An introduction to integers - what they are, and how to add them

1. Mrs. Haataja
6th Grade Math

3.  Are numbers
 Can be positive or
negative
 Do NOT have
decimals
 Do NOT have
fractions

4. INTEGERS NON- INTEGERS
 5
 10059
 -33
 -478
 29
 4.5
 -3.33
 2/3
 -6 ½
 -83.9

5. When you count, you say
1, 2, 3, 4, 5…
You are listing INTEGERS
 To count in the other
direction, it is -1, -2, -3, -4, -
5…

6. POSITIVE TEMPERATURE READING
ALL NUMBERS IN THIS PHOTO ARE
POSITIVE
AVERAGE PER GAME VALUE IS
NEGATIVE (THIS IS AN OLD IPOD!)

7. POSITIVE NEGATIVE
 When the temperature
is above zero
 When you are above
ground
 When you earn money
 In hockey, when your
team scores a goal while
you are on the ice
 When the temperature
is below zero
 When you are below
ground
 When you spend money
 In hockey, when the
other team scores a goal
while you are on the ice

9.  Positive integers increase in increments of one
as you move to the right
 Negative integers mirror this moving to the left
of zero, however, even though they appear to
be getting bigger, they are actually getting
smaller
 -5 is one number smaller than -4, for example

10. You already know how to
add positive integers…you
just haven’t called them
integers before!

11.  5 + 3 = 8
 You just added the integers
positive 5 and positive 3 and
found out the answer was
positive 8!

12.  Adding negative integers is just like adding
positive integers…only difference…the answer
will have a negative sign
 -6 +(-5) = -11
 All you do is ignore the negative signs and add
the numbers, then put the negative sign back in
your answer
 THIS ONLY WORKS IF BOTH NUMBERS
ARE NEGATIVE!!

14.  On the previous slide we saw a diagram of the
problem 6 + (-2)
 To solve this, they started at zero and moved to
the right 6 places – to represent the positive 6
 Next, they moved left 2 places – this
represented the -2
 They landed on the number 4 (positive 4)
which is the answer

15.  Using a number line is a great way to practice
when you are first learning to add numbers
with different signs – but there is another way
 We can use the absolute value of a number and
subtraction to solve addition problems
involving integers of different signs

17.  Absolute value is the distance
between a number and zero
 It does not matter which direction
you are moving to get back to zero –
all that is important is how many
steps it takes to get there

18.  It is written as vertical lines on either
side of a number
 |12|, is 12
 |-23|, is 23
 Absolute values are ALWAYS
positive

19.  Here’s how with the help of absolute value…
 1) find the absolute value of each number being
added
 2) subtract the smaller absolute value from the
larger absolute value
 3) the sign of the number with the larger
absolute value is the sign of the answer

20.  21 + 29 = 50
 -21 + (-29) = -50
 29 + (-21) = 8
|29| = 29 |-21| = 21
29 – 21 = 8
29 is +, so answer is +
 21 + (-29) = -8
|-29| = 29 |21| = 21
29 – 21 = 8
29 is -, so answer is -

21. All photos from flickr.com, all have a creative commons license
 Slide 2: Photographer: Ciccio Pizzettaro
Title: Question Mark Taken: 1/23/2010
 Slide 3: Photographer: Kenyee
Title: Floating Integers Taken: 8/22/2008
 Slide 6 Photographer Rob Friesel found_drama
Title: Is that a…positive integer? Taken: 1/25/2013
 Slide 6: Photographer: Frank Wales
Title: I should have quit while I was ahead Taken:
11/19/2007

22.  Slide 8: Photographer: Ethan Hein
Title: Even Integers Subgroup Taken: 4/11/2008
 Slide 13: Photographer gfinder
Title: Goalfinder Math integer-numberline 1
Taken: 3/1/2012
 Slide 16 Photographer: gfinder
Title: Goalfinder Math Absolute-value-of-an-
integer Taken: 3/1/2012
 Slide 20 Photographer danmachold
Title: clock Taken: 2/3/2011