Topicmb9c4cf675e947708_1528449000663_0Topic

Operations on roots

Levelmb9c4cf675e947708_1528449084556_0Level

Third

Core curriculummb9c4cf675e947708_1528449076687_0Core curriculum

I. Real numbers. The student:

1) performs operations (addition, subtraction, multiplication, division, exponentiation, roots, logarithms) in a set of real numbers.

Timingmb9c4cf675e947708_1528449068082_0Timing

45 minutes

General objectivemb9c4cf675e947708_1528449523725_0General objective

Interpreting and manipulating information presented in both mathematical and popular science texts, as well as in the form of graphs, diagrams, tables.

Specific objectivesmb9c4cf675e947708_1528449552113_0Specific objectives

1. Communicating in English, developing mathematical, scientific, technical and IT competences; developing learning skills.

2. Revision of the definition of the square rootrootroot and cubic root.

3. Revision of the rules for operations on the roots.

Learning outcomesmb9c4cf675e947708_1528450430307_0Learning outcomes

The student:

- revises the definition of the square root and cubic root,

- revises the rules for operations on the roots.

Methodsmb9c4cf675e947708_1528449534267_0Methods

1. Brainstorming.

2. Competition.

Forms of workmb9c4cf675e947708_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmb9c4cf675e947708_1528450127855_0Introduction

Students, working in groups with the use of the brainstorming method, review the information known so far about the roots and operations on roots. They write the information on the boards. After finishing the task, they present their results and the teacher verifies their conclusions and clarifies any doubts.

Proceduremb9c4cf675e947708_1528446435040_0Procedure

The teacher informs students that the aim of the lesson is to review and consolidate the information about square and cubic roots and rules on operations on roots.

Students, working in groups, analyze the interactive drawing, which presents information about the properties of square and cubic roots.

Task
Students compare the information contained in the drawing with this included on their boards.

[Interactive illustration]

Discussion:

Is the square root of a rational number always a rational number?
Is the square rooting always feasible? And how about cubic root?mb9c4cf675e947708_1527752256679_0Is the square root of a rational number always a rational number?
Is the square rooting always feasible? And how about cubic root?

Conclusions students should come up with:

- Roots of some rational numbers are not rational numbers (e.g. $\sqrt{2}$).

- There are no square roots of negative numbers.

Students take part in an individual task competition.

The competition has three stages. For each correctly performed calculation, the student receives 1 point, wrongly (-1). Students who have obtained a minimum of 3 points proceed to the next stage.

Stage 1.

Task
Calculate.

a) $\sqrt{121}$

b) $\sqrt[3]{64}$

c) $\sqrt[3]{-729}$

Task
Calculate the value of the following expressions.

a) $2\sqrt{16}-3\sqrt{625}+5\sqrt{169}$

b) $2\cdot (2\sqrt{49}+4\sqrt[3]{-216}-3\sqrt{81})$

c) $\sqrt{289}-6\sqrt{144}+\sqrt[3]{-125}$

Stage 2.

Task
Calculate using the appropriate operation on roots.

a) $\sqrt{144\cdot 81}$

b) $\sqrt[3]{-125\cdot 343}$

c) $\sqrt[3]{27\cdot 512}$

Task
Calculate the value of the rootrootroot.

a) $\sqrt{\frac{64}{225}}$

b) $\sqrt[3]{\frac{1331}{-125}}$

c) $\sqrt[3]{\frac{-216}{-1000}}$

Stage 3.

Task
Calculate.

a) $\sqrt{9\cdot 15+9\cdot 3+9\cdot 7}$

b) $\sqrt[3]{8\cdot 11+8\cdot 9+8\cdot 7}$

The teacher summarizes the results of the competition. The students who scored the most points are rewarded with excellent grades.

Using the information learned, students independently solve the tasks.

Task
Calculate the value of the expression.

a) $\sqrt{{33}^2+{44}^2}$

b) $\sqrt[3]{27\cdot 3+27\cdot 5}$

c) $5\sqrt{150}:\sqrt{6}+\sqrt[3]{-54:2}\cdot \sqrt[3]{3^7:(-81)}$

An extra task:
The rectangular cuboid volume is equal to 6000 cmIndeks górny 3³. Calculate the height of this cuboid if it is twice as long as the edge of its base.

Lesson summarymb9c4cf675e947708_1528450119332_0Lesson summary

Students do the revision exercises.

And formulate conclusions to remember.

- Roots of some rational numbers are not rational numbers (e.g. $\sqrt{2}$).
- There are no square roots of negative numbers.mb9c4cf675e947708_1527752263647_0- Roots of some rational numbers are not rational numbers (e.g. $\sqrt{2}$).
- There are no square roots of negative numbers.

Selected words and expressions used in the lesson plan

arithmetic rootarithmetic rootarithmetic root

degree of the rootdegree of the rootdegree of the root

multiplication of rootsmultiplication of rootsmultiplication of roots

properties of operations on rootsproperties of operations on rootsproperties of operations on roots

rootrootroot