Topicmccbfdf93f44cbf13_1528449000663_0Topic

Multiplying the decimal fractions

Levelmccbfdf93f44cbf13_1528449084556_0Level

Second

Core curriculummccbfdf93f44cbf13_1528449076687_0Core curriculum

V. The operations with the common and decimal 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.

Timingmccbfdf93f44cbf13_1528449068082_0Timing

45 minutes

General objectivemccbfdf93f44cbf13_1528449523725_0General objective

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

Specific objectivesmccbfdf93f44cbf13_1528449552113_0Specific objectives

1. Mental multiplicationmental multiplicationMental multiplication of the decimal fractions.

2. Written multiplicationwritten multiplicationWritten multiplication of the decimal fractions.

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

Learning outcomesmccbfdf93f44cbf13_1528450430307_0Learning outcomes

The student:

- does the mental multiplicationmental multiplicationmental multiplication of the decimal fractions,

- multiplies the decimal fractions using the written method.

Methodsmccbfdf93f44cbf13_1528449534267_0Methods

1. Brainstorming.

2. Situational analysis.

Forms of workmccbfdf93f44cbf13_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmccbfdf93f44cbf13_1528450127855_0Introduction

Each student brings the calculator for the lesson.

The students revise the written methods of multiplying the natural numbers and multiplying the decimal fractionsdecimal fractionsdecimal fractions by the natural number.

Proceduremccbfdf93f44cbf13_1528446435040_0Procedure

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

Pair work. The students draw the table with four rows and four columns. They write step by step the following numbers in the first column: 2; 0.2; 0.02; 0.002, and the following numbers in the first row: 3; 0.3; 0.03; 0.003. They complete the table, by using the calculator and calculating the operations.

Discussion: What are the differences between the results in the same row of the table? What are the differences between the results in the same column of the table? What does the number of the digits after the decimal point depend on? What method can be used to calculate the productproductproduct of the decimal fractions?

The students can come up with the following conclusions:

- The results of the row (column)of the table differ only in the number of the digits after the decimal point.
- The number of the digits after the decimal point depends on the number of the decimal digits of the both factors.
- To multiply the decimal fractionsdecimal fractionsdecimal fractions we multiply these numbers first, ignoring the decimal points. Next, we place the decimal point in the productproductproduct to get the same number of the decimal digits as the sum of number of decimal digits in the decimal fractions which are multiplied.

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

Task 1

Calculate mentally:

a) 0,5 · 0,7

b) 0,003 · 1,2

c) 0,11 · 0,004

d) 0,45 · 0,2

The students work in pairs. They use the written multiplication to calculate:

7809 · 3, 5042 · 3, 5042 · 4011.

Next, they use a calculator to calculate:

78,09 · 0,3,

5,042 · 2,5,

0,065 · 401,1.

Discussion:

What is the difference between the products of 7809 · 3 and 78,09 · 0,3? And between the products
5042 · 25 i 5,042 · 2,5 or he products of 65 · 4011 i 0,065 · 401,1? What does the number of the digits after the decimal point depend on? What written method should we use to calculate the multiplication of the decimal fractions?

The students can come up with the conclusions:

- The results of the products differ only in the number of the digits after the decimal point.
- The number of the digit after the decimal point depends on the number of digits in the decimal fraction which is multiplied.
- To multiply the decimal fractionsdecimal fractionsdecimal fractions we multiply these numbers first, ignoring the decimal points. Next, we place the decimal point in the productproductproduct to get the same number of the decimal digits as the sum of number of decimal digits in the decimal fractions which are multiplied.

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

Task 2

Calculate using the written method of multiplication:

a) 467,21 · 0,14

b) 5,3 · 231,7

c) 9001,5 · 0,548

Task 3

Marcin took part in the boat race. On the first day he sailed 22.6 of the nautical mile, on the second day the 18.9 of the nautical mile and on the third day 20.1. How many kilometres has Marcin sailed during these days if one nautical mile equals approximately 1.852 km?mccbfdf93f44cbf13_1527752256679_0Marcin took part in the boat race. On the first day he sailed 22.6 of the nautical mile, on the second day the 18.9 of the nautical mile and on the third day 20.1. How many kilometres has Marcin sailed during these days if one nautical mile equals approximately 1.852 km?

The students work individually using their computers. They watch the slideshow to do the following task.

[Slideshow]

Task 4

Answer the following questions:

a) How much are we going to pay for 2.4 kg of pears?
b)  How much are we going to pay for 1.8 kg of apples and 2.1 kg of oranges?
c) How much less should we pay for 1.5 kg of plums than per 2.7 kg of bananas?

An extra task:

Calculate:

${\left(4,3\right)}^2+{\left(1,2\right)}^2$

Lesson summarymccbfdf93f44cbf13_1528450119332_0Lesson summary

The students do the summarising tasks.

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

- To multiply the decimal fractions we multiply these numbers first, ignoring the decimal points. Next, we place the decimal point in the product to get the same number of the decimal digits as the sum of number of decimal digits in the decimal fractions which are multiplied.mccbfdf93f44cbf13_1527752263647_0- To multiply the decimal fractions we multiply these numbers first, ignoring the decimal points. Next, we place the decimal point in the product to get the same number of the decimal digits as the sum of number of decimal digits in the decimal fractions which are multiplied.

Selected words and expressions used in the lesson plan

decimal fractionsdecimal fractionsdecimal fractions

productproductproduct

mental multiplicationmental multiplicationmental multiplication

written multiplicationwritten multiplicationwritten multiplication

factorfactorfactor

pricepriceprice

greater numbergreater numbergreater number

smaller numbersmaller numbersmaller number