Introduction
Real Numbers including Integers
Integers are the set of whole numbers and their opposites - positive integers, negative integers and zero. There are no fractions, decimals or percent.
Watch this YouTube clip to refresh your memory about integers.
Task
Lets explore Integers!
When, where, how and why we use integers.
Integers are used to represent scenarios.
For example, we removed 7 pages from our scrapbook, this would be represented by -7 integer.
We added 30 grams of butter to our cake mix, this would be represented by 30 (+30) integer.
you try - https://nicolehenke.typeform.com/to/uje0Wo
Integers have opposites.
The opposite of -5 is 5,
the opposite of -14 is 14,
the opposite of 121 is -121.
What about zero? Does zero have an opposite?
show me what you know about opposite integers - https://nicolehenke.typeform.com/to/o4mnQl
Comparing integers
Number lines are helpful when comparing integers
____________________________________________________________
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
The numbers to the left are less than the numbers on the right, and the numbers to the right are greater than the number to the left.
Locate - 4 and +1 on the number line, - 4 is less than 1
When comparing integers we use the < less than or > greater than symbols, so - 4 < 1
Locate 3 and -5 - which one is greater? 3 is to the right so 3 > - 5
Hints & Tips - Positive integers always have greater value than negative integers.
Zero always has less value than positive integers but greater value than negative integers.
Let's compare integers - https://nicolehenke.typeform.com/to/N09afN
Ordering Integers
Number lines are helpful when ordering integers
___________________________________________________________
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
We can order numbers from greatest to least value or from least to greatest value
For example, ordering - 3, 5 and -1
locate these on a number line, which number has the least value (the most left) - 3,
next most left number is - 1
and finally number 5 is to the right so it has the most value.
So to order these numbers we would have - 3, - 1, 5
(NB. our hints and tips for comparing integers can be applied when ordering integers)
Your turn - https://nicolehenke.typeform.com/to/eDTabf
Process
Addition and Subtraction with Positive and Negative Integers
Addition and subtraction of positive and negative numbers can be illustrated on a number line using three simple rules:
1. The first number tells you where to start.
2. The first sign (the operation sign) indicates which way to go, + to the right, –to the left.
3. If the second sign is positive (or blank) continue in the same direction, but if the second sign is negative then do the opposite.
____________________________________________________________________________________
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Adding a Positive Number
3 + 2 = 5 Start at positive 3 and move to the right 2 places to finish at positive 5
-4 + 3 = -1 Start at negative 4 and move to the right 3 places to finish at negative 1
Adding a Negative Number
2 + -4 = -2 Start at positive 2, the + sign suggests go to the right, but the negative sign indicates do the opposite, left 4 places
-3 + -2 = -5 Start at negative 3, the + sign suggests go to the right, but the negative sign indicates do the opposite, left 2 places
You try - https://nicolehenke.typeform.com/to/JqzWxa
Subtracting a Positive Number
8 –10 = -2 Start at positive 8 and move to the left 10 places to finish at negative 2
-4 –5 = -9 Start at negative 4 and move to the left 5 places to finish at negative 9
Subtracting a Negative Number
3 –-5 = 8 Start at positive 3, the –sign suggests go to the left, but the negative sign indicates do the opposite, right 5 places
-2 –-6 = 4 Start at negative 2, the –sign suggests go to the left, but the negative sign indicates do the opposite, right 6 places
Try these questions - https://nicolehenke.typeform.com/to/X9DdVO