Topicme1b4d688b8ceb3ab_1528449000663_0Topic

Operations on common and decimal fractionsdecimal fractionsdecimal fractions

Levelme1b4d688b8ceb3ab_1528449084556_0Level

Second

Core curriculumme1b4d688b8ceb3ab_1528449076687_0Core curriculum

V. The operations with the common and decimal fractionsdecimal fractionsdecimal fractions. The student:
3) does the simple calculations with the common and decimal fractions at the same time;

7) calculates the value of the simple arithmetic expressions using the rules of the orderorder of operationsorder of operations;

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

Timingme1b4d688b8ceb3ab_1528449068082_0Timing

45 minutes

General objectiveme1b4d688b8ceb3ab_1528449523725_0General objective

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

Specific objectivesme1b4d688b8ceb3ab_1528449552113_0Specific objectives

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

2. Using the proper order of the operations .

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

Learning outcomesme1b4d688b8ceb3ab_1528450430307_0Learning outcomes

The student:

- adds, subtracts, multiplies and divides the common and decimal fractionsdecimal fractionsdecimal fractions,

- uses the proper order of the operations.

Methodsme1b4d688b8ceb3ab_1528449534267_0Methods

1. Learning game.

2. Situational analysis.

Forms of workme1b4d688b8ceb3ab_1528449514617_0Forms of work

1. Individual work.

2. Pair work.

Lesson stages

Introductionme1b4d688b8ceb3ab_1528450127855_0Introduction

The teacher prepares for each group of students:

- the sheet of paper with the table of six rows and two columns. In the first row the student writes step by step in each field one of the following operations:

$0,04:\frac{2}{10};0,75+\frac{1}{5};\frac{4}{5}\cdot 1,2;40\frac{1}{5}-39,9;2\frac{1}{2}:1,25;0,24+\frac{3}{5}$.

In the second row the student writes step by step one of the following operations:

$\frac{5}{9}\cdot 1,1;\frac{25}{17}\cdot 0,34;\frac{36}{56}:0,5;6,125-4\frac{1}{4};1\frac{1}{5}\cdot 1,2;\frac{2}{5}\cdot 0,4.$

- a set of 12 cards. The student places one of the following writing on each card.

$0,84;2A;0,29F;\frac{96}{100}E;0,95T;\frac{2}{10}S;\frac{4}{25}H;1,44C;1\frac{7}{8}A;1\frac{2}{7}N;\frac{1}{2}A;\frac{11}{18}B;$

- twelve –faced dice.

The students revise the addition, the subtraction the multiplication and the division of common and decimal fractionsdecimal fractionsdecimal fractions and the order of operations.

Procedureme1b4d688b8ceb3ab_1528446435040_0Procedure

The teacher introduces the topic of the lesson: doing the operations on the common and decimal fractions at the same time.

The students work individually using their computers. They are going to analyse the slideshow concerning the operations on the common and decimal fractionsdecimal fractionsdecimal fractions at the same time.

[slideshow]

Discussion: How can we do the operations on the common and decimal fractions at the same time? Does the order of operation on the common and decimal fractionsdecimal fractionsdecimal fractions differ from the order of the operation on the natural numbers?  

The students can come up with the following conclusions:

Doing the operations on the common and decimal fractionsdecimal fractionsdecimal fractions at the same time,

- we convert the decimal fraction in the common fractions or if it is possible the common fraction in the finite decimal fractionme1b4d688b8ceb3ab_1527752263647_0we convert the decimal fraction in the common fractions or if it is possible the common fraction in the finite decimal fraction;

- the order of the operations remains the same as the order on the natural numbersme1b4d688b8ceb3ab_1527752256679_0the order of the operations remains the same as the order on the natural numbers.

Learning game. Each pair gets the set prepared by the teacher: the sheet of paper with the table, 12 cards and the dice. The students take turns in throwing the dice and choosing the operation they are going to do. Next, the student looks for the cards with the appropriate result and place it in the field of the table. If the operation the student drew had been done earlier he loses his turn. The letters read step by step will make the key word: the name of the Polish scientist. The winner is the student who guesses the key word first.

The solution: Stefan Banach

After completing the task the students use their computers to give the answers to the following questions: Who was Stefan Banach? When did he live? What century was it?

The students give the following answers:

- Stefan Banach was Polish mathematician who lived at turn of 19th and 20th century.

The students work individually doing the operations on the common and decimal fractionsdecimal fractionsdecimal fractions at the same time. They compare their results in pairs.

Task
Calculate:

a. $(\frac{3}{4}-\frac{1}{5})·4,2$

b. $5,1·\frac{10}{17}+1,5$

c. $(\frac{2}{3}{)}^2+3,65$

d. $2,5·\frac{2}{5}:0,7$

Task
Write the task in the form of the arithmetic expression and calculate its value

a. Increase the number of $\frac{2}{3}$ by the productproductproduct of the numbers $\frac{1}{4}$ and 3,5.

b.Multiply the differencedifferencedifference of the numbers 2,4 and $\frac{2}{5}$.

c. Reduce the quotationquotationquotation of the numbers $1\frac{1}{10}$ by 0,25 by the differencedifferencedifference of the numbers $5\frac{1}{10}$ and 4,5.

An extra task:
Put the bracketsbracketsbrackets in such a way you will get the correct result.

$2\frac{2}{5}·2+1\frac{4}{5}:0,2-0,3=3$

Lesson summaryme1b4d688b8ceb3ab_1528450119332_0Lesson summary

The students do the summarising tasks.

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

Doing the operations on the common and decimal numbers at the same time:
- we convert the decimal fraction in the common fractionscommon fractionscommon fractions or if it is possible the common fraction in the finite decimal fraction;
- the order of the operations remains the same as the order on the natural numbers.

Selected words and expressions used in the lesson plan

bracketsbracketsbrackets

common fractionscommon fractionscommon fractions

decimal fractionsdecimal fractionsdecimal fractions

differencedifferencedifference

order of operationsorder of operationsorder of operations

productproductproduct

quotationquotationquotation

squaresquaresquare

sumsumsum