Topicm4aca053542877b9d_1528449000663_0Topic

Operations on powers of the same exponents

Levelm4aca053542877b9d_1528449084556_0Level

Second

Core curriculumm4aca053542877b9d_1528449076687_0Core curriculum

I. Powers of natural bases. The student:

3) multiplies powers of different bases and same exponentssame exponentssame exponents.

Timingm4aca053542877b9d_1528449068082_0Timing

45 minutes

General objectivem4aca053542877b9d_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm4aca053542877b9d_1528449552113_0Specific objectives

1. Applying the theorems about product and quotient of powers of the same bases.

2. Calculating values of powers, using the theorems about product and quotient of powers of the same bases.

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

Learning outcomesm4aca053542877b9d_1528450430307_0Learning outcomes

The student:

- applies the theorems about product and quotient of powers of the same bases,

- calculates values of powers, using the theorems about product and quotient of powers of the same bases.

Methodsm4aca053542877b9d_1528449534267_0Methods

1. Discussion.

2. Thematical contest.

Forms of workm4aca053542877b9d_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm4aca053542877b9d_1528450127855_0Introduction

Students revise the theorems about product and quotient of powers of the same bases.

Procedurem4aca053542877b9d_1528446435040_0Procedure

Task
Students work individually, using computers. They calculate values of expressions containing powers.

[Geogebra applet]

Conclusions:

Operations in the examples are done according to the following order:

1. Operations in parentheses.
2. Exponentiation.
3. Multiplication and division.
4. Addition and subtraction.

The teacher announces thematical contest. Students work in pairs. The pair that solves the compulsory and extra tasks first gets the highest mark.

Task
Calculate.

a) $7,5^2:2,5^2=$

b) ${\left(\frac{5}{2}\right)}^3:{10}^3=$

c) ${\left(1\frac{2}{3}\right)}^4:{(0,9)}^4=$

d) ${\left(1\frac{2}{3}\right)}^2:{\left(\frac{5}{6}\right)}^2=$

Task
Insert the appropriate numbers into dotted spaces.

a) $4^2\cdot {(-5)}^2=..{.}^2$

b) ${\left(\frac{1}{4}\right)}^4\cdot {16}^4=..{.}^4$

c) ${\left(2\frac{1}{6}\right)}^6\cdot {(-2)}^6=..{.}^6$

d) ${(-\frac{3}{2})}^2\cdot {(-\frac{2}{3})}^2=..{.}^2$

e) ${\left(\frac{1}{4}\right)}^7\cdot {16}^7\cdot {\left(\frac{1}{2}\right)}^7=..{.}^7$

Task
Calculate.

a) ${\left(5a:b\right)}^4$

b) ${\left(25a^2:b\right)}^2$

c) ${\left(5a:b^2\right)}^3$

d) ${\left(5a^{3}b:a{b}^2\right)}^2$

Task
How many times the area of a square whose side is equal to 4x is longer than the area of a square whose side is equal to x?m4aca053542877b9d_1527752256679_0How many times the area of a square whose side is equal to 4x is longer than the area of a square whose side is equal to x?

Task
Insert proper numbers in dotted spaces.

a) ${\left(\frac{1}{3}\right)}^4:{\left(\frac{1}{3}\right)}^4=..{.}^4$

b) ${(-\frac{5}{3})}^2:{(-\frac{5}{3})}^2=..{.}^2$

c) ${\left(2\frac{1}{5}\right)}^4:{(-\frac{1}{5})}^4=..{.}^4$

d) ${\left(\frac{1}{4}\right)}^3\cdot 8^3:{\left(2\right)}^3=..{.}^3$

e) ${(0,2)}^2:{\left(\frac{1}{5}\right)}^2:2^2=..{.}^2$

An extra task:
Write the quotient $4:0,{001}^4$ in the form of the power.

Lesson summarym4aca053542877b9d_1528450119332_0Lesson summary

Students do the revision exercises.

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

Operations in the examples are done according to the following order:
1. Operations in parentheses.
2. Exponentiation.
3. Multiplication and division.
4. Addition and subtraction.m4aca053542877b9d_1527752263647_0Operations in the examples are done according to the following order:
1. Operations in parentheses.
2. Exponentiation.
3. Multiplication and division.
4. Addition and subtraction.

Selected words and expressions used in the lesson plan

base of the powerbase of the powerbase of the power

exponent of the powerexponent of the powerexponent of the power

power with the natural exponentpower with the natural exponentpower with the natural exponent

product of powers of the same exponentsproduct of powers of the same exponentsproduct of powers of the same exponents

quotient of powers of the same exponentsquotient of powers of the same exponentsquotient of powers of the same exponents

shorter version of multiplicationshorter version of multiplicationshorter version of multiplication

same exponentssame exponentssame exponents