Topicm363f1987339b607b_1528449000663_0Topic

Operations on rootsoperations on rootsOperations on roots

Levelm363f1987339b607b_1528449084556_0Level

Second

Core curriculumm363f1987339b607b_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.

Timingm363f1987339b607b_1528449068082_0Timing

45 minutes

General objectivem363f1987339b607b_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm363f1987339b607b_1528449552113_0Specific objectives

1. Transforming algebraic expressions containing rootsexpressions containing rootsexpressions containing roots.

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

Learning outcomesm363f1987339b607b_1528450430307_0Learning outcomes

The student transforms algebraic expressions containing rootsexpressions containing rootsexpressions containing roots.

Methodsm363f1987339b607b_1528449534267_0Methods

1. Discussion.

2. Thematical contest.

Forms of workm363f1987339b607b_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm363f1987339b607b_1528450127855_0Introduction

The teacher introduces the subject of the lesson – transforming algebraic expressions containing rootsexpressions containing rootsexpressions containing roots. Students revise the rules of operations on numbers – the commutative property of multiplicationcommutative property of multiplicationcommutative property of multiplication and the commutative property of additioncommutative property of additioncommutative property of addition and the distributive property of multiplication over additiondistributive property of multiplication over additiondistributive property of multiplication over addition.

Procedurem363f1987339b607b_1528446435040_0Procedure

Students analyse examples in groups:

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

Task
Students open the slideshow and discuss the example of multiplying expressions containing roots.m363f1987339b607b_1527752256679_0open the slideshow and discuss the example of multiplying expressions containing roots.

[Slideshow]

Students’ conclusions:

- To multiply two expressions containing roots, we use the commutative property of multiplication. We multiply the number by the number and the root by the root.- We can add and subtract only these roots that have the same number under the radical and are of the same degree.m363f1987339b607b_1527752263647_0- To multiply two expressions containing roots, we use the commutative property of multiplication. We multiply the number by the number and the root by the root.- We can add and subtract only these roots that have the same number under the radical and are of the same degree.

Students use shaped abilities in exercises.

Task
Write in the simplest form:

a) $\frac{1}{4}\sqrt{6}·8\sqrt{8}$

b) $2\sqrt{3}·12\sqrt{12}$

c) $3\sqrt[3]{-2}·\frac{1}{9}\sqrt[3]{32}$

d) $\frac{1}{3}\sqrt[3]{27}·6\sqrt[3]{128}$

Task
Calculate:

a) $3\sqrt{2}·(4\sqrt{5}-4\sqrt{10})$

b) $2\sqrt{5}·(3\sqrt{15}+\sqrt{35})$

c) $-\sqrt{6}·(4\sqrt{3}-5\sqrt{2})$

d) $2\sqrt{3}·(\sqrt{12}-\sqrt{18})$

Task
Let $A=2\sqrt{3}$ , $B=\sqrt{3}-4\sqrt{2}$, $C=-\sqrt{12}+3\sqrt{2}$.

Write in the simplest form:

a) $A·B$

b) $A·C$

c) $B+C$

d) $C-B$

Task
Calculate:

a) $(\frac{2\sqrt{5}}{4}{)}^2$

b) $(\frac{3\sqrt{7}}{13}{)}^2$

c) $(\frac{5\sqrt[3]{10}}{2}{)}^3$

d) $(\frac{{\displaystyle 4\sqrt[3]{4}}}{{\displaystyle 9}}{)}^3$

An extra task
Calculate the value of the expression:

$2\sqrt[3]{2}·(\sqrt[3]{20}-4\sqrt[3]{24})$

Lesson summarym363f1987339b607b_1528450119332_0Lesson summary

Students do the revision exercises.

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

- To multiply two expressions containing roots, we use the commutative property of multiplication. We multiply the number by the number and the root by the root.- We can add and subtract only these roots that have the same number under the radical and are of the same degree.m363f1987339b607b_1527752263647_0- To multiply two expressions containing roots, we use the commutative property of multiplication. We multiply the number by the number and the root by the root.- We can add and subtract only these roots that have the same number under the radical and are of the same degree.

Selected words and expressions used in the lesson plan

commutative property of additioncommutative property of additioncommutative property of addition

commutative property of multiplicationcommutative property of multiplicationcommutative property of multiplication

cube root of a numbercube root of a numbercube root of a number

distributive property of multiplication over additiondistributive property of multiplication over additiondistributive property of multiplication over addition

expressions containing rootsexpressions containing rootsexpressions containing roots

numbernumbernumber

operations on rootsoperations on rootsoperations on roots

rational numberrational numberrational number

square root of a numbersquare root of a numbersquare root of a number

transforming expressionstransforming expressionstransforming expressions