Topicm248bbbef875b16c3_1528449000663_0Topic

Divisors of the natural numbers

Levelm248bbbef875b16c3_1528449084556_0Level

second

Core curriculumm248bbbef875b16c3_1528449076687_0Core curriculum

II. Operations on the natural numbers. The student:
13) finds the greatest common divisorthe greatest common divisorthe greatest common divisor (GCD) in the less difficult situation than GCD (600, 72), GCD (140, 567), GCD (10000, 48), GCD (910, 2016) and he determines the leastthe leastthe least common multiple of two natural numbers using the method of prime factorization.

Timingm248bbbef875b16c3_1528449068082_0Timing

45 minutes

General objectivem248bbbef875b16c3_1528449523725_0General objective

Reading, interpreting and processing data presented in various forms.

Specific objectivesm248bbbef875b16c3_1528449552113_0Specific objectives

1) You recognise the divisors of the natural numbers.

2) Indicating the greatest common divisorthe greatest common divisorthe greatest common divisor of two natural numbers.

3) Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Learning outcomesm248bbbef875b16c3_1528450430307_0Learning outcomes

The student:
- recognises and writes down the divisors of the natural numbers,

- identifies the greater common divisor of two natural numbers.

Methodsm248bbbef875b16c3_1528449534267_0Methods

1) Brainstorming.

2) Situational analysis.

Forms of workm248bbbef875b16c3_1528449514617_0Forms of work

1) Individual work.

2) Pair work.

Lesson stages

Introductionm248bbbef875b16c3_1528450127855_0Introduction

The students prepare 10 cards with oneoneone of the following numbers: 2, 3, 4, 6, 8, 12, 15, 24, 30 or 48.

The students revise the information about the division with the remainderthe remainderthe remainder.

Procedurem248bbbef875b16c3_1528446435040_0Procedure

Teacher introduces the topic of the lesson: discovering the notion of the divisor of the natural numbernatural numbernatural number. They are also going to determine the greater common divisor of two natural numbers.

Task 1
The students work individually using their computers. They are going to analyse the slideshow concerning the divisors of the number 6.

[SLIDESHOW]

Discussion: What number is the leastthe leastthe least divisor of number six? Is the number 1 divisor of each natural numbernatural numbernatural number? What number is the greatest divisor of the number 6? Is each natural numbernatural numbernatural number a divisor of itself? What numbers are the divisors of zerozerozero?

The students may draw the following conclusions:
- Number 1 is the leastthe leastthe least divisor of number 6 and each natural numbernatural numbernatural number.
- The greatestthe greatestThe greatest divisor of number 6 is 6.
- Every natural non‑zero number is its greatest divisor.
- All positive natural numbers are the divisors of zerozerozero.

Depending on the gained information the students write the divisors of the following numbers:

Task 2
Write all the divisors of the following numbers:

a) 4

b) 18

c) 25

d) 36

Task 3
Write down all the even divisors of number 40.

Task 4
Pair work. OneoneOne student writes all the divisors of number 27 and the other oneoneone all divisors of number 45. Next, the students compare the numbers they have written and they identify the common divisors of the numbers 27 and 45. They choose the greatest one.

Task 5
The students work individually using their computers. They are going to watch the illustration and note how the greatest common divisorthe greatest common divisorthe greatest common divisor is written.

[ILLUSTRATION]

Task 6
The students work in pairs. OneoneOne students draw two of the cards they have prepared for the lesson. The other student indicates and write the greatest common divisorthe greatest common divisorthe greatest common divisor of the drawn numbers. Then, they swap their roles and repeat the activity three times.

Task7
Artur has bought 42 sweets and 28 tangerines for his birthday party. How many children can he invite if each child is to get the same number of the tangerines and the sweets?

An extra task:
Use the Internet to look for the information about perfect numbers. Give three examples of them.

Lesson summarym248bbbef875b16c3_1528450119332_0Lesson summary

The students do the summarising tasks.
Then they sum up the classes drawing the conclusion to memorise:
- Number 1 is the leastthe leastthe least divisor of every natural numbernatural numbernatural number.
- Every natural non‑zero number is its greatest divisor.
- All positive natural numbers are the divisors of zerozerozero.

Selected words and expressions used in the lesson plan

divisor of the numberdivisor of the numberdivisor of the number

the greatest common divisorthe greatest common divisorthe greatest common divisor

natural numbernatural numbernatural number

the greatestthe greatestthe greatest

the leastthe leastthe least

the remainderthe remainderthe remainder

perfect numberperfect numberperfect number

zerozerozero

oneoneone