Topicm3f3b2a9ad6d12176_1528449000663_0Topic

Simplifying and extending common fractions

Levelm3f3b2a9ad6d12176_1528449084556_0Level

Second

Core curriculumm3f3b2a9ad6d12176_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

3) simplifies and extends common fractions;

4) finds the common denominator of common fractions;

12) compares fractions (common and decimal)

V. on common and deciman fractions. The student:

4) compares fractions using their difference

Timingm3f3b2a9ad6d12176_1528449068082_0Timing

45 minutes

General objectivem3f3b2a9ad6d12176_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm3f3b2a9ad6d12176_1528449552113_0Specific objectives

1. Simplifying and extending common fractions.

2. Comparing common fractions with the common denominatordenominatordenominator or numerator.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm3f3b2a9ad6d12176_1528450430307_0Learning outcomes

The student:

- simplifies and extends common fractions,

- finds common denominator of common fractions.

Methodsm3f3b2a9ad6d12176_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm3f3b2a9ad6d12176_1528449514617_0Forms of work

1. Individual work.

2. Work with the whole class.

Lesson stages

Introductionm3f3b2a9ad6d12176_1528450127855_0Introduction

Students revise ways of comparing common fractions of the same numerator or denominatordenominatordenominator.

- If two fractions have equal denominators, then the one that has a greater numerator is greater.

- If two fractions have equal numerators, then the one that has smaller denominator is greater.

The teacher introduced the subject of the lesson – comparing fractionscomparing fractionscomparing fractions of different numerators and denominators.

Procedurem3f3b2a9ad6d12176_1528446435040_0Procedure

Students analyse the tasks about dividing pizza into parts. They draw conclusions.

Task 1

Boys ordered three identical pizzas. Marek divided his into sixteen equal parts and ate four of them. Darek divided his into eight equal parts and ate two. Tomek divided his into four equal parts and ate one part. Which one of the boys has the most pizza left?m3f3b2a9ad6d12176_1527752263647_0Boys ordered three identical pizzas. Marek divided his into sixteen equal parts and ate four of them. Darek divided his into eight equal parts and ate two. Tomek divided his into four equal parts and ate one part. Which one of the boys has the most pizza left?

[Illustration 1]

[Illustration 2]

[Illustration 3]

Students should draw the following conclusions:

- Boys have the same amount of pizza left, then: $\frac{12}{16}=\frac{6}{8}=\frac{3}{4}$.

- If we divide the numerator and the denominatordenominatordenominator by the same numbersame numbersame number, different than zero, then the value of the fraction doesn’t change.

The teacher informs the students that this operation is called simplifying the fractionsimplifying the fractionsimplifying the fraction.

Task 2

Students work individually, using computers. Their task is to observe when we can simplify a common fraction.

[Geogebra Applet 1]

After having completed the exercise, students present the result of their observation. They should draw the following conclusions:

- We can simplify a common fraction, if its numerator and denominator have a common divisor, greater than 1.
- The fractions that cannot be simplified are called reduced fractions.m3f3b2a9ad6d12176_1527752256679_0- We can simplify a common fraction, if its numerator and denominator have a common divisor, greater than 1.
- The fractions that cannot be simplified are called reduced fractions.

Task 3

Students simplify the following common fractions to obtain reduced fractions: $\frac{18}{30},\frac{12}{88},\frac{15}{45},\frac{24}{36}.$

Task 4

Students compare the coloured parts of equal rectangles.

[Illustration 4]

Conclusions:

The coloured part is the same in both rectangles, so: $\frac{2}{3}=\frac{4}{6}$.

The teacher informs the students that there exists and operation in which from fraction $\frac{2}{3}$ we can obtain fraction $\frac{4}{6}$ and it is called extending the fractionextending the fractionextending the fraction.

Task  5

Students work individually, using computers. Their task is to observe what is extending a common fraction.

[Geogebra Applet 2]  

After having completed the exercise, students present the result of their observation. They should draw the following conclusions:

- Extending fractions is multiplying the numerator and denominator by the same number, greater than 1.

- The value of the extended fraction doesn’t change.

Task 6

Students extend each of the fractions $\frac{1}{2},\frac{3}{12},\frac{15}{18},\frac{3}{4}$ to have the denominator equal 36.

Task 7

Students extend the common fractions so that they have the same numerator or denominator. Then they compare them, using the rules from the beginning of the class.

a) $\frac{2}{3}$ and $\frac{5}{6}$

b) $\frac{4}{7}$ and $\frac{8}{11}$

c) $\frac{2}{3}$ and $\frac{5}{7}$

An extra task:

Kasia and Basia were both reading the same book that has 140 pages. On Saturday Kasia read $\frac{2}{7}$ of the book and Basia 30 pages. Write the part of book that Basia read in the form of reduced fractionreduced fractionreduced fraction. Which girl read greater part of the book?

Lesson summarym3f3b2a9ad6d12176_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

- To simplify a fraction, we have to divide the  numeratornumeratornumerator and denominatordenominatordenominator by the same numbersame numbersame number, greater than 1.

- We can simplify a common fraction, if its numerator and denominator have a common divisor, greater than 1.

- The fractions that cannot be simplified, they are called reduced fractions.

- Extending fractions is multiplying the numerator and denominator by the same number, greater than 1.

Selected words and expressions used in the lesson plan

comparing fractionscomparing fractionscomparing fractions

denominatordenominatordenominator

extending the fractionextending the fractionextending the fraction

reduced fractionreduced fractionreduced fraction

same denominatorsame denominatorsame denominator

same numbersame numbersame number

simplifying the fractionsimplifying the fractionsimplifying the fraction