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## Multiplication as groups of objects

# More ways to multiply

CCSS.Math:

## Video transcript

If we have 2 groups and
in each group I have 4, so that's one group
of 4, and then here is my second
group of 4, we already know that we could
write this as 2 times 4, which is the same
thing as 4 plus 4. Notice I have two 4's here. I have 4 plus another 4. Well, if I have 4 plus 4,
or if I have 2 groups of 4, either way, I'm going to
have a total of 8 things. And you see that
right over here. We have 1, 2, 3, 4,
5, 6, 7, 8 things. What I want you to do
is pause the video now and try to group these
same 8 things, but to group it in other ways so
that we can represent 8 as the product of whole numbers. Here I've represented 8
as the product of 2 and 4. 2 times 4 is 8. See if you can represent
8 as the product of other whole numbers,
or as whole numbers in different ways, grouping
it in different ways. So I assume you've
paused the video. So let's try it out ourselves. So one thing we
could do, we could view this instead
of as 2 groups of 4, we can view 8 as 4 groups of 2. So that's 1 group of 2, 2
groups of 2, 3 groups of 2, 4 groups of 2. So we could write that
4 times 2 is equal to 8. And we could view this as
the same thing as, literally, 4 2's. We have one 1, 2, 3, 4 2's. Each of these have 2 in them. So we're going to
say 1, 2, 3, 4 2's. 2 plus 2, plus 2,
plus 2 is equal to 8. These are both equivalent. 4 times 2, literally
4 groups of 2. That's the same thing as taking
4 2's and adding them together. Notice, we have 2
2's right over here. We added them together, 1, 2. Here, we have 4 2's
and we're adding them together, 1, 2, 3, 4. We take our 4 2's and
we add them together. How else could we represent 8? Well, we literally could
view it as 8 groups of 1. So let's do that. So 8 groups of 1
would look like this. That's 1 group of 1,
2, 3, 4, 5, 6, 7, 8. So we could write this
down as 8 times 1. 8 times 1 is, once
again, equal to 8. And if we wanted to write this
down as repeated addition, well, this is literally 8 1's. So 1 plus 1, plus 1,
plus 1, plus 1, plus 1. Let's see. That's 1, 2, 3, 4, 5, 6, 7, 8. 1, 2, 3, 4, 5, 6, 7, 8. 1 plus 1, plus 1, plus 1,
plus 1, plus 1, plus 1, plus 1 is equal to 8. Now, you might be
a little stumped. Well, what's another
way of getting to 8? Well, you could literally
view it as 1 group of 8. So let me view it that way. So this is just 1 entire
group of 8, the whole thing. The whole thing is a group of 8. So let me scroll over to
the right a little bit. We could write this
down as 1 times 8. And 1 times 8 is equal to 8. And how would we view that? Well, we only have one 8 now. We don't have to add that
one 8 to anything else. So if we wanted to do it the
way we've done the last few, we could literally write it
down as we just have one 8. Well, one 8 is clearly
going to just be equal to 8. So now let me ask
you another question. So far we've been focused
on each of these groups, but what if we actually
view this as 4 groups of 8. Then how many things are
we actually going to have? So let me make this very clear. So we have 1 group of eight 8,
2 groups of 8, 3 groups of 8, and 4 groups of 8. So we would view this
as 4 times 8, or which is going to be the same thing
as 8 plus 8, plus 8, plus 8. 4 8's. What is this going
to be equal to? A And I encourage you
to pause the video and figure it out right now. Well, there's a couple
of ways that you could have thought about this. You could have literally
just counted these. Or you could say, well, let's
see, you can skip count by 8. 8, 16, 24, 32. Or you could have said, 8
plus 8 is 16, plus 8 is 24, plus 8 is 32. Or you could have literally
just counted the triangles here.