Topicma5d3d1feaf088563_1528449000663_0Topic

Subtracting common fractions of the same denominatorssubtracting common fractions of the same denominatorsSubtracting common fractions of the same denominators

Levelma5d3d1feaf088563_1528449084556_0Level

Second

Core curriculumma5d3d1feaf088563_1528449076687_0Core curriculum

V. Operations on decimal and common fractions. The student:

1) adds, subtracts, multiplies and divides common fractions of one- or two‑ciphers numbers as well as mixed numbers.

Timingma5d3d1feaf088563_1528449068082_0Timing

45 minutes

General objectivema5d3d1feaf088563_1528449523725_0General objective

Performing simple calculations in memory or more difficult operations using the long methods, and applying this skills in practical situations.

Specific objectivesma5d3d1feaf088563_1528449552113_0Specific objectives

1. Subtracting common fractions of the same denominatorssame denominatorssame denominators.

2. Subtracting mixed numbers in which fractional parts have the same denominators.

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

Learning outcomesma5d3d1feaf088563_1528450430307_0Learning outcomes

The student:

- subtracts common fractions of the same denominators,

- subtracts mixed numbers in which fractional parts have the same denominators.

Methodsma5d3d1feaf088563_1528449534267_0Methods

1. Situational analysis.

2. Discussion.

Forms of workma5d3d1feaf088563_1528449514617_0Forms of work

1. Individual work.

2. Work with the whole class.

Lesson stages

Introductionma5d3d1feaf088563_1528450127855_0Introduction

Students revise the rules of adding common fractions of the same denominatorssame denominatorssame denominators and mixed numbers in which the fractional parts have the same denominators.

The teacher informs students that in this class they will learn to subtract common fractions of the same denominators and mixed numbers in which the fractional parts have the same denominators.

Procedurema5d3d1feaf088563_1528446435040_0Procedure

Task 1

Students think about ways to subtract fractions of the same denominatorssame denominatorssame denominators. The teachers asks questions to help them:

- How many pieces of pizza will be left, if we divide the pizza into 12 parts and eat 5 of them?

- What part of water will be left in the bottle if we take $\frac{1}{4}$ from a full bottle?

- What part of juice will be left in the glass, if in the beginning it was filled in $\frac{4}{5}$, and we took $\frac{2}{5}$ of that?

Students make drawings to help them and write down proper calculations. Using their knowledge about adding fractions, they formulate a rule describing the subtraction of common fractions of the same denominators.

[Illustration 1]

Conclusion:

- To subtract two fractions of the same denominatorssame denominatorssame denominators, we subtract their numerators and leave the denominator the same.

- To subtract a fraction from the whole, we can convert the whole into an improper fraction and then do the subtraction.

- If we obtain a cancellable fraction as a result, we can simplify it.

Task 2

Students use their obtained knowledge to do the calculations. They write the result as a reduced fraction.

a) $\frac{{\displaystyle 3}}{4}-\frac{1}{4}$

b) $\frac{{\displaystyle 7}}{10}-\frac{3}{10}$

c) $\frac{{\displaystyle 14}}{19}-\frac{7}{19}$

d) $\frac{{\displaystyle 24}}{35}-\frac{9}{35}$

e) $1-\frac{2}{3}$

f) $1-\frac{5}{8}$

Task 3

Students work individually, using computers. They open the slideshow and see how we subtract mixed numbers. After having completed the exercise, students present the results of their observations.

[Slideshow]

Students should draw the following conclusions:

- To subtract mixed numbers, we can convert these numbers into improper fractions and then do the subtraction according to the rules.
- We can also first subtract the whole parts and then the fractional parts.
- When the numerator of the minuend is smaller than the numerator of the subtrahend, we change one whole of the minuend into a fraction.ma5d3d1feaf088563_1527752256679_0- To subtract mixed numbers, we can convert these numbers into improper fractions and then do the subtraction according to the rules.
- We can also first subtract the whole parts and then the fractional parts.
- When the numerator of the minuend is smaller than the numerator of the subtrahend, we change one whole of the minuend into a fraction.

Task 4

Students revise acquired skills by doing the calculations. The result should be written in the form of reduced fraction.

a) $2\frac{5}{9}-1\frac{3}{9}$

b) $5\frac{10}{17}-3\frac{5}{17}$

c) $3\frac{9}{12}-2\frac{3}{12}$

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

e) $3\frac{5}{7}-1\frac{6}{7}$

An extra task:

Calculate, while remembering about the order of operations.

a) $5\frac{10}{16}-\left(2\frac{3}{16}+1\frac{8}{16}\right)$

b) $4\frac{5}{7}+\left(3\frac{4}{7}-1\frac{5}{7}\right)$

Lesson summaryma5d3d1feaf088563_1528450119332_0Lesson summary

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

- To subtract two fractions of the same denominators, we subtract their numerators and leave the denominator the same.
- To subtract a fraction from the whole, we can convert the whole into an improper fraction and then do the subtraction.
- If we obtain a cancellable fraction as a result, we can simplify it.ma5d3d1feaf088563_1527752263647_0- To subtract two fractions of the same denominators, we subtract their numerators and leave the denominator the same.
- To subtract a fraction from the whole, we can convert the whole into an improper fraction and then do the subtraction.
- If we obtain a cancellable fraction as a result, we can simplify it.

Selected words and expressions used in the lesson plan

converting into mixed numbersconverting into mixed numbersconverting into mixed numbers

differencedifferencedifference

fractional partfractional partfractional part

same denominatorssame denominatorssame denominators

simplifying fractionssimplifying fractionssimplifying fractions

subtracting common fractions of the same denominatorssubtracting common fractions of the same denominatorssubtracting common fractions of the same denominators

subtracting mixed numbers in which the fractional parts have the same denominatorsubtracting mixed numbers in which the fractional parts have the same denominatorsubtracting mixed numbers in which the fractional parts have the same denominator

whole partwhole partwhole part