Topicmdebf7ca2f92c0da6_1528449000663_0Topic

Comparison of natural numbers

Levelmdebf7ca2f92c0da6_1528449084556_0Level

Second

Core curriculummdebf7ca2f92c0da6_1528449076687_0Core curriculum

I. Natural numbers of the decimal natural system . The student:

3) compares the natural numbers.

Timingmdebf7ca2f92c0da6_1528449068082_0Timing

45 minutes

General objectivemdebf7ca2f92c0da6_1528449523725_0General objective

Reading, interpreting and processing data presented in various forms.

Specific objectivesmdebf7ca2f92c0da6_1528449552113_0Specific objectives

1. Comparing the natural numbers.

2. Putting the natural numbers in the ascendingascendingascending and descendingdescendingdescending order.

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

Learning outcomesmdebf7ca2f92c0da6_1528450430307_0Learning outcomes

The student:

- compares the natural numbers,

- puts the numbers in the ascendingascendingascending or descendingdescendingdescending order.

Methodsmdebf7ca2f92c0da6_1528449534267_0Methods

1. Brainstorming.

2. Learning game.

Forms of workmdebf7ca2f92c0da6_1528449514617_0Forms of work

1. Individual work.

2. Pair work.

Lesson stages

Introductionmdebf7ca2f92c0da6_1528450127855_0Introduction

Every student prepares the deck of 15 cards cut out of the paper. The top is marked with any colour or pattern to distinguish the deck from the other cards.

Every card has the following numbers written on them:

3540; 35400; 354; 453; 4053; 4305; 43500; 46540; 406540; 46305; 35435; 3504; 53060; 2540 or 205040.

Proceduremdebf7ca2f92c0da6_1528446435040_0Procedure

The teacher introduces the topic of the lesson: comparing the natural numbers.

Discussion:

Which number is largerlargerlarger 27 or 256? What about 50 or 50000? Which number is larger 340 or 840? What about  25100 or  25198? If two numbers in the decimal system have the different number of digitsdigitsdigits which one is larger? And what about if they have the same number of digits?

The students can come up with the following conclusions:

- If two natural numbers have different number of digits in their decimal system the larger is the one with more digits.
- To compare the numbers with the same number of digits we compare step by step their digits starting from the left side.mdebf7ca2f92c0da6_1527752256679_0- If two natural numbers have different number of digits in their decimal system the larger is the one with more digits.
- To compare the numbers with the same number of digits we compare step by step their digits starting from the left side.

The students work on their own using their computers. They are going to compare the given natural numbers.

Task 1

Open the applet and compare the given numbers using the following signs: <, > or =.

[Geogebra applet]

The students analyse the example and consider what the expression „putting in ascendingascendingascending or descendingdescendingdescending order” means.

Example:

The ascendingascendingascending order of numbers:

 3 < 15 < 19 < 58 < 120 < 300

The descendingdescendingdescending order of numbers:

250 > 190 > 145 > 87 > 53 > 2

As the result of the discussion the following conclusions can be drawn:

- The ascending order means writing them from the smallest to the largest.
- The descending order means writing them from the largest to the smallest one.mdebf7ca2f92c0da6_1527752263647_0- The ascending order means writing them from the smallest to the largest.
- The descending order means writing them from the largest to the smallest one.

The students use the decks of cards they have prepared for the lesson. They are going to put them in the specified order.

Task 2

a) Put the cards with four‑digit numbers in order from the smallest to the largest.

b) Put the cards with five‑digit numbers in the descending order.

c) Put the all cards in the ascending order.

Students play the card game called “The war”. They work in pairs using their decks of cards.

Task 3

Play the game „The war”.  Shuffle your cards, then take out the top card of your deck  cards both at the same time. Compare the numbers on your cards. The player who has the card with the largerlargerlarger number takes both cards and adds them to his deck. If the two cards played are of the equalequalequal value there is a war”. Both players place next card of their pile face down, and then another card face‑up. The owner of the higher face‑up card wins the war and takes all the cards. The winner is the person who takes all the opponent’s cards.

An extra task:

Put in the descending order the following numbers:

$7^2 + 2^2$

${\left(7+2\right)}^2$

$65000 : 1000 - 700 : 100$

$6 \cdot (630 : 70)$

$49000 : 1000 + 6$

Lesson summarymdebf7ca2f92c0da6_1528450119332_0Lesson summary

The students do the summarising tasks. 

Then they sum up the class drawing the conclusions to memorise:

- If two natural numbers have different number of digitsdigitsdigits in their decimal system the larger is the one with more digits.

- To compare the numbers with the same number of digits we compare step by step their digits starting from the left side.

- The ascending order means writing the numbers from the smallest to the largest one.

- The descending order means writing the numbers from the largest to the smallest one.

Selected words and expressions used in the lesson plan

comparison of the natural numberscomparison of the natural numberscomparison of the natural numbers

descendingdescendingdescending

ascendingascendingascending

largerlargerlarger

smallersmallersmaller

equalequalequal

digitsdigitsdigits

even numbereven numbereven number

odd numberodd numberodd number

the war (card game)the war (card game)the war (card game)