Topicm8465d1c1e5f15aad_1528449000663_0Topic

Adding the fractions with different denominatorsdifferent denominatorsdifferent denominators

Levelm8465d1c1e5f15aad_1528449084556_0Level

Second

Core curriculumm8465d1c1e5f15aad_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

3) reduces and expands the common fractioncommon fractioncommon 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.

Timingm8465d1c1e5f15aad_1528449068082_0Timing

45 minutes

General objectivem8465d1c1e5f15aad_1528449523725_0General objective

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

Specific objectivesm8465d1c1e5f15aad_1528449552113_0Specific objectives

1. Adding  the common 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 outcomesm8465d1c1e5f15aad_1528450430307_0Learning outcomes

The student:

- Adds the fractions and the mixed numbers with different denominatorsdifferent denominatorsdifferent denominators,

- converts the fractions to the same denominator.

Methodsm8465d1c1e5f15aad_1528449534267_0Methods

1. Learning game.

2. Situational analysis.

Forms of workm8465d1c1e5f15aad_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm8465d1c1e5f15aad_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 formula: $\frac{1}{\square }\frac{1}{\square }$ which they got from their teacher.

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

- When we add the fractions with the same denominatorssame denominatorssame denominators we add the numerators and the denominator remains the same.

- When we add the mixed numbers we calculate the sum of the integers and the sum of the fractions. We should remember to reduce the fraction to the simplest form.

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

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

Procedurem8465d1c1e5f15aad_1528446435040_0Procedure

The teacher informs the students they are going to find out the method of adding the fractions and mixed numbers with different denominators.

The students prepare the board of the game and the cards with numbers they have made at home.

The students draw two cards and put them in the empty places of the board to get two fractions. They are going to give the number which can be the common denominator of these two fractions. The other person can get an extra point by giving the smaller common denominator. Then, the students draw the cards again and repeat the activity. The winner is the person who gets more points.

[Slideshow]

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

The teacher writes the example: $\frac{1}{4}+\frac{1}{3}$. He uses the model of pizza to illustrate the addition. He asks the following question: Can we present the fractions $\frac{1}{4}$ and $\frac{1}{3}$ in a different way?

The students should suggest converting the fractions to the same denominator for example 12. The teacher calculates the following: $\frac{1}{4}+\frac{1}{3}=\frac{3}{12}+\frac{4}{12}=\frac{7}{12}$

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

Task 1

The students add the fractions with different denominators:

a) $\frac{3}{4}+\frac{1}{2}$,

b) $\frac{3}{10}+\frac{2}{5}$,

c) $\frac{7}{12}+\frac{3}{4}$,

d) $\frac{3}{8}+\frac{2}{4}$,

e) $\frac{2}{5}+\frac{7}{15}$.

The students should notice, that:

One of the way of looking for the same denominator is writing down the subsequent multiple of the bigger denominator.

We can always expand the first fraction by the denominator of second fraction and the second one by the denominator of the first one.

Task 2

The students add mixed numbers whose fractions have different denominators:

a) $2\frac{1}{4}+3\frac{2}{3}$,

b) $6\frac{3}{7}+5\frac{2}{6}$,

c) $1\frac{7}{10}+4\frac{1}{4}$,

d) $8\frac{3}{5}+7\frac{2}{9}$,

e) $3\frac{2}{8}+11\frac{7}{12}$.

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

When we add the mixed numbers whose fraction parts have different denominators we should convert the fractions to the same denominator first. Then we calculate the sum of the integers and the sum of the fractions We should remember to write the result in the simplest form after excluding the  integers and reducing the fraction.m8465d1c1e5f15aad_1527752256679_0When we add the mixed numbers whose fraction parts have different denominators we should convert the fractions to the same denominator first. Then we calculate the sum of the integers and the sum of the fractions We should remember to write the result 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 addition.

$\frac{1}{2}+\frac{1}{3}=\frac{5}{6}$

$\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$

$\frac{1}{4}+\frac{1}{5}=\frac{9}{20}$

They write the results as in the example without converting the fractions to the same denominator:

a) $\frac{1}{7}+\frac{1}{6}$,

b) $\frac{1}{5}+\frac{1}{6}$,

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

d) $\frac{1}{7}+\frac{1}{4}$.

Lesson summarym8465d1c1e5f15aad_1528450119332_0Lesson summary

The students do the summarising tasks.

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

- When we add the fractions with different denominators we have to convert them to the same denominators first by reducing or expanding the fraction. Next, we should add them in the same way as the fractions with the same denominators.
- When we add the mixed numbers whose fraction parts have different denominators we should convert the fractions to the same denominator first. Then we calculate the sum of the integers and the sum of the fractions We should remember to write the result in the simplest form after excluding the integers and reducing the fraction.m8465d1c1e5f15aad_1527752263647_0- When we add the fractions with different denominators we have to convert them to the same denominators first by reducing or expanding the fraction. Next, we should add them in the same way as the fractions with the same denominators.
- When we add the mixed numbers whose fraction parts have different denominators we should convert the fractions to the same denominator first. Then we calculate the sum of the integers and the sum of the fractions We should remember to write the result 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 fractioncommon fractioncommon fraction

mixed numbermixed numbermixed number

different denominatorsdifferent denominatorsdifferent denominators

addition of the fractionsaddition of the fractionsaddition of the fractions

addition of the mixed numbersaddition of the mixed numbersaddition of the mixed numbers

expanding the fractionsexpanding the fractionsexpanding the fractions

reducing the fractionsreducing the fractionsreducing the fractions

same denominatorssame denominatorssame denominators