Topicme92613b555d384dc_1528449000663_0Topic

Converting decimal fractions into common fractionsconverting decimal fractions into common fractionsConverting decimal fractions into common fractions

Levelme92613b555d384dc_1528449084556_0Level

Second

Core curriculumme92613b555d384dc_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

8) writes the finite decimal fractionsdecimal fractionsdecimal fractions in a form of common fractionscommon fractionscommon fractions.

Timingme92613b555d384dc_1528449068082_0Timing

45 minutes

General objectiveme92613b555d384dc_1528449523725_0General objective

Doing the simple operations of mental calculation or more difficult ones in writing and using these abilities in practical situations.

Specific objectivesme92613b555d384dc_1528449552113_0Specific objectives

1. Writing the finite decimal fractions in a form of common fractions.

2. Reducing the common fractions.

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

Learning outcomesme92613b555d384dc_1528450430307_0Learning outcomes

The student:

- writes the finite decimal fractions in a form of common fractions,

- reduces the common fractions.

Methodsme92613b555d384dc_1528449534267_0Methods

1. Learning game.

2. Situational analysis.

Forms of workme92613b555d384dc_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionme92613b555d384dc_1528450127855_0Introduction

The teacher prepares a set of 34 cards for each group. There are one of the following numbers on each of them:
$0,3;\frac{3}{10};0,03;\frac{3}{100};0,003;\frac{3}{1000};0,27;\frac{27}{100};0,027;\frac{27}{1000};0,207;\frac{207}{1000};2,4;2\frac{4}{10};20,04;20\frac{4}{100};2,044;2\frac{44}{1000};8,8;8\frac{8}{10};8,888;8\frac{888}{1000};0,1;\frac{1}{10};0,25;\frac{1}{4};0,5;\frac{1}{2};0,75;\frac{3}{4};0,125;\frac{1}{8}.$

The students take part in the learning game. They revise the reading and the reducing of the decimal fractionsdecimal fractionsdecimal fractions.

The teacher presents the quiz. The students write the answers A, B or C next to the task on the card prepared earlier. After completing the tasks the students swap the cards. They compare their answers with the ones presented below. They assess their own work. 

Quiz:

1. The fraction 37.307 means:

A. thirty seven and thirty seven thousandths,
B. thirty seven and three hundred seven hundredths,
C. thirty seven and three hundred seven thousandths.

2. The irreducible form of the fraction $\frac{72}{90}$ is the one of:

A. $\frac{4}{5}$,
B. $\frac{3}{4}$,
C. $\frac{8}{10}$.

3. The fraction of twenty and eight hundredths is written as:

A. $\frac{28}{100}$,
B. $20\frac{8}{10}$,
C. $20\frac{8}{100}$.

4. Tick the incorrect equality.

A. $\frac{{\displaystyle 16}}{60}=\frac{4}{15}$,
B. $\frac{{\displaystyle 35}}{100}=\frac{5}{20}$,
C. $3\frac{{\displaystyle 36}}{1000}=3\frac{9}{250}$.

The correct answers are the following ones:

1. C, 2. A, 3. C, 4. B, 5. A.

Procedureme92613b555d384dc_1528446435040_0Procedure

Teacher introduces the topic of the lesson: converting the decimal fractionsdecimal fractionsdecimal fractions into the common ones.

The students work individually using their computers. They are going to analyse the slideshow concerning the conversion of the decimal fractions into the common ones.

[Slideshow]

Discussion: What is the connection between the denominatordenominatordenominator of the common fraction and the number of the decimal places in the decimal fraction? What method should be used to convert the decimal fractions into the common ones?  

The students come up with the following conclusions:

- We write one and as many zeros as there are places after the decimal point of the converted decimal fraction as a denominator e.g. 10 if there was one decimal place, 100 if there were two places , 1000 if there were three places etc.
- The number which occurred after the decimal place of the decimal fraction is written in the numerator. The whole numbers remain the same.me92613b555d384dc_1527752256679_0- We write one and as many zeros as there are places after the decimal point of the converted decimal fraction as a denominator e.g. 10 if there was one decimal place, 100 if there were two places , 1000 if there were three places etc.
- The number which occurred after the decimal place of the decimal fraction is written in the numerator. The whole numbers remain the same.

