Topicmbd3c22f9f473723d_1528449000663_0Topic

Factoring in perfect square factorsfactoring in perfect square factorsFactoring in perfect square factors

Levelmbd3c22f9f473723d_1528449084556_0Level

Second

Core curriculummbd3c22f9f473723d_1528449076687_0Core curriculum

II. Roots. The student:

4) calculates the rootrootroot of product and quotient of two numbers, factors out and factors in perfect squaresquaresquare factors.

Timingmbd3c22f9f473723d_1528449068082_0Timing

45 minutes

General objectivembd3c22f9f473723d_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmbd3c22f9f473723d_1528449552113_0Specific objectives

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

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

Learning outcomesmbd3c22f9f473723d_1528450430307_0Learning outcomes

The student factors in perfect squaresquaresquare factors.

Methodsmbd3c22f9f473723d_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workmbd3c22f9f473723d_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmbd3c22f9f473723d_1528450127855_0Introduction

The teacher informs students that during this class they will learn how to factorfactorfactor in perfect rootrootroot squares. This is usually done in order to compare valuesvaluesvalues of roots.

Procedurembd3c22f9f473723d_1528446435040_0Procedure

Students in groups analyse the following examples:

They give own examples and together check if they are correct.

Task
Students open Slideshow, check their assumptions and draw a conclusion.

[Slideshow]

The conclusion students should draw:

- In order to factor in perfect square factors we write the number in front of the root in form of the root. Then we use the theorem about the product of roots and do the multiplication.mbd3c22f9f473723d_1527752263647_0- In order to factor in perfect square factors we write the number in front of the root in form of the root. Then we use the theorem about the product of roots and do the multiplication.

Students use shaped abilities in exercises.

Task
Factor in perfect square factorsfactor in perfect square factorsFactor in perfect square factors.

a) $5\sqrt{2},4\sqrt{3},3\sqrt{5},5\sqrt{11}$

b) $5\sqrt[3]{2},4\sqrt[3]{3},3\sqrt[3]{5},-4\sqrt[3]{4}$

c) $4\sqrt{\frac{1}{3}},12\sqrt{\frac{3}{7}},\frac{1}{2}\sqrt[3]{5},\frac{2}{3}\sqrt{10}$

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

a) $4\sqrt{2}=\sqrt{\dots }$

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

c) $\sqrt{\dots }=\frac{1}{7}\sqrt{11}$

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

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

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

b) $2\sqrt{7}...7\sqrt{2}$

c) $4\sqrt[3]{3}...3\sqrt[3]{4}$

d) $6\sqrt[3]{7}...7\sqrt[3]{6}$

Task
The side of the square FIndeks dolny 1₁ is equal to $3\sqrt{5}$ cm, and the side of the square FIndeks dolny 2₂ is equal to $6\sqrt{3}$ cm. Which square has a greater area?mbd3c22f9f473723d_1527752256679_0The side of the square FIndeks dolny 1₁ is equal to $3\sqrt{5}$ cm, and the side of the square FIndeks dolny 2₂ is equal to $6\sqrt{3}$ cm. Which square has a greater area?

An extra task:
Arrange the numbers in increasing order $2\sqrt{6},3\sqrt{2},\frac{1}{2}\sqrt{19},10\sqrt{0,4}$.

Lesson summarymbd3c22f9f473723d_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 in perfect square factors we write the number in front of the root in form of the root. Then we use the theorem about the product of roots and do the multiplication.mbd3c22f9f473723d_1527752263647_0- In order to factor in perfect square factors we write the number in front of the root in form of the root. Then we use the theorem about the product of roots and do the multiplication.

Selected words and expressions used in the lesson plan

comparing rootscomparing rootscomparing roots

cube rootcube rootcube root

factorfactorfactor

factor in perfect square factorsfactor in perfect square factorsfactor in perfect square factors

factoring in perfect square factorsfactoring in perfect square factorsfactoring in perfect square factors

numbernumbernumber

rootrootroot

squaresquaresquare

square rootsquare rootsquare root

valuesvaluesvalues