 1 – a task to do
Arrange numbers from the smallest one to the greatest one, by marking them on the number linenumber linenumber line first:

$-1\frac{1}{5};1,4;-1,8;\frac{3}{5};1\frac{1}{4};-0,4;\frac{1}{2}$.

Table 2 – a task to do
Insert a proper sign in the dotted place: <, =, >.

a) $\frac{4}{7}...\frac{5}{7}$

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

c) $-\frac{1}{4}...-\frac{1}{3}$

d) $-3,14...-3,15$

Table 3 – a task to do
Insert such a number in the dotted place that the inequality is true.

a) $1,37<...<1,38$

b) $-4,51<...<-4,52$

c) $\frac{5}{6}<...<\frac{5}{7}$

d) $-2\frac{1}{2}<...<-2\frac{1}{3}$

Table 4 – a task to do
Give any three rational numbersrational numbersrational numbers that are greater than -2,37 and smaller than -2,36.

An extra table:
Insert such numbers in the dotted places that the condition is true:
$-\frac{3}{\square }<-\frac{3}{8}<-\frac{\square }{8}$.

Groups present results of their work. The teacher clarifies the doubts and grades groups’ work.

Lesson summarym32e925d608ce61cf_1528450119332_0Lesson summary

Students do the revision exercises.

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

- Numbers can be compared by marking their position on the number linenumber linenumber line.

- Each positive number is greater than the negative number. Out of two positive numbers the one located further from 0 on the number line is greater.

- Out of two negative numbers the one located closer to 0 on the number linenumber linenumber line is greater.

Selected words and expressions used in the lesson plan

comparing numberscomparing numberscomparing numbers

fractionsfractionsfractions

number linenumber linenumber line

rational numbersrational numbersrational numbers

task tablestask tablestask tables