Topicmc52196a9448ed95c_1528449000663_0Topic

Comparing common fractions with the same denominators or numerators

Levelmc52196a9448ed95c_1528449084556_0Level

Second

Core curriculummc52196a9448ed95c_1528449076687_0Core curriculum

IV. Common and decimal fractions.

The student:

1) reduces and expands common fractions,

2) converts common fractions to the same denominator,

3) compares fractions (common and decimals).

Timingmc52196a9448ed95c_1528449068082_0Timing

45 minutes

General objectivemc52196a9448ed95c_1528449523725_0General objective

Simple reasoning, presenting arguments justifying the reasoning, distinguishing between the proof and the example.

Specific objectivesmc52196a9448ed95c_1528449552113_0Specific objectives

1) Comparing common fractions.

2) Arranging fractions in the ascendingascendingascending and descendingdescendingdescending order.

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

Learning outcomesmc52196a9448ed95c_1528450430307_0Learning outcomes

The student:

- compares simple fractions with the same denominators or numerators,

- arranges fractions with different denominators and numerators in the ascendingascendingascending or descendingdescendingdescending order.

Methodsmc52196a9448ed95c_1528449534267_0Methods

1) Talk.

2) Situation alanalysis.

Forms of workmc52196a9448ed95c_1528449514617_0Forms of work

1) Individual work.

2) Class work.

Lesson stages

Introductionmc52196a9448ed95c_1528450127855_0Introduction

The students revise the methods of comparing fractionscomparing fractionscomparing fractions with the same denominators or numerators and mixed numerals. They also revise the methods of expanding and reducing fractionsreducing fractionsreducing fractions (includingirreducible fractions).

- If two fractions have the same numerator, then the fraction with the smaller denominator is the greater number.

- If two fractions have the same denominator, then the fraction with the greater denominator is the greater number.

- To decide which of the mixed numerals is greater, we should compare the integers first. If the integers are equal, we compare the fractions.

- To expand a fraction, we multiply the numerator and the denominator by the same (non‑zero) number.

- To reduce a fraction, we divide the numerator and the denominator by the same number which is not 0 or 1.

- A fraction which cannot be reduced is called an irreducible fraction.

Proceduremc52196a9448ed95c_1528446435040_0Procedure

The teacher informs the students that they are going to learn how to compare fractionsto compare fractionsto compare fractions with different denominators and numerators.

The students compare the fractions $\frac{2}{8}$ and $\frac{3}{9}$, using the numeric axles.

They mark one fraction on each axis.

[Illustration1]

On the basis of the position of the fractions in the number line the students notice that $\frac{2}{8}<\frac{3}{9}$.

The teacher asks the following question:

Should we always use the number line to compare fractionsto compare fractionsto compare fractions with different denominators and numerators?

After discussion the students come up with the conclusion:

When two fractions contain different numerators and denominators it is easy to compare them by converting the fractions to the same denominator.mc52196a9448ed95c_1527752263647_0When two fractions contain different numerators and denominators it is easy to compare them by converting the fractions to the same denominator.

Task
The students convert the fractions to the same denominator and compare the fractions:

a) $\frac{2}{5}$ and $\frac{3}{8}$

b) $\frac{5}{13}$ and $\frac{1}{3}$

c) $\frac{6}{5}$ and $\frac{25}{27}$

d) $3\frac{3}{8}$ and $3\frac{3}{8}$

e) $4\frac{5}{14}$ and $4\frac{10}{28}$

Task
The students do the simple text task using the expansion and the reduction of common fractions.

During the last school election Ola gained $\frac{6}{13}$ of all the votes, and Tomek $\frac{2}{3}$ of all the votes.
Who won: Ola or Tomek?

An extra task
The students write the decimal fraction greater than $\frac{1}{3}$, using all ten numbers.

Lesson summarymc52196a9448ed95c_1528450119332_0Lesson summary

The students do the summarising tasks.

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

- When two fractions contain different numerators and denominators it is easy to compare them by converting the fractions to the same denominator.

Selected words and expressions used in the lesson plan

ascendingascendingascending

comparing fractionscomparing fractionscomparing fractions

convert the fraction into the same denominatorconvert the fraction into the same denominatorconvert the fraction into the same denominator

descendingdescendingdescending

equal fractionsequal fractionsequal fractions

expanding fractionsexpanding fractionsexpanding fractions

greater fractiongreater fractiongreater fraction

reducing fractionsreducing fractionsreducing fractions

smaller fractionsmaller fractionsmaller fraction

to compare fractionsto compare fractionsto compare fractions