Topicm1a378d0177994c06_1528449000663_0Topic

Factoring out perfect square factorsfactoring out perfect square factorsFactoring out perfect square factors

Levelm1a378d0177994c06_1528449084556_0Level

Second

Core curriculumm1a378d0177994c06_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.

Timingm1a378d0177994c06_1528449068082_0Timing

45 minutes

General objectivem1a378d0177994c06_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm1a378d0177994c06_1528449552113_0Specific objectives

1. Factoring out perfect square factorsfactoring out perfect square factorsFactoring out perfect square factors.

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

Learning outcomesm1a378d0177994c06_1528450430307_0Learning outcomes

The student factors out perfect square factors.

Methodsm1a378d0177994c06_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm1a378d0177994c06_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm1a378d0177994c06_1528450127855_0Introduction

The teacher introduces the subject of the lesson – factoring out perfect square factorsfactoring out perfect square factorsfactoring out perfect square factors. Factoring out perfect squares is simplifying expressions containing roots.

Procedurem1a378d0177994c06_1528446435040_0Procedure

Students in groups analyse the following examples.

They give own examples (also of roots in which we cannot factorfactorfactor out perfect square factors) and together check if they are correct.

Task
They check their assumptions using computers and draw a conclusion.

[Slideshow]

The conclusion students shoud draw:

- In order to factor out a perfect square factor, we need to write the number under the radical as such a product that at least one of them is a root of a rational number. Then, we need to use the fact that the root of the product is equal to the product of roots.m1a378d0177994c06_1527752263647_0- In order to factor out a perfect square factor, we need to write the number under the radical as such a product that at least one of them is a root of a rational number. Then, we need to use the fact that the root of the product is equal to the product of roots.

Students use shaped abilities in exercises.

Task
FactorfactorFactor out perfect square factors.

a) $\sqrt{20},\sqrt{500},\sqrt{32},\sqrt{128},\sqrt{27},\sqrt{150}$

b) $\sqrt[3]{54},\sqrt[3]{24},\sqrt[3]{192},\sqrt[3]{32},\sqrt[3]{2000},\sqrt[3]{625}$

Task
FactorfactorFactor out perfect square factors.

a) $\sqrt{720}$

b) $\sqrt{2187}$

c) $\sqrt{3000}$

d) $\sqrt[3]{10368}$

Task
Insert such numbernumbernumber in the dotted space that the equality is true.

a) $\sqrt{80}=...\sqrt{5}$

b) $\sqrt{250}=...\sqrt{10}$

c) $\sqrt[3]{-40}=...\sqrt[3]{5}$

d) $\sqrt[3]{-108}=...\sqrt[3]{4}$

Task
Fill in.

a) $\sqrt{45}=3\sqrt{?}$

b) $\sqrt{68}=2\sqrt{?}$

c) $\sqrt[3]{128}=4\sqrt[3]{?}$

d) $\sqrt[3]{135}=3\sqrt[3]{?}$

Task
Calculate the valuevaluevalue of the expression $3x^3-2x^2+8x$ for $x=\sqrt{3}$.

An extra task:
Write the expression in a simplified form $\sqrt{72}-\sqrt{112}+\sqrt{672}$.m1a378d0177994c06_1527752256679_0Write the expression in a simplified form $\sqrt{72}-\sqrt{112}+\sqrt{672}$.

Lesson summarym1a378d0177994c06_1528450119332_0Lesson summary

Students do the revision exercises.

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

- In order to factor out a perfect square factor, we need to write the number under the radical as such a product that at least one of them is a root of a rational number. Then, we need to use the fact that the root of the product is equal to the product of roots.m1a378d0177994c06_1527752263647_0- In order to factor out a perfect square factor, we need to write the number under the radical as such a product that at least one of them is a root of a rational number. Then, we need to use the fact that the root of the product is equal to the product of roots.

Selected words and expressions used in the lesson plan

cube of a numbercube of a numbercube of a number

cube rootcube rootcube root

factorfactorfactor

factoring out perfect square factorsfactoring out perfect square factorsfactoring out perfect square factors

numbernumbernumber

prime factorizationprime factorizationprime factorization

rational numberrational numberrational number

square of a numbersquare of a numbersquare of a number

square rootsquare rootsquare root

valuevaluevalue