INTEGERSMrs. Haataja

6th Grade Math

What are integers?

Integers

Are numbers Can be positive or

negative Do NOT have

decimals Do NOT have

fractions

Examples

INTEGERS NON- INTEGERS

5 10059 -33 -478 29

4.5 -3.33 2/3 -6 ½ -83.9

Integers

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…

IntegersPOSITIVE TEMPERATURE READING ALL NUMBERS IN THIS PHOTO ARE POSITIVE

AVERAGE PER GAME VALUE IS NEGATIVE (THIS IS AN OLD IPOD!)

Positive and Negative Integers

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

On a number line

On a number line

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

Adding integers

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

Adding POSITIVE integers

5 + 3 = 8 You just added the

integers positive 5 and positive 3 and found out the answer was positive 8!

Adding NEGATIVE integers

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!!

Adding integers with different signs

Adding integers with different signs

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

Adding integers with different signs

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

What is absolute value?

Absolute Value

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

Absolute Value

It is written as vertical lines on either side of a number

|12|, is 12 |-23|, is 23 Absolute values are ALWAYS

positive

Adding integers with different signs

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

4 problems with two integers

21 + 29 = 50 -21 + (-29) = -50 29 + (-21) = 8

|29| = 29 |-21| = 2129 – 21 = 829 is +, so answer is + 21 + (-29) = -8

|-29| = 29 |21| = 2129 – 21 = 829 is -, so answer is -

Works cited

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

Works cited

Slide 8: Photographer: Ethan HeinTitle: 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