Topicm3aba87146cecc94b_1528449000663_0Topic

Multiplication and division of the integers

Levelm3aba87146cecc94b_1528449084556_0Level

Second

Core curriculumm3aba87146cecc94b_1528449076687_0Core curriculum

Reading, interpreting and processing data presented in various forms.

Timingm3aba87146cecc94b_1528449068082_0Timing

45 minutes

General objectivem3aba87146cecc94b_1528449523725_0General objective

Reading, interpreting and processing data presented in various forms.

Specific objectivesm3aba87146cecc94b_1528449552113_0Specific objectives

1) Multiplying and dividing the integers.

2) Solving the text task concerning multiplying and dividing of the integers.

3) Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Learning outcomesm3aba87146cecc94b_1528450430307_0Learning outcomes

The student:

- multiplies and divides the integers,

- specifies the sign of the product and the quotient of the integers.

Methodsm3aba87146cecc94b_1528449534267_0Methods

1) Learning game.

2) Situational analysis.

Forms of workm3aba87146cecc94b_1528449514617_0Forms of work

1) Individual work.

2) Pair work.

3) Class work.

Lesson stages

Introductionm3aba87146cecc94b_1528450127855_0Introduction

The student prepares the cards and bring them to the class. There is one of the following numbers on each card: -9, -8, -7, -7, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The teacher introduces the topic of the lesson: multiplying and dividing the integers with the same and different signs.

Revision of the definition and the method of calculating the square and the cube of any natural number.

Procedurem3aba87146cecc94b_1528446435040_0Procedure

The students work individually using their computers. They are going to watch the multiplication of two natural numbers with the same and different signs.

[Slideshow]

The students solve the tasks in pairs using the information they have learned. They take out the cards with the numbers.

One student draws two cards and gives the product of the drawn numbers. The other person check if the result is correct by using the calculator. Then, they change their roles and repeat the activity for few times. If the result is correct the student gets one point, if the result is wrong he loses one point. The person who gets the largest number of points wins and gets an award (e.g. “+”).

Discussion – when the product of two numbers is positive and when it is negative.

To sum up the discussion the conclusion could be drawn:

The product of two numbers with different signs is negative.
The product of two numbers with the same signs is positive.m3aba87146cecc94b_1527752263647_0The product of two numbers with different signs is negative.
The product of two numbers with the same signs is positive.

The students analyse the examples of division written by the teacher and come up with the conclusion:

8 : 2 = 4

(- 8) : (- 2) = 4

(- 8) : 2 = (- 4)

8 : (- 2) = (- 4)

Conclusion
The quotient of two numbers with different signs is negative.
The quotient of two numbers with the same signs is positive.m3aba87146cecc94b_1527752256679_0The quotient of two numbers with different signs is negative.
The quotient of two numbers with the same signs is positive.

The students determine the product and the exponents of the integers paying attention to the signs of the results. They draw the conclusions.

Task
Calculate.

a) 2 ∙ (- 3) ∙ 3 (- 2)

b) (- 2) ∙ (- 3) ∙ 3 (- 2)

c) 2 ∙ (- 3) ∙ 3 (- 2) ∙ 6 ∙ (- 1)

d) 2 ∙ (- 3) ∙ (- 3) (- 2) ∙ 6 ∙ (- 1)

Task
Calculate.

a) (- 4)Indeks górny 2²

b) (- 7)Indeks górny 2²

c) (- 2)Indeks górny 3³

d) (- 3)Indeks górny 3³

Conclusions
The product of the integers different from zero is:
- positive, when there is an even number of the negative factors,
- negative, when there is odd number of the negative factors.
The square of the negative number is always the positive number.
The cube of the negative number is always the negative number.m3aba87146cecc94b_1527712094602_0The product of the integers different from zero is:
- positive, when there is an even number of the negative factors,
- negative, when there is odd number of the negative factors.
The square of the negative number is always the positive number.
The cube of the negative number is always the negative number.

An extra task
Calculate the arithmetic mean of the numbers: - 5, 2, - 1, - 4.

Lesson summarym3aba87146cecc94b_1528450119332_0Lesson summary

The students do the summarising tasks.

Then they sum up the class drawing the conclusions to memorise:

- The product (quotient) of two numbers with different signs is negative.

- The product (quotient) of two numbers with the same signs is positive.

- The product of the integers different from zero is:

- positive, when there is an even number of the negative factors,

- negative, when there is an odd number of the negative factors.

- The square of the negative numbernegative numbernegative number is always the positive numberpositive numberpositive number.

- The cube of the negative numbernegative numbernegative number is always the negative numbernegative numbernegative number.

Selected words and expressions used in the lesson plan

absolute valueabsolute valueabsolute value

division of the numbers with different signsdivision of the numbers with different signsdivision of the numbers with different signs

division of the numbers with the same signsdivision of the numbers with the same signsdivision of the numbers with the same signs

integerintegerinteger

multiplication of the numbers with different signsmultiplication of the numbers with different signsmultiplication of the numbers with different signs

multiplication of the numbers with the same signsmultiplication of the numbers with the same signsmultiplication of the numbers with the same signs

negative numbernegative numbernegative number

positive numberpositive numberpositive number