Topicm60292119468f9019_1528449000663_0Topic

Subtracting the fractions with different denominators

Levelm60292119468f9019_1528449084556_0Level

Second

Core curriculumm60292119468f9019_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

3) reduces and expands the common fraction,

 4) convert the common fractions to the same denominator.

V. The operations on 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.

Timingm60292119468f9019_1528449068082_0Timing

45 minutes

General objectivem60292119468f9019_1528449523725_0General objective

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

Specific objectivesm60292119468f9019_1528449552113_0Specific objectives

1. Subtracting the fractions.

2. Calculating the value of operations consisting of subtracting the fractions.

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

Learning outcomesm60292119468f9019_1528450430307_0Learning outcomes

The student:

- subtracts the fractions with different denominators,

- converts the fractions to the common denominator.

Methodsm60292119468f9019_1528449534267_0Methods

1. Class game.

2. Situational analysis.

Forms of workm60292119468f9019_1528449514617_0Forms of work

1. Individual work.

2. Pair work.

3. Class work.

Lesson stages

Introductionm60292119468f9019_1528450127855_0Introduction

Students bring the cards with the numbers 2‑9 written on them and a board game made of a piece of paper of A‑4 size with the: $\frac{1}{\square }$.

The students revise the method of subtracting the mixed numbers and the fractions with the same denominator, reducing and expanding the common fractions.

- When we subtract the fractions with the same denominator we subtract the numerators and the denominator remains the same.

- When we subtract the fraction of the whole we can convert the whole number into the improper fraction.

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

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

Procedurem60292119468f9019_1528446435040_0Procedure

The teacher informs the students they are going to find out the method of subtracting the fractions with different denominators.

The students work in pairs.

They put the board of the game and the cards with numbers they have made at home at the desks in front of them.

The students draw a card and put it into the empty place of the board to get the first fraction. They are going to give the number which can be the common denominator of the fractions. An extra point can be added by giving the smaller common denominator. Then, the students draw the new cards, make new fractions and repeat the activity. The winner is the pair of students who gets more points.

[Slideshow]

The students work individually using their computers. They are going to watch the method of subtracting the common fractions with different denominators.

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

When we subtract the fractions with different denominators we have to convert them to the same denominators first by reducing or expanding the fraction. Next, we should subtract them in the same way as the fractions with the same denominators.

Task

The students convert the fractions to the same denominator and subtract the fractions. They reduce the fractions to the simplest form:

a) $\frac{4}{5}-\frac{1}{3}$,

b) $\frac{3}{7}-\frac{4}{21}$,

c) $\frac{5}{6}-\frac{1}{5}$,

d) $\frac{3}{4}-\frac{1}{5}$.

Task

The students convert the fractions to the same denominator and subtract the fractions. They reduce the fractions to the simplest form:

a) $5\frac{1}{4}-2\frac{1}{6}$,

b) $4\frac{1}{3}-2\frac{1}{6}$,

c) $6\frac{7}{12}-2\frac{1}{2}$,

d) $6\frac{5}{6}-3\frac{1}{8}$,

e) $2\frac{3}{7}-\frac{2}{5}$.

The students should come up with the following conclusion:

We should remember to write the result of subtracting in the simplest form after excluding the integers and reducing the fraction.m60292119468f9019_1527752256679_0We should remember to write the result of subtracting in the simplest form after excluding the integers and reducing the fraction.

An extra task:

The students watch the fractions and the results of the subtraction:

a) $\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$,

b) $\frac{1}{3}-\frac{1}{4}=\frac{1}{12}$,

c) $\frac{1}{5}-\frac{1}{6}=\frac{1}{30}$.

Task

Write the results as in the examples above.

a) $\frac{1}{4}-\frac{1}{5}$,

b) $\frac{1}{6}-\frac{1}{7}$,

c) $\frac{1}{7}-\frac{1}{8}$,

d) $\frac{1}{8}-\frac{1}{9}$.

Lesson summarym60292119468f9019_1528450119332_0Lesson summary

The students do the summarising tasks.

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

- When we subtract the fractions with different denominators we have to convert them to the same denominators first by reducing or expanding the fraction. Next, we should subtract them in the same way as the fractions with the same denominators. We should remember to write the result of subtracting in the simplest form after excluding the integers and reducing the fraction.m60292119468f9019_1527752263647_0When we subtract the fractions with different denominators we have to convert them to the same denominators first by reducing or expanding the fraction. Next, we should subtract them in the same way as the fractions with the same denominators. We should remember to write the result of subtracting in the simplest form after excluding the integers and reducing the fraction.

Selected words and expressions used in the lesson plan

irreducible fractionirreducible fractionirreducible fraction

common denominatorcommon denominatorcommon denominator

mixed numbermixed numbermixed number

different denominatorsdifferent denominatorsdifferent denominators

subtraction of the fractionssubtraction of the fractionssubtraction of the fractions

subtraction of the mixed numberssubtraction of the mixed numberssubtraction of the mixed numbers

expanding the fractionsexpanding the fractionsexpanding the fractions

reducing the fractionsreducing the fractionsreducing the fractions

same denominatorssame denominatorssame denominators

order of operationsorder of operationsorder of operations