Topicm833fd112fa59bd5c_1528449000663_0Topic

Distance on the number line

Levelm833fd112fa59bd5c_1528449084556_0Level

Second

Core curriculumm833fd112fa59bd5c_1528449076687_0Core curriculum

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

9) calculates values of arithmetic expression that require arithmetic calculations on integers or numbers written as common fractions, mixed numbers and decimal fractions, also rational negative, not more difficult than:

$-\frac{1}{2}÷0,25+5,25÷0,05-7\frac{1}{2}\cdot (2,5-3\frac{2}{3})+1,25$.

Timingm833fd112fa59bd5c_1528449068082_0Timing

45 minutes

General objectivem833fd112fa59bd5c_1528449523725_0General objective

Doing simple calculations mentally or using the long method in more difficult examples, using these abilities in practical situations.

Specific objectivesm833fd112fa59bd5c_1528449552113_0Specific objectives

1. Marking number sets on the number line.

2. Calculating distances between numbers on the number line.

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

Learning outcomesm833fd112fa59bd5c_1528450430307_0Learning outcomes

The student:

- marks number sets on the number line,

- calculates distances between numbers on the number line.

Methodsm833fd112fa59bd5c_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm833fd112fa59bd5c_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm833fd112fa59bd5c_1528450127855_0Introduction

Students revise information they learnt about rational numbers on previous classes.

The teacher introduces the subject of the lesson - marking number sets on the number linenumber linenumber line and calculating distances between numbers on the number linenumber linenumber line.

Procedurem833fd112fa59bd5c_1528446435040_0Procedure

Task

Students work individually, using computers. Their task is to observe the way of calculating distances between numbers on the number linenumber linenumber line.

[Slideshow]

In groups, students discuss presented examples, make theories and verify them on specific examples, possibly by using calculators. Then they draw conclusions and write them down.

Conclusions:

- The distance between any two numbers located on the number linenumber linenumber line is equal to the length of a line segment connecting points corresponding to these numbers.

- In order to calculate the distance on the number linedistance on the number linedistance on the number line between two numbers, we need to subtract the smaller number from the greater number.

Students use obtained information to do exercises.

Task

Calculate the distance between numbers.m833fd112fa59bd5c_1527752263647_0Calculate the distance between numbers.

a) -3,5 and -7,5

b) $4\frac{1}{3}and-5\frac{1}{4}$

c) -3,76 and 3,95

Task

Calculate distances between numbers A and C, B and F, D and E, A and F marked on the number linenumber linenumber line.

 [Illustration 1]

The teacher gives examples of double inequalities and ways of marking sets of their solutions on the number linenumber linenumber line.

Example:
If we know that a certain number x is greater than -1 and smaller than 5, then it means that number x meets the condition: -1 < x < 5.
All numbers x that meet this condition can be marked on the number line.m833fd112fa59bd5c_1527752256679_0Example:
If we know that a certain number x is greater than -1 and smaller than 5, then it means that number x meets the condition: -1 < x < 5.
All numbers x that meet this condition can be marked on the number line.

[Illustration 2]

If we know that a certain numbercertain numbercertain number x is greater than or equal to 1 and smaller than or equal to 3, then it means that number x meets the condition: 1 ≤ x ≤ 3.

All numbers x that meet this condition can be marked on the number linenumber linenumber line.

[Illustration 3]

Students use obtained information to do exercises.

Task

Mark the set of numbers that meets the following condition.

a) -2 ≤ x < 4

b) -2,5 < x ≤ 0,5

c) 4 ≤ x ≤ 5,5

d) -3 < x < 0

Task

Give the condition that numbers marked on the number linenumber linenumber line meets.

a) [Illustration 4]

b) [Illustration 5]

c) [Illustration 6]

d) [Illustration 7]

Task

Identify all numbers that meet the condition.

a) x ≤ 3 and x is a natural number.

b) x < 3 and x is a positive integerpositive integerpositive integer.

An extra task:

How many natural numbersnatual numbersnatural numbers n meet the following condition: -2 ≤ n ≤ 0?

Lesson summarym833fd112fa59bd5c_1528450119332_0Lesson summary

Students do the revision exercises.

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

- The distance between any two numbers located on the number linenumber linenumber line is equal to the length of a line segment connecting points corresponding to these numbers.

- In order to calculate the distance on the numberdistance on the number linedistance on the number line between two numbers, we need to subtract the smaller number from the greater number.

Selected words and expressions used in the lesson plan

certain numbercertain numbercertain number

distance on the number linedistance on the number linedistance on the number line

natural numbersnatual numbersnatural numbers

number linenumber linenumber line

positive integerpositive integerpositive integer