Using the gained information the students convert the decimal fractions into the common ones. Then, in pairs they compare the results.

Task 1

Write the following fractions in the decimal and common forms.

a) thirteenth hundredths,
b) five and seven thousandths,
c) eighteen and twenty three thousandths,
d) six and six tenths.

Task 2

Match in pairs the equal fractions. Fill the gaps with the appropriate letters of  A, B, C, D, E or F.

1) $5.6,$
2) $5.06,$
3) $6.005,$
4) $6.5,$ 
5) $6.05,$
6) $5.006.$

A) $6\frac{5}{100},$
B) $5\frac{6}{1000},$
C) $5\frac{6}{10},$
D) $6\frac{5}{1000},$ 
E) $6\frac{5}{10},$ 
F) $5\frac{6}{100}.$

1. ___ 2. ___ 3. ___ 4. ___ 5. ___ 6. ___

Task 3

Write the decimal fractionsdecimal fractionsdecimal fractions in a form of the common ones and reduce them if it is possible.

a) 0.17,
b) 2.04,
c) 0.023,
d) 0.35,
e) 13.09,
f) 15.002,
g) 7.125,
h) 34.6.

Task 4

Match in pairs the equal fractions. Fill the gaps with the appropriate letters of  A, B, C, D, E or F.

1) $0.375,$
2) $0.25,$
3) $0.15,$
4) $0.08,$ 
5) $0.65,$
6) $0.625.$

A) $\frac{13}{20},$
B) $\frac{3}{8},$
C) $\frac{2}{25},$
D) $\frac{5}{8},$ 
E) $\frac{1}{4},$ 
F) $\frac{3}{20}.$

1. ___ 2. ___ 3. ___ 4. ___ 5. ___ 6. ___

The students play the „Memory game” to revise the conversion of the decimal fractions in common ones.

The students sit around the table and work in groups of three or four. They put the cards writing side down in front of them. One students takes two cards, if the fractions written on them are equal he puts them aside and takes another two. If the fractions aren’t equal he covers them and ends his turn. The student on his left continues the game. The game is over when all the pairs are found.

An extra task:

Write the following decimal fractionsdecimal fractionsdecimal fractions in a form of the irreducible common fractionscommon fractionscommon fractions.

a) 31.55555,

b) 15.4048,

c) 0.84645.

Lesson summaryme92613b555d384dc_1528450119332_0Lesson summary

The students do the summarising tasks.

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

When we convert the decimal fraction in the common one we:

- don’t change the whole numbers;
- write the number which occurred after the decimal point in the decimal fraction as the numerator of the common fraction;
- write one and as many zeros as there are places after the decimal point of the converted decimal fraction as a denominator e.g. 10 if there was one decimal place, 100 if there were two places , 1000 if there were three places etc.me92613b555d384dc_1527752263647_0- don’t change the whole numbers;
- write the number which occurred after the decimal point in the decimal fraction as the numerator of the common fraction;
- write one and as many zeros as there are places after the decimal point of the converted decimal fraction as a denominator e.g. 10 if there was one decimal place, 100 if there were two places , 1000 if there were three places etc.

Selected words and expressions used in the lesson plan

common fractionscommon fractionscommon fractions

converting decimal fractions into common fractionsconverting decimal fractions into common fractionsconverting decimal fractions into common fractions

decimal fractionsdecimal fractionsdecimal fractions

decimal placedecimal placedecimal place

denominatordenominatordenominator

descendingdescendingdescending

irreducible form of fractionirreducible form of fractionirreducible form of fraction

numeratornumeratornumerator

reducing the common fractionreducing the common fractionreducing the common fraction