Topicmc734c6bafbcbd031_1528449000663_0Topic

Converting mixed numbers into fractions

Levelmc734c6bafbcbd031_1528449084556_0Level

Second

Core curriculummc734c6bafbcbd031_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

5) converts improper fractions into mixed numbers and mixed numbers into improper fractions.

Timingmc734c6bafbcbd031_1528449068082_0Timing

45 minutes

General objectivemc734c6bafbcbd031_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmc734c6bafbcbd031_1528449552113_0Specific objectives

1. Introducing concepts: a proper fraction, an improper fractionimproper fractionimproper fraction, a mixed numbermixed numbermixed number.

2. Converting an improper fraction into a mixed number and a mixed number into an improper fraction.

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

Learning outcomesmc734c6bafbcbd031_1528450430307_0Learning outcomes

The student:

- identifies improper and proper fractions,

- converts mixed numbers into improper fractions.

Methodsmc734c6bafbcbd031_1528449534267_0Methods

1. Educational game.

2. Situational analysis.

Forms of workmc734c6bafbcbd031_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc734c6bafbcbd031_1528450127855_0Introduction

Before the class, students prepare 12 squares, each having a side 12 cm long.

4 green squares are divided into 6 equal parts, 4 blue squares are divided into 5 equal parts and
4 red squares are divided into 3 equal parts. They also prepare a template with 4 such squares.

Students revise the concept of the fraction.

- A fraction describes a part of a whole divided into equal parts.

Educational game:

Students work in groups, using the cards brought to the class.

In the first stage of the game, students have one square of each colour available. They can use only one of the squares drawn on the template of squares.

One by one, students give examples of the common fractions they know, of denominators 6, or 3, for example: $\frac{5}{6},\frac{3}{4},\frac{1}{3}.$

The task of the other players is to fill the templates with appropriate fractions, by filling proper part of the template with the right card with fraction.

Students start the second stage of the game by considering the following questions:

- How many blue pieces we need to fill more than two squares?
- How many green pieces we need to fill more than three squares?
- How many red parts we need to fill more than one square?
- How to describe the filled parts with fractions?

Conclusions:

- To fill more than one square drawn on the template, the number of coloured parts of the square must be greater than the number of parts the square of a given colour got divided into.

- Fractions with which we can describe filled parts of the squares on the templates can be
in the form of $\frac{12}{5},\frac{21}{6},\frac{5}{3}.$

In this stage of the game, students can use all the coloured pieces they prepared before. They can also use all the squares drawn on the template.

One by one, students give examples of common fractions of denominators 6, 4 or 3, such that the other players need to fill more than one square.

It can be for example fractions: $\frac{12}{5},\frac{21}{6},\frac{5}{3}.$

Other players’ task is to fill squares drawn on the template as fast as possible, by filling appropriate parts of drawn squares with appropriate cards. In this stage, students fill more than one square each time.

The teacher introduces the subject of the class – proper and improper fractions. Students will learn how to change improper fractions into mixed numbers.

Proceduremc734c6bafbcbd031_1528446435040_0Procedure

Task 1

Students write down the fractions that occurred in the first stage on the left side of the piece of paper and those that occurred in the second stage on the right side. They think about the difference between them.

Students should draw the following conclusions:

- Fractions on the left side are numbers smaller than 1. The numerator of these fractions is smaller than the denominator. They are called proper fractions.

- Fractions on the right side are numbers greater than 1. The numerator of these fractions is greater than the denominator. They are called improper fractions.

- If the numerator and the denominator are equal, then the fraction is improper.

Task 2

Students stick 12 equal blue parts in their notebooks, creating squares. Their task is to write down how many squares they obtain and how many parts are left.

[Illustration 1]

Students should draw the following conclusions:

- $\frac{12}{5}$ of a square are 2 whole squares and $\frac{2}{5}$ of a square:

[Illustration 2]

- Mixed numbermixed numberMixed number consists of two parts: whole part and fractional part.

[Illustration 3]

Task 3

Students work individually, using computers. Their task is to convert mixed numbers into improper fractions.

[Geogebra applet]

Task 4

Students think about the operations that need to be performed in order to convert improper fractionimproper fractionimproper fraction into mixed number. Using the following drawings, they write down the fraction $\frac{5}{2}$ as a mixed number.

[Illustration 4]

Students should draw the following conclusions:

- We need to do the operation:

$5:2=2r1,$therefore $\frac{5}{2}=2\frac{1}{2}.$

- The quotient of the division of the numerator by the denominator of the improper fraction is the whole part of the mixed numbermixed numbermixed number and the rest is the numerator of the fraction.

Task 5

Students write down the improper fractions in the form of mixed numbers: $\frac{15}{6},\frac{{\displaystyle 15}}{{\displaystyle 3}},\frac{{\displaystyle 15}}{{\displaystyle 9}}.$

Task 6

Students think about the operations that need to be done to convert the mixed number into the improper fraction. Using the drawing below, they write down the mixed number $2\frac{1}{2}$ in the form of improper fractions.mc734c6bafbcbd031_1527752263647_0Students think about the operations that need to be done to convert the mixed number into the improper fraction. Using the drawing below, they write down the mixed number $2\frac{1}{2}$ in the form of improper fractions.

[Illustration 5]

- We need to do the operation:

$2·2+1=5,$ therefore $2\frac{1}{2}=\frac{2·2+1}{2}=\frac{5}{2}$

- Converting a mixed numbermixed numbermixed number into a fraction we need to calculate the numerator of the fraction. The denominator is the same as the denominator of the fractional part of the mixed numberfractional part of the mixed numberfractional part of the mixed number.

Task 7

Students write down the mixed numbers in the form of improper fractions: $2\frac{1}{3},4\frac{3}{5},1\frac{5}{7}.$

An extra task:

Write down all fractions whose numerator is 6, that are not smaller than 1 and are not greater than 2.

Lesson summarymc734c6bafbcbd031_1528450119332_0Lesson summary

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

- Proper fraction is a fraction whose numerator is smaller than the denominator
- Improper fraction is a fraction whose numerator is greater than the denominator.
- Mixed number consists of two parts: whole part and fractional part.
- The quotient of the division of the numerator by the denominator of the improper fraction is the whole part of the mixed number and the rest is the numerator of the fraction.
- Converting a mixed number into a fraction we need to calculate the numerator of the fraction. The denominator is the same as the denominator of the fractional part of the mixed number.mc734c6bafbcbd031_1527752256679_0- Proper fraction is a fraction whose numerator is smaller than the denominator
- Improper fraction is a fraction whose numerator is greater than the denominator.
- Mixed number consists of two parts: whole part and fractional part.
- The quotient of the division of the numerator by the denominator of the improper fraction is the whole part of the mixed number and the rest is the numerator of the fraction.
- Converting a mixed number into a fraction we need to calculate the numerator of the fraction. The denominator is the same as the denominator of the fractional part of the mixed number.

Selected words and expressions used in the lesson plan

common fractioncommon fractioncommon fraction

fractional part of the mixed numberfractional part of the mixed numberfractional part of the mixed number

improper fractionimproper fractionimproper fraction

mixed numbermixed numbermixed number

proper fractionproper fractionproper fraction

rest from division of natural numbersrest from division of natural numbersrest from division of natural numbers

whole part of the mixed numberwhole part of the mixed numberwhole part of the mixed number