Topicm01b4ce68a531c178_1528449000663_0Topic

Comparing fractions with the same numerators or denominators

Levelm01b4ce68a531c178_1528449084556_0Level

Second

Core curriculumm01b4ce68a531c178_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

12) compares fractions (common and decimal).

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

4) compares fractions using their difference.

Timingm01b4ce68a531c178_1528449068082_0Timing

45 minutes

General objectivem01b4ce68a531c178_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm01b4ce68a531c178_1528449552113_0Specific objectives

1. Comparing common fractions with the same denominators.

2. Comparing common fractions with the same numerators.

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

Learning outcomesm01b4ce68a531c178_1528450430307_0Learning outcomes

The student:

1. Compares common fractions with the same denominators.

2. Compares common fractions with the same numerators.

Methodsm01b4ce68a531c178_1528449534267_0Methods

1. Discussion.

2. Situatinal analysis.

Forms of workm01b4ce68a531c178_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm01b4ce68a531c178_1528450127855_0Introduction

Students revise how we write down a common fractioncommon fractioncommon fraction and its parts and what they mean: the numeratornumeratornumerator, the denominatordenominatordenominator and the fraction bar.

- The common fractioncommon fractioncommon fraction consists of the numeratornumeratornumerator, the denominatordenominatordenominator and the fraction bar.

- The denominatordenominatordenominator indicates how many equal parts the whole has been divided into.

- The numeratornumeratornumerator indicates how many parts have been taken.

To determine the coordinates of the point described by a fraction, we need to check into how many parts the unit segment was divided and how many marked parts there are between the point and 0.

Procedurem01b4ce68a531c178_1528446435040_0Procedure

Students compare fractions with the same numerators in practical situations.

Task

Two identical pizzas were divided into 12 equal parts. Marek ate a piece of one pizza, and Darek ate 5 pieces of the other pizza.

a) What part of each pizza was left?

b) What fraction of each pizza is this?

c) Which pizza remains larger now?

[Illustration 1]

Task

Students draw a number linenumber linenumber line and mark the fractions $\frac{4}{9}$ and $\frac{7}{9}$ , and then they write down which number is greater.

Task

Students draw two equal rectangles and then divide the first one into 3 equal parts and the other into 8 equal parts. In each of them, they mark one part with a colour. Their task is to write down in the form of a fraction what part of the rectangle was coloured and determine which one of them is greater.

Task

Students draw a number linenumber linenumber line and mark the fractions $\frac{2}{3}$ and $\frac{2}{5}$ on it and then write down which part is greater.

Task

Students work individually, using computers. Their task is to compare the fractions marked on the circles.

[Geogebra Applet]

After completing the exercises, students present their results of their observations. They should draw the following conclusions:m01b4ce68a531c178_1527752256679_0conclusions:

- If two fractions have equal denominators, then the one that has a greater numerator is greater.m01b4ce68a531c178_1527752256679_0- If two fractions have equal denominators, then the one that has a greater numerator is greater.

- If two fractions have equal numerators, then the one that has smaller denominator is greater.m01b4ce68a531c178_1527752256679_0- If two fractions have equal numerators, then the one that has smaller denominator is greater.

An extra taskm01b4ce68a531c178_1527752263647_0An extra task

Write down all fractions whose numerator is 8 which are greater than 1/5 and smaller than 1.m01b4ce68a531c178_1527752263647_0Write down all fractions whose numerator is 8 which are greater than 1/5 and smaller than 1.

Lesson summarym01b4ce68a531c178_1528450119332_0Lesson summary

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

- If two fractions have equal denominators, then the one that has a greater numeratorgreater numeratorgreater numerator is greater.

- If two fractions have equal numerators, then the one that has smaller denominatordenominatordenominator is greater.

Selected words and expressions used in the lesson plan

common fractioncommon fractioncommon fraction

denominatordenominatordenominator

greater numeratorgreater numeratorgreater numerator

number linenumber linenumber line

numeratornumeratornumerator