Topicm6f67b2c2c2c7f368_1528449000663_0Topic

Division of the common fractions

Levelm6f67b2c2c2c7f368_1528449084556_0Level

Second

Core curriculumm6f67b2c2c2c7f368_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:
3) reduces and expands the common fraction,

 5) presents the improper fraction in a form of the mixed number, and the mixed number in a form of improper fraction.

V. The operations with the common and decimal fractions. The student:
1) adds, subtracts, multiplies, divides the common fractions with the one or two‑digit denominators, and mixed numbers.

Timingm6f67b2c2c2c7f368_1528449068082_0Timing

45 minutes

General objectivem6f67b2c2c2c7f368_1528449523725_0General objective

Matching a mathematical model to a simple situation and using it in various contexts.

Specific objectivesm6f67b2c2c2c7f368_1528449552113_0Specific objectives

1. Dividing the simple fractions.

2. Solving the task using division of common fractions.

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

Learning outcomesm6f67b2c2c2c7f368_1528450430307_0Learning outcomes

The student:

- divides common fractions;

- calculates the reciprocal of the number.

Methodsm6f67b2c2c2c7f368_1528449534267_0Methods

1. Class game.

2. Situational analysis.

Forms of workm6f67b2c2c2c7f368_1528449514617_0Forms of work

1. Individual work.

2. Work in pairs.

3. Group work.

Lesson stages

Introductionm6f67b2c2c2c7f368_1528450127855_0Introduction

Students prepare and bring the cards with the numbers 1‑9 written on them.

The students revise the notion of the improper fraction and the method of multiplication of the common fractions.

- When we multiply the common fractions we multiply the numerator by the numerator and the denominator by the denominator.

Procedurem6f67b2c2c2c7f368_1528446435040_0Procedure

The teacher informs the students are going to discover the method of dividing the common fractions.

The students work in pairs.

One student draws two cards and makes the common fraction. The letter of the first card is the numerator, the letter of the other card is the denominator of the fraction. The students use the pencil as a fraction bar. The other student makes such a fraction of his cards that the product of both fractions equals 1.

The students draw the conclusion – in what case the product of two fractions equals 1.

If the product of two fractions different from zero equals 1 , they are reciprocal of one another.m6f67b2c2c2c7f368_1527752263647_0If the product of two fractions different from zero equals 1 , they are reciprocal of one another.

Task
Complete the table:

[table]

The students discuss the result and come up with the conclusion:

The number 0 has not the reciprocal.

The reciprocal of number 1 is 1.

The students analyse the example written by the teacher.

The cake was divided into identical parts, each of them was $\frac{1}{6}$ part of the cake. How many pieces was the cake divided into?

$1:\frac{1}{6}=6$

Answer: It was divided into 6 pieces.

The students are going to watch the slideshow to learn the method of division the natural number by the mixed number.

The students draw the conclusion:

To divide the natural number by the fraction , the number should be multiplied by the reciprocal of the fractionm6f67b2c2c2c7f368_1527752256679_0To divide the natural number by the fraction , the number should be multiplied by the reciprocal of the fraction.

The students divide the natural numbers by the mixed numbers.

Task
Calculate:

a. $3:2\frac{1}{3}$

b. $7:1\frac{1}{2}$

c.$10:3\frac{4}{5}$

After completing the task the students come up with the conclusion:

To divide the natural number by the mixed number we should convert the mixed number to the improper fraction first, then divide the natural number by the fraction.

The teachers writes down the example:

$\frac{3}{4}:\frac{5}{7}=\frac{3}{4}·\frac{7}{5}=\frac{3·7}{4·5}=\frac{21}{20}=1\frac{1}{20}$

The students analyse the example above and draw the conclusion:

To divide the common fraction by the other common fraction we should multiply the first fraction by the reciprocal of the second one.

The students complete the task on their own and draw the conclusion:

Task
Calculate:

a. $\frac{4}{9}:\frac{5}{7}$

b.$\frac{3}{7}:\frac{9}{14}$

c.$1\frac{7}{8}:2\frac{3}{4}$

Conclusion:
When the dividend or the divisor is a mixed number it should be converted to the improper fraction.

An extra task:
The division of given number firstly by $\frac{3}{4}$, then by $\frac{4}{5}$.

Lesson summarym6f67b2c2c2c7f368_1528450119332_0Lesson summary

The students do the summarising tasks.
Then they sum up the class drawing the conclusions to memorise:

- If the product of two fractions different from zero equals 1 , they are reciprocal of one another. To divide the natural number by the fraction , the number should be multiplied by the reciprocal of the fraction.

- To divide the natural number by the mixed number we should convert the mixed number to the improper fraction first, then divide the natural number by the fraction.

- To divide the common fraction by the other common fraction we should multiply the first fraction by the reciprocal of the second one.

- When dividend or divisor is a mixed number it should be converted to the improper fraction.

Selected words and expressions used in the lesson plan

common fractioncommon fractioncommon fraction

irreducible fractionirreducible fractionirreducible fraction

mixed numbermixed numbermixed number

multiplication of the fractionmultiplication of the fractionmultiplication of the fraction

natural numbernatural numbernatural number

quotientquotientquotient

reciprocal of the numberreciprocal of the numberreciprocal of the number

reducible fractionreducible fractionreducible fraction

the simplest formthe simplest formthe simplest form