Topicm91e1a6949932a5fd_1528449000663_0Topic

Rationalizing the denominatorrationalizing the denominatorRationalizing the denominator

Levelm91e1a6949932a5fd_1528449084556_0Level

Second

Core curriculumm91e1a6949932a5fd_1528449076687_0Core curriculum

II. Roots. The student:

4) calculates the root of product and quotient of two numbers, factors out and factors in perfect square factors;

5) multiplies and divides roots of the same degree.

Timingm91e1a6949932a5fd_1528449068082_0Timing

45 minutes

General objectivem91e1a6949932a5fd_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm91e1a6949932a5fd_1528449552113_0Specific objectives

1. Rationalizing the denominatorrationalizing the denominatorRationalizing the denominator.

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

Learning outcomesm91e1a6949932a5fd_1528450430307_0Learning outcomes

The student rationalizes the denominatordenominatordenominator.

Methodsm91e1a6949932a5fd_1528449534267_0Methods

1. Discussion.

2. Chain of associations.

Forms of workm91e1a6949932a5fd_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm91e1a6949932a5fd_1528450127855_0Introduction

The teacher introduced the subject of the class – rationalizing the denominatorrationalizing the denominatorrationalizing the denominator.

Procedurem91e1a6949932a5fd_1528446435040_0Procedure

Rationalizing the denominator is transforming the fraction in such a way that its value does not change and at the same time it is written without using the irrational number in the denominator.m91e1a6949932a5fd_1527752263647_0Rationalizing the denominator is transforming the fraction in such a way that its value does not change and at the same time it is written without using the irrational number in the denominator.

Students discuss the example of removing the square rootsquare rootsquare root of two from the denominator of the fraction. They pay attention to the number by which we multiply the numeratornumeratornumerator and the denominatordenominatordenominator.

Example:

Task
Using computers, student get to see next example of rationalizing the denominatorrationalizing the denominatorrationalizing the denominator.

[Slideshow]

By doing the chain of associations, students make notes in pairs. They fill next parts of the chain with elements of the algorithm of removing the cube root from the denominator of the fraction.m91e1a6949932a5fd_1527752256679_0By doing the chain of associations, students make notes in pairs. They fill next parts of the chain with elements of the algorithm of removing the cube root from the denominator of the fraction.

They compare their observations with the following example.

Example:

Students use shaped abilities in exercises.

Task
Rationalize the denominatordenominatordenominator.

a) $\frac{6}{\sqrt{3}}$

b) $\frac{2}{3\sqrt{5}}$

c) $\frac{9}{\sqrt{3}}$

d) $\frac{\sqrt{2}}{\sqrt{7}}$

e) $\frac{3+\sqrt{3}}{2\sqrt{3}}$

Task
Insert proper sign in the dotted space < , > .

a) $\frac{3}{\sqrt{2}}...\frac{5}{2\sqrt{2}}$

b) $\frac{12}{5\sqrt{3}}...\frac{9}{\sqrt{3}}$

c) $\frac{7}{5\sqrt{5}}...\frac{7}{{\displaystyle 2}\sqrt{5}}$

d) $\frac{3}{\sqrt[3]{3}}...\frac{5}{{\displaystyle 2\sqrt[3]{3}}}$

Task
Calculate.

a) $\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{8}}+\frac{1}{\sqrt{32}}$

b) $\frac{1}{\sqrt{5}}+\frac{1}{3\sqrt{5}}+\frac{1}{5\sqrt{5}}$

c) $\frac{6}{\sqrt{50}+\sqrt{2}}$

An extra task:
Solve the equation $x\sqrt{2}=\sqrt{32}-\sqrt{20}$.

Lesson summarym91e1a6949932a5fd_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

Rationalizing the denominator is transforming the fraction in such a way that its value does not change and at the same time it is written without using the irrational number in the denominator.m91e1a6949932a5fd_1527752263647_0Rationalizing the denominator is transforming the fraction in such a way that its value does not change and at the same time it is written without using the irrational number in the denominator.

Selected words and expressions used in the lesson plan

comparing numberscomparing numberscomparing numbers

cube rootcube rootcube root

denominatordenominatordenominator

numbernumbernumber

numeratornumeratornumerator

operations on rootsoperations on rootsoperations on roots

rationalizing the denominatorrationalizing the denominatorrationalizing the denominator

square rootsquare rootsquare root

transforming expressionstransforming expressionstransforming expressions

valuevaluevalue