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**MULTIPLICATION OF INTEGERS**

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**Pre requisite knowledge**

1.concept of integers 2.concept of representation of integers on number line. 3.concept of addition and subtraction of integers. 4.concept of multiplication of two whole numbers.

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Teaching points 1.while multiplying a positive integer and a negative integer,we multiply them as whole numbers and put a minus sign before the product . We thus get a negative integer 2. The product of two negative integers is a positive integer.we multiply the two negative integers as whole numbers and put the positive sign before the product.

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**Product of two in tegers**

Continued 3. If the number of negative integers in a product is even, then the product is a positive integer. If the number of negative integers in a product is odd, then the product is a negative integer. Product of two in tegers by activity method.

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**Instructional objectives**

To enable students to know that multiplication of integers is repeated addition 2.to enable students to know that multiplication of two positive integers through patterns. 3.to enable students to multiply two negative integers. 4.to enable students to find the product of theree or more negative integers 5.to enable students to find the product of two integers by activity method.

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**Multiplication of positive and negative integers**

Multiplication of wholenumbers is repeated addition 5+5+5=3x5=15 Addition of integers can be represented in the same way (-5)+(-5)+(-5)=-15=3x(-5) -5 -20 -15 -10

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**Multiplication of a negative integer and a positive integer**

Find (-3)x5 through the following pattern 3x5=15 2x5=10=(15-5) 1x5=5=(10-5) 0x5=5-5=0 -1x5=0-5=-5 -2x5=-5-5=-10 -3x5=-10-5=-15 We already have 3x(-5)=-15 So we get (-3)x5=-15=3x(-5) While multiplying a positive integer and a negative integer,we multiply them as wholenumbers and put a minus sign before the product.we thus get a negative integer

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**Continued We already have 3x(-5)= -15 So we get (-3)x5 = -15 = 3x(-5)**

While multiplying a positive integer and a negative integer,we multiply them as whole numbers and put a minus sign before the product. We thus get a negative integer .

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**Multiplication of two negative integers.**

Observe the pattern for (-3)x(-2) (-3)x4=-12 (-3)x3=-12-(-3)= = -9 (-3)x2=(-9)-(-3)-9+3= -6 (-3)x1=(-6)-(-3)=-3 (-3)x0= -3-(-3)=0 (-3)x -1=0-(-3)=3 (-3)x(-2)=3-(-3)=6

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Continued from the pattern , we observe (-3)x(-1)=3=3x1 (-3)x(-2)=6= 3x2 the product of two negative integers is a positive integer. We multiply the two negative integers as whole numbers and put the positive sign before the product

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**Product of three or more negative integers**

(-4)x(-3)=12 (-4)x(-3)x(-2)=[(-4)x(-3)]x(-2)=12x(-2)= -24 (-4)x(-3)x(-2)x(-1)=[(-4)x(-3)x(-2)]x(-1) =(-24)x(-1)

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Continued If the number of negative integers in a product is even , then the product is a positive integer . If the number of negative integers in a product is odd, then the product is a negative integer.

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**Materials required for the activity**

1.chart paper 2.pencil 3.sketch pens 4.scale

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**Two find the product of two integers by activity method**

-4 -3 -2 -1 1 2 -5 3 5 4 -2 1 4 -4 -5 -3 -1 2 3 5

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**Activity continued -1 P(2) -2 2 -4 -3 -1 -1 1 3 -1 4 -1 -4 -3 -2 2 3**

1 3 -1 4 -1 -4 -3 -2 2 3 -4 -1 1 4

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**Activity continued -4 -1 2 -3 -2 1 1 4 -2 3 P(-2) -1 1 3 - 4 1 2 -3 3**

3 P(-2) -1 1 3 - 4 1 2 -3 3 6 5 4 -2 6

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**Home Assignment 1.find (-31)x(-100). 2.find (-45)x18 3.find 70x(-19)**

4.find (-18)x(-5)x(-4) 5.find (-3)x(-6)x(-2)x(-1)

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For Educational Use Only © 2010 10.5 Factoring x 2 + bx + c Brian Preston Algebra 1 2009-2010.

For Educational Use Only © 2010 10.5 Factoring x 2 + bx + c Brian Preston Algebra 1 2009-2010.

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