Topicm66b7c6c6ddf499d7_1528449000663_0Topic

Dividing the decimal fractions

Levelm66b7c6c6ddf499d7_1528449084556_0Level

Second

Core curriculumm66b7c6c6ddf499d7_1528449076687_0Core curriculum

V. The operations with the common and decimal fractionsdecimal fractionsdecimal fractions. The student:

2) adds, subtracts, multiplies, divides the decimal fractions by mental calculation (in the simplest operations), in writing or using the calculator (in the difficult ones);

8) does the operations with the decimal fractions using his own, proper strategies or using the calculator.

Timingm66b7c6c6ddf499d7_1528449068082_0Timing

45 minutes

General objectivem66b7c6c6ddf499d7_1528449523725_0General objective

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

Specific objectivesm66b7c6c6ddf499d7_1528449552113_0Specific objectives

1. Mental divisionmental divisionMental division of the decimal fractions.

2. Written divisionwritten divisionWritten division of the decimal fractions.

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

Learning outcomesm66b7c6c6ddf499d7_1528450430307_0Learning outcomes

The student:

- does the mental divisionmental divisionmental division of the decimal fractions,

- divides the decimal fractions using the written method.

Methodsm66b7c6c6ddf499d7_1528449534267_0Methods

1. Learning game.

2. Situational analysis.

Forms of workm66b7c6c6ddf499d7_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm66b7c6c6ddf499d7_1528450127855_0Introduction

The teacher prepares a set of three cards including one of the following letters: A, B or C.

The students play learning game and revise the written method of dividing the natural numbers. They also divide the decimal fractionsdecimal fractionsdecimal fractions by the natural numbers and multiply the decimal fractions by 10, 100 and 1000.

The students work in groups of three or four. They make up the name of their team and write it on the board. The teacher presents the questions. The team which first gives the correct answer: A, B or C gets a point. The teacher writes the points to the appropriate team. The winner is the team with the greatest number of points.

Quiz:

1. The result of the product of 0.0436 · 1000 is larger than the result of the product:

A. 0,0673 · 100
B. 0,05 · 1000
C. 7,789 · 10

2. The quotationquotationquotation of 0.042 : 3 equals:

A. 0.14
B. 0.014
C. 0.0014

3.Which of the quotations doesn’t equal 7.4?

A. 88.8 : 12
B. 222 : 3
C. 51.8 : 7

4. The quotation of the number eight thousand five hundred sixty by the number eight equals:

A. one thousand seven
B. one thousand seventy
C. one thousand seven hundred

5. Tick the incorrect equality.

A. 56.4 : 8 = 7.05
B. 3.57 : 3 = 1.19
C. 5.5 : 11 = 0.05

The correct answers are the following:

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

Procedurem66b7c6c6ddf499d7_1528446435040_0Procedure

The teacher introduces the topic of the lesson: dividing the decimal fractionsdecimal fractionsdecimal fractions.

Discussion:

What is the difference between the quotationquotationquotation of  73.5 : 1.5 and the quotation of 735 : 15? And the quotation of  7.35 : 0.15? The following quotations are equal:  73.5: 1.5; 735 : 15 and 7,35 : 0,15. Do you know why?

The students come up with the following conclusions:

- In the quotation of 735 : 15 the dividend and the divisor are ten times larger than in the quotation of 73.5 : 1.5.
- In the quotation of 7.35 : 0.15 the dividend and the divisor are ten times smaller than in the quotation of 73.5 : 1.5.
- If the dividend and the divisor are increased or reduced by the same number of times the result of the quotation doesn’t change.m66b7c6c6ddf499d7_1527752263647_0- In the quotation of 735 : 15 the dividend and the divisor are ten times larger than in the quotation of 73.5 : 1.5.
- In the quotation of 7.35 : 0.15 the dividend and the divisor are ten times smaller than in the quotation of 73.5 : 1.5.
- If the dividend and the divisor are increased or reduced by the same number of times the result of the quotation doesn’t change.

Using the gained information the students divide the decimal fractions on their own. Then, in pairs they compare the results.

Task 1

Increase the dividenddividenddividend and the divisordivisordivisor to be able to divide the decimal fraction by the natural number.

a) 3.5 : 0.7

b) 0.48 : 0.4

c) 1.25 : 0.005

d) 0.072 : 0.9.

The students work individually using their computers. They are going to analyse the slideshow concerning the written divisionwritten divisionwritten division of the decimal fractionsdecimal fractionsdecimal fractions.

[Slideshow]

Discussion: How can we do the written division of the decimal fraction?

The students can come up with the following conclusion:

- First we multiply the dividenddividenddividend and the divisordivisordivisor by 10, 100 or 1000, 10000… to make the divisor the natural number. Next, we do the division of the decimal fraction by the natural number.

Using the gained information the students do the written divisionwritten divisionwritten division of  the decimal fractions on their own. Then, in pairs they compare the results.

Task 2

Use the written method to calculate:

a) 236.5 : 0.5

b) 1.1284 : 0.02

c) 9.945 : 1.3

d) 162.64 : 0.004.

Task 3

Basia has bought 0.65 kilo of sweets and she paid 9.75 PLN. How much would she pay for 1.15 kilo of these sweets?

An extra task:

What number should be multiplied by 3.45 to get the result equal the sum of the numbers 27.161 and 16.4125.

Lesson summarym66b7c6c6ddf499d7_1528450119332_0Lesson summary

The students do the summarising tasks.

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

- To divide the decimal fractions we move the decimal points in both fractions so many places to the right to get the divisor of the natural number.
- Next, we do the written division of the numbers we have gained.m66b7c6c6ddf499d7_1527752256679_0- To divide the decimal fractions we move the decimal points in both fractions so many places to the right to get the divisor of the natural number.
- Next, we do the written division of the numbers we have gained.

Selected words and expressions used in the lesson plan

decimal fractionsdecimal fractionsdecimal fractions

dividenddividenddividend

divisordivisordivisor

mental divisionmental divisionmental division

moving the decimal point to the rightmoving the decimal point to the rightmoving the decimal point to the right

quotationquotationquotation

smaller numbersmaller numbersmaller number

written divisionwritten divisionwritten division