Topicm7c7a06cbe5fc5ba3_1528449000663_0Topic

Operations with common fractions

Levelm7c7a06cbe5fc5ba3_1528449084556_0Level

Second

Core curriculumm7c7a06cbe5fc5ba3_1528449076687_0Core curriculum

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;

6) calculates the squares and the cubes of the common , decimal fractions and mixed numbers;

7) calculates the value of the simple arithmetic expressions using the rules of the order of operationsorder of operationsorder of operations.

Timingm7c7a06cbe5fc5ba3_1528449068082_0Timing

45 minutes

General objectivem7c7a06cbe5fc5ba3_1528449523725_0General objective

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

Specific objectivesm7c7a06cbe5fc5ba3_1528449552113_0Specific objectives

1. Operations with the common fractions.

2. Solving the task using the operations with the common fractions.

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

Learning outcomesm7c7a06cbe5fc5ba3_1528450430307_0Learning outcomes

The student:

- solves the task using the operations with the common fractions,

- calculates the value of the simple arithmetic expressions using the rules of the order of operationsorder of operationsorder of operations.

Methodsm7c7a06cbe5fc5ba3_1528449534267_0Methods

1. Class game.

2. Situational analysis.

Forms of workm7c7a06cbe5fc5ba3_1528449514617_0Forms of work

1. Individual work.

2. Pair work.

3. Class work.

Lesson stages

Introductionm7c7a06cbe5fc5ba3_1528450127855_0Introduction

Students prepare and bring the cards with the written following fractions:
$1\frac{3}{4},2\frac{1}{2},3\frac{4}{5},7\frac{5}{6},\frac{4}{7},2\frac{3}{8},1\frac{2}{9},5\frac{9}{10}.$
There is only one number on each card.

The students revise the methods of adding, subtracting, multiplying, exponentiation and dividing the common fractions.

Procedurem7c7a06cbe5fc5ba3_1528446435040_0Procedure

The teacher informs the students they are going to develop the ability of doing the operations with the fractions .

The students work in pairs using the cards they have prepared.

One of the person draws two fractions, the other one chooses the operation which he is going to complete ( addition, subtraction, multiplication, division). Them he writes the appropriate calculations using the fractions which he has drawn. They check in pairs if the result is correct . Next, the student change their roles and repeat the activity.

[Slideshow]

Task 1

The students work individually using their computers. They analyse the animation presenting the order of the operations with the common fractions. 

They come up with the conclusion:

The order of the operations with the fractions:

Firstly we do the operations in brackets.

Then exponentiation, multiplication or division (in order they appear).

Finally the addition or subtraction (in order they appear).

Students use the information above to do the following calculations:

Task 2

Calculate:

a) $\frac{2}{15}+\frac{4}{5}·\frac{1}{3}$

b) $(\frac{2}{5}+\frac{3}{4}):6\frac{2}{3}$

c) $3\frac{{\displaystyle 1}}{5}·(5\frac{1}{4}-1\frac{3}{4})$

d) $1\frac{3}{7}-\frac{3}{7}·\frac{2}{3}$

Task  3

In a bottle there is $\frac{1}{3}$ of a litre of juice, in a jug $\frac{1}{2}$ of a litre more. How much more of the juice is in the jug than in the bottle?

Task 4

Calculate:

a) $(\frac{2}{3}{)}^3$

b) $(1\frac{2}{5}{)}^2$

Task 5

Michael picked up $\frac{2}{9}$ of a litre of wild strawberries, John $\frac{4}{9}$ of a litre, and Tom $\frac{5}{9}$ of a litre. Did these three friends pick up more or less wild strawberries than one litre?m7c7a06cbe5fc5ba3_1527752256679_0Michael picked up $\frac{2}{9}$ of a litre of wild strawberries, John $\frac{4}{9}$ of a litre, and Tom $\frac{5}{9}$ of a litre. Did these three friends pick up more or less wild strawberries than one litre?

An extra task:

In a class $\frac{1}{3}$ of all the students go to the swimming lesson, and four students more what means half a class attend the dancing classes. How many students are there in that class? 

Lesson summarym7c7a06cbe5fc5ba3_1528450119332_0Lesson summary

The students do the summarising tasks.

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

When we do the operations with the common fractions we:
Firstly we do the operations in brackets.
Then exponentiation, multiplication or division (in order they appear).
Finally the addition or subtraction (in order they appear).m7c7a06cbe5fc5ba3_1527752263647_0When we do the operations with the common fractions we:
Firstly we do the operations in brackets.
Then exponentiation, multiplication or division (in order they appear).
Finally the addition or subtraction (in order they appear).

Selected words and expressions used in the lesson plan

addition of the fractionsaddition of the fractionsaddition of the fractions

subtraction of the fractionssubtraction of the fractionssubtraction of the fractions

multiplication of the fractionsmultiplication of the fractionsmultiplication of the fractions

division of the fractionsdivision of the fractionsdivision of the fractions

reciprocal of the numberreciprocal of the numberreciprocal of the number

reducible fractionreducible fractionreducible fraction

irreducible fractionirreducible fractionirreducible fraction

mixed numbermixed numbermixed number

order of operationsorder of operationsorder of operations

improper fractionimproper fractionimproper fraction