unit 2.1  using models to multiply integers
what we need to know
 Multiplication is repeated addition
 Integers are the positive and negative whole numbers, including 0.
 Integers are the positive and negative whole numbers, including 0.
class notes
more information
I must confess... In my opinion, this unit seems to be written out of order. In order to give it a little bit more of logic, I am going to show you the RULES OF SIGN for multiplication (which are the same for division) here, even though in your book they show them next part of the unit. Now, in order to make this unit much, much easier, you REALLY HAVE to memorize them:
Using number lines to multiply integers
Positive times a positive
This reads 2 groups of 5
This reads 5 groups of 2
Let's take the first example:
So, as you can see, multiplying a positive integer times a positive integer results in a positive integer.
Positive times a negative
One of the properties of multiplication is the following, which we called the COMMUTATIVE PROPERTY:
This will allow us to multiply a positive and a negative integer:
Notice that we could have applied the same principle to (2) x 5,which we would read as "5 groups of 2.
NEGATIVE TIMES A NEGATIVE
Let's think about as a double negative. For example, "IT IS NOT NOT GOING TO RAIN" really means it is GOING TO RAIN. So the result of two negative numbers IS a positive number:
This would read (2) groups of (5). This is... kind of not possible.
2 groups of (5) gets us to  10. But here is the thing.... because the 2 TRULY is a  2.... then

So, when you have two negatives, "ignore" (for a moment) the negative sign of the 2, and for a little bit, let's think about this as 2 groups of 5.
WHEN YOU MULTIPLY TWO NEGATIVES, IGNORE THE NEGATIVE OF ONE NUMBER, FIND THE ANSWER, AND THEN FLIP THE DIRECTION OF THE ARROW.

MORE EXAMPLES
Three groups of 4
using algebra tiles to multiply integers
 We know that (2) x 3 has a negative counter. So we "take the opposite".
 This means (2) groups of (3) tiles  From the "algebra tile bank", we bring 2 groups of 3 red tiles, to end up with 6 red tiles, or (6). 
 We can read this as (3) groups of (1). This, however is not possible.
 Since THE COUNTER is negative, we take the opposite. That is, we take (+3) groups of (+1).  This is 3 yellow tiles, or (+3). 
another way to look at it
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review  workbook
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