This document provides an overview of integers for a 6th grade mathematics class. It defines integers as whole numbers along with their negative counterparts. Integers are represented on a number line with positive numbers to the right of zero and negative numbers to the left. Rules for ordering integers and performing addition and subtraction of integers are explained. Key concepts covered include adding/subtracting positive and negative integers, using a number line to model integer operations, and defining the additive inverse property. Examples are provided to illustrate integer operations and properties. Students are assigned homework practicing integer addition and subtraction on a number line.

1. SUBJECT :- MATHEMATICS
CLASS:-6TH
TOPIC :- INTEGERS
MADE BY:- SEEMA SINGH

2. CONTENTS TO BE COVERED
• Define Integers
• Explain integers on a number line
• Define ordering of integers
• Find addition and subtraction of integers
• Define addition and subtraction of
integers on a number line.
• Additive Inverse

3. Define integers
• Students you all already know about the whole
numbers ie 0,1,2,3,4….
• When we put the negative numbers also along with
these whole numbers we call them INTEGERS

4. Integers on a number line
• This figure represents a line with some points marked at equal distance.
• There is a point on it which is marked as 0.The points on the right of zero
are termed as positive integers whereas points on the left of the zero are
negative integers and are marked as -1,-2,-3,-4 and so on.
• This kind of representation is termed as number line representation.
• To mark +2 on the number line we move 2 steps from 0 on the number
line similarly to represent -5 we move 5 steps from left of 0 on the
number line

5. • Let us again observe the integers that are represented on the number line
• We know that 5 < 9 (9 is greater than 5) and placed on the number line 4
points on right of 5
• Similarly,
0 < 5 (5 is greater than 0) and 5 is placed 5 steps on right of 0.
-2 < 0 (0 is greater than -2) and -2 is placed 2 steps on the left of 0.
-7 < -2 (-2 is greater than -7) and -7 is placed 5 steps on the left of -2.
• Thus we have seen that, in the number line the bigger numbers are placed
right and smaller at the left.

6. Addition of Two positive Number
• Let us understand this concept with an example:
• A boy is stepping on the staircase. He goes six stairs
up from the ground and halts for a while, then goes
up four more stairs. How many stairs he goes up
from the ground?
(+6) + (+4) = +6 + 4 = +10
So number of steps moved by boy from ground is 10

7. Addition of two negative integers
• Let us understand this concept with an example:
• In a game you have to pick up any two pieces of paper on which
a number is written. You have to add the numbers written on
these two papers . Suppose you get -2 & -5 .What is the
addition or sum of these two negative numbers?
(-2) + (-5) = -(2 + 5) = -7

8. Addition of two integers(one +ve and
other –ve)
• Let us understand this concept with an example:
• In a game you have to pick up any two pieces of paper on which
a number is written. You have to add the numbers written on
these two papers . Suppose you get +5 & -9 .What is the
addition or sum of these two negative numbers?
(+5) + (-9) = -4

9. • Now we will learn addition of two positive integer on the number line.
• Let us say we want to add 6 & 4 ie 6 + 4
So for that we move 6 steps to the right from 0 and then on reaching 6
we move 4 steps ahead on the number line from 6 and reach 10.
Thus, we get 6+4 = 10
Addition of 2 +ve integers on the number
line

10. Addition of 2 -ve integers on the number
line
• Now we will learn addition of two positive integer on the number line.
• Let us say we want to add -5 & -4 ie (-5) + (-4)
So for that we move 5 steps to the left from 0 and then on reaching -5
move 4 steps ahead on left on the number line and thus we reach -9.
Thus, we get (-5) + (-4) = -(5 + 4)= -9
So we have seen when we add two positive integers their sum is
positive (+ve) and when we add two negative integers their sum is
negative (-ve)

11. Examples
• An ant is moving on a number line . It moves 6 points right from zero and then
comes two points back? Where is it at present?
It will be at
6 + (-2) = 4th point to right of zero

12. • An ant is moving on a number line . It moves 6 points left from zero and then
comes 4 points to right? Then where is it at present?
It will be at
- 6 + (+4) = -2 ie 2nd point to left of zero

13. Additive Inverse
• Now let us understand and know the concept of additive inverse.
• Suppose the ant walks three points toward right side (+3) of zero and walk back
three points (-3) towards the zero .Where does it reach?
3 + (-3) = 0, So additive inverse of 3 is -3
Similarly , 2 + (-2) = 0, So additive inverse of 2 is -2
• Hence , these are called as additive inverse

14. Addition by grouping of +ve integers
and the –ve integers
• For better understanding let us take an example
• Find out the sum of (-10) + (+5) +(-7) +(+2)
Here we are going to group +ve integer and -ve integer separately together
ie (-10) + (-7) + (+5) +(+2)
= (-17)+ (+7) = - (+10) = -10

15. Additive inverse based question
• For better understanding let us take an example
• Find out the Subtract (-5) from (-10)
Sol: (-10) – (-5) = (-10) + (additive inverse of -5)
ie (-10) + 5 = -5

16. Home Assignment

19. Home Assignment
• Solve the following with the help of
number line:
– 3 + 4 = ?
– 8 - 4 = ?
– 5 - 9 = ?
– -3 - 4 = ?