Topicmebcc052e9866e154_1528449000663_0Topic

Multiplication and division of rational numbers

Levelmebcc052e9866e154_1528449084556_0Level

Second

Core curriculummebcc052e9866e154_1528449076687_0Core curriculum

V. Calculations on common and decimal fractions. The student:

9) calculates values of arithmetic expression that require arithmetic calculations on integers or numbers written as common fractions, mixed numbers and decimal fractions, also rational negative, not more difficult than:

$-\frac{1}{2}÷0,25+5,25÷0,05-7\frac{1}{2}\cdot (2,5-3\frac{2}{3})+1,25$.

Timingmebcc052e9866e154_1528449068082_0Timing

45 minutes

General objectivemebcc052e9866e154_1528449523725_0General objective

Doing simple calculations mentally or using the long method in more difficult examples, using these abilities in practical situations.

Specific objectivesmebcc052e9866e154_1528449552113_0Specific objectives

1. Multiplying and dividing rational numbers.

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

Learning outcomesmebcc052e9866e154_1528450430307_0Learning outcomes

The student:

- multiplies and divides rational numbers.

Methodsmebcc052e9866e154_1528449534267_0Methods

1. Discussion.

2. Individual task contest.

Forms of workmebcc052e9866e154_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmebcc052e9866e154_1528450127855_0Introduction

Students revise information they learnt about rational numbersrational numbersrational numbers on previous classes. The teacher announces thematical quiz. The person who calculates the most examples the fastest gets two pluses.

The teacher introduces the subject of the lesson – multiplying and dividing rational numbersrational numbersrational numbers.

Proceduremebcc052e9866e154_1528446435040_0Procedure

Task

Students work individually, using computers. Their task is to observe how the sign of the product changes, depending on the number of negative factors.

[Geogebra applet]

In groups, students discuss presented examples, make theories and verify them on specific examples, possibly by using calculators. Then they make a note including various cases of multiplying rational numbersrational numbersrational numbers.

Conclusions:

- If in multiplication of rational numbersrational numbersrational numbers different than zero there is an even number of negative factors, then the sign of the product is positive.

- If in multiplication of rational numbersrational numbersrational numbers different than zero there is an odd number of negative factors, then the sign of the product is negative.

- Dividing rational numbersrational numbersrational numbers by a number different than zero can be replaced with multiplying by the multiplicative inverse of the divisor.

Individual task contest.

Students do the contest tasks, using properties of multiplication and division of rational numbersrational numbersrational numbers.

They can go to the next level after verifying results from the previous level.

Three students with the best time score get the highest marks, three following – second highest marks.

Contest task

Without doing the calculation, decide if the result is a positive or negative numbernegative numbernegative number.

a) $-(-10)\cdot (-12)\cdot (-14)$

b) $-(-(-2))\cdot (-8)$

c) $(-5{)}^3$

d) $-(-(-4{)}^2)$

Contest task

What sign does the number x have if the expression $-\left({(-4)}^5\right)\cdot (-x)$ is.

a) A positive numberpositive numberpositive number.

b) A negative numbernegative numbernegative number.

Contest task

Calculate.

a) $\frac{4}{7}·(-1\frac{1}{2})$

b) $-2,4\cdot (-1\frac{4}{5})$

c) $-4\frac{2}{5}:1\frac{1}{4}$

d) $-3,2:(-2,8)$

Contest task

Divide the product of numbersproduct of numbersproduct of numbers -4 and $\frac{2}{3}$ by the quotient of numbersquotient of numbersquotient of numbers -2 and -$\frac{1}{4}$.

Contest task

Is there a number x that meets the condition $\frac{x\cdot x\cdot x}{x\cdot x\cdot x\cdot x}=-x$ ?

Justify the answer.

An extra task:
Give two rational numbers such that their product is smaller from each one of these numbers.mebcc052e9866e154_1527752263647_0An extra task:
Give two rational numbers such that their product is smaller from each one of these numbers.

Lesson summarymebcc052e9866e154_1528450119332_0Lesson summary

Students do the revision exercises.

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

- If in multiplication of rational numbersrational numbersrational numbers different than zero there is an even number of negative factors, then the sign of the product is positive.

- If in multiplication of rational numbersrational numbersrational numbers different than zero there is an odd number of negative factors, then the sign of the product is negative.

- Dividing rational numbersrational numbersrational numbers by a number different than zero can be replaced with multiplying by the multiplicative inverse of the divisor.

Selected words and expressions used in the lesson plan

negative numbernegative numbernegative number

positive numberpositive numberpositive number

product of numbersproduct of numbersproduct of numbers

quotient of numbersquotient of numbersquotient of numbers

rational numbersrational numbersrational numbers