Topicmaf67debe4ff7ca0f_1528449000663_0Topic

A common fractions as a quotient

Levelmaf67debe4ff7ca0f_1528449084556_0Level

Second

Core curriculummaf67debe4ff7ca0f_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

2) present a fractionfraction as a quotientfraction as a quotient of natural numbers and a quotient of natural numbers as a common fraction.

Timingmaf67debe4ff7ca0f_1528449068082_0Timing

45 minutes

General objectivemaf67debe4ff7ca0f_1528449523725_0General objective

Reading and interpreting data presented in various form and processing it.

Specific objectivesmaf67debe4ff7ca0f_1528449552113_0Specific objectives

1. Writing a fraction in the form of a quotient of natural numbers.

2. Writing the quotient of two natural numbers as a fraction.

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

Learning outcomesmaf67debe4ff7ca0f_1528450430307_0Learning outcomes

The student:

- writes fraction in the form of a quotient of natural numbers,

- writes the quotient of two numbers as a common fraction.

Methodsmaf67debe4ff7ca0f_1528449534267_0Methods

1. Situational analysis.

2. Discussion.

Forms of workmaf67debe4ff7ca0f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmaf67debe4ff7ca0f_1528450127855_0Introduction

Students are divided into four groups. Each group gets one of the questions prepared by the teacher.

- How to divide fairly four chocolate bars between three people?
- How to divide fairly five chocolates between nine students?
- How to divide fairly two pizzas between six people?
- How to divide fairly three apples between five people?

Students’ task is to make proper drawings and find solutions to the problems.

Proceduremaf67debe4ff7ca0f_1528446435040_0Procedure

Students present the obtained solutions and together discuss how to write them down:

Exemplary form of solution that students can propose:

How to divide fairly four chocolate bars between three people?

[Illustration 1]

$4:3=1 r 1 \mathrm{or} 4:3=\frac{4}{3}$

Task 1

Students work individually, using computers. Their task is to observe how we write down the quotient of numbers using a common fraction.

[Geogebra applet]

After having finished the exercises, students present the results of their observations. They should draw the following conclusions:

- The result of each division by number different than zero can be written down in the form of a fraction.
- The dividend is the numerator of the fraction and divisor is the denominator.
- The fraction bar replaces the sign of division.maf67debe4ff7ca0f_1527752263647_0- The result of each division by number different than zero can be written down in the form of a fraction.
- The dividend is the numerator of the fraction and divisor is the denominator.
- The fraction bar replaces the sign of division.

Task 2

Students write the quotients in the form of reduced fractions.

a) 6 : 21

b) 12 : 48

c) 8 : 5

d) 18 : 12

Task 3

Students write the fraction as a quotientfraction as a quotientfraction as a quotient of two numbers.

a) $\frac{2}{15}$

b) $\frac{7}{12}$

c) $\frac{3}{16}$

d) $\frac{15}{24}$

Task 4

Students solve the text exercises.

They make proper drawings and write down the answer:
- Kasia has 250 cm of ribbon. She wants to divide in into 6 pieces. What is the length of one piece?
- Five students bought all juice in the school canteen – 12 glasses. How cant hey divide it between themselves?maf67debe4ff7ca0f_1527752256679_0They make proper drawings and write down the answer:
- Kasia has 250 cm of ribbon. She wants to divide in into 6 pieces. What is the length of one piece?
- Five students bought all juice in the school canteen – 12 glasses. How cant hey divide it between themselves?

An extra task:

Calculate using the simplification of fractions

a) 810 : 162

b) 1920 : 240

Lesson summarymaf67debe4ff7ca0f_1528450119332_0Lesson summary

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

- The result of each division by number different than zero can be written down in the form of a fraction.
- The dividend is the numeratornumeratornumerator of the fraction and divisordivisordivisor is the denominatordenominatordenominator.
- The fraction barfraction barfraction bar replaces the sign of division.

Selected words and expressions used in the lesson plan

denominatordenominatordenominator

dividentdividentdivident

dividing the numerator by the denominatordividing the numerator by the denominatordividing the numerator by the denominator

dividing with the restdividing with the restdividing with the rest

divisordivisordivisor

fraction as a quotientfraction as a quotientfraction as a quotient

fraction barfraction barfraction bar

numeratornumeratornumerator