Topicmc8204678bf965ad0_1528449000663_0Topic

Numbers in the decimal numeral system

Levelmc8204678bf965ad0_1528449084556_0Level

Second

Core curriculummc8204678bf965ad0_1528449076687_0Core curriculum

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

1) writes down and reads the natural multi‑digit numbers;

Timingmc8204678bf965ad0_1528449068082_0Timing

45 minutes

General objectivemc8204678bf965ad0_1528449523725_0General objective

Reading, interpreting and processing data presented in various forms.

Specific objectivesmc8204678bf965ad0_1528449552113_0Specific objectives

1. Writing the natural numbers in a form of the sum.

2. Specifying the position of the digit in the number.

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

Learning outcomesmc8204678bf965ad0_1528450430307_0Learning outcomes

The student:

- writes down the natural numbers in a form of the sum,

- points out the unit digitunit digitunit digit, the tens digittens digittens digit, the hundreds digithundreds digithundreds digit in the number.

Methodsmc8204678bf965ad0_1528449534267_0Methods

1. Brainstorming.

2. Situational analysis.

Forms of workmc8204678bf965ad0_1528449514617_0Forms of work

1. Pair work.

2. Individual work.

Lesson stages

Introductionmc8204678bf965ad0_1528450127855_0Introduction

The students are going to work in pairs. The teacher prepares the set of cards for each pair of students. There is one of the following amounts on the cards:

97 PLN, 79 PLN, 425 PLN, 245 PLN, 452 PLN, 703 PLN, 730 PLN, 307 PLN, 370 PLN or 288 PLN.

Every student prepares “the banknotes “ and “the coins” for the lesson:

- 10 smaller and 10 largerlargerlarger cards (as „banknotes”) cut out of the paper. He writes “10 PLN” on the smallersmallersmaller cards and “100 PLN”on the larger ones;

- 10 circles cut out of the paper as the coins. They write “1 PLN” on each of them.

Every student also prepares the sheet of paper with the list of numbers:

1.
2.
3.
4.
5.

The students revise how the symbols used to write down the numbers are called and how many Arabic numerals are used in our numeral system.

Proceduremc8204678bf965ad0_1528446435040_0Procedure

Teacher introduces the topic of the lesson: discovering the method of writing down the natural numbers in a form of the sum and identifying the position of the digit in the number.

Task 1

The students work in pairs. They use the sets the teacher has prepared. The first student (the client of a bank) draws the card with the amountamountamount written on it, the other student (the cashier) reads it aloud and pays the sum by giving the appropriate number of coins and banknotes. The client writes the amount of money in the form of the sum.

After five turns they swap their roles.

The students work individually. They are going to write down the sum of the given amountamountamount of money in the form of the sum.

Task 2

Write down the following amounts depending on the formula below:

$247 PLN = 2 · 100 PLN + 4 · 10 PLN + 7 · 1 PLN$

a) $571 PLN$
b) $63 PLN =$
c) $306 PLN =$
d) $940 PLN =$
e) $800 PLN =$
f) $50 PLN =$

The students still work individually. They are going to write down the amount of money depending on the coins and the banknotes it consists of.

Task 3

What are the following amounts? Write your answer using digitals.
a) nine 100 PLN banknotes, five 10 PLN banknotes and six 1 PLN coins,
b) six 10 PLN banknotes and two 1 PLN coins,
c) three 100 PLN banknotes and two 1 PLN coins,
d) four 100 PLN banknotes and eight 10 PLN banknotes,
e) five 100 PLN banknotes.mc8204678bf965ad0_1527752263647_0What are the following amounts? Write your answer using digitals.
a) nine 100 PLN banknotes, five 10 PLN banknotes and six 1 PLN coins,
b) six 10 PLN banknotes and two 1 PLN coins,
c) three 100 PLN banknotes and two 1 PLN coins,
d) four 100 PLN banknotes and eight 10 PLN banknotes,
e) five 100 PLN banknotes.

On the basis of completed tasks and their knowledge the students revise which digit in the number 682
is called the hundreds digithundreds digithundreds digit, the tens digittens digittens digit and the units digitunit digitunits digit.

Discussion:

Why do we call the numeral system we use the decimal system?
Why do we call the numeral system we use the positional system?
The discussion can end by drawing the following conclusions:
- The numeral system which we use is called the decimal system because 10 units make one ten, 10 tens make one hundred etc.
- The numeral system which we use is called the positional system because the meaning of the digit in the number depends on the place, so on the position which it has in the number e.g. the numbers 54 and 45 are not equal.mc8204678bf965ad0_1527752256679_0Why do we call the numeral system we use the decimal system?
Why do we call the numeral system we use the positional system?
The discussion can end by drawing the following conclusions:
- The numeral system which we use is called the decimal system because 10 units make one ten, 10 tens make one hundred etc.
- The numeral system which we use is called the positional system because the meaning of the digit in the number depends on the place, so on the position which it has in the number e.g. the numbers 54 and 45 are not equal.

Task 4

The students work individually using their computers. They are going to write down the number depending on the information how many hundreds, tens and units it consists of.

[Geogebra applet]

The students write the numbers  from 1 to 5 selected by the teacher on the cards.

After completing the task they swap their cards and check the answers they have given.

Task 5

Use the digits to write:

1. the largest three‑digit number with three different digits,

2. the smallest three‑digit number with the hundreds digithundreds digithundreds digit of 4 and the tens digittens digittens digit of 2,

3. the number five hundreds larger than 321,

4. the number 7 unit smaller than 700,

5. the number which will be made after changing the places of the digits of units and hundreds in the number 563.

An extra task

Find out on the Internet the information about the binary numeral system. Using this system write the number 255.

Lesson summarymc8204678bf965ad0_1528450119332_0Lesson summary

The students do the summarising tasks. 

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

- The decimal numeral system is most commonly used system.

- In the decimal systemdecimal systemdecimal system ten units make one ten, 10 tens make one hundred , 10 hundreds make one thousand etc.

- In the positional systempositional systempositional system the meaning of the digit in the number depends on the place, so on the position which it has in the number e.g. the numbers 54 and 45 are not equal.

Selected words and expressions used in the lesson plan

decimal systemdecimal systemdecimal system

positional systempositional systempositional system

unit digitunit digitunit digit

tens digittens digittens digit

hundreds digithundreds digithundreds digit

largerlargerlarger

smallersmallersmaller

banknotebanknotebanknote

coincoincoin

amountamountamount