Multiplying Integers: Why is -3 x -4 = +12?
‘The Rules’ and ‘The Reasons’,
‘The How’ and ‘The Why’
for Multiplying Integers.
I uploaded a couple pages of my Math Model Book for a ‘Pair-a-Dimes’ post, “Assessment & Rote Learning: Math Conundrums“… and thought I would share these very practical resources here.
The first page has The Rules for Multiplying and Dividing Integers.
Next, using counters, I look at Why the Rules for Multiplying Integers Work*. I call this lesson “Why is a negative times a negative a positive?” and slowly build up to this at the end of the lesson. I enjoy seeing the a-hah moments in students when they finally understand this concept.
*It is very important to have pre-taught the concept of zero before this lesson, (the same negative and positive number together cancel each other out: together -4 and +4 = 0).
But what about division you might ask? I find this harder to show with counters so I usually explain that every multiplication question has two equivalent, related division questions:
If 3 x 4 = 12 Then 12 ÷ 4 = 3 and 12 ÷ 3 = 4
So if, -3 x -4 = +12 Then +12 ÷ – 4 = -3 and +12 ÷ -3 = -4
This makes further sense to students when they realize that multiplying two integers with opposite signs = negative, and they can see that the same rings true for division as well.
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