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common core state support video
this is fifth grade math
the standard is five N F five
this standard says that
we need to interpret multiplication as scaling
by comparing the size of a product to the size of one factor on the basis of
the size of the other factor,
but without performing the indicated multiplication
what might be easiest to do is look at some numeric examples
to see exactly what the standard is saying
let's take a nice easy product
let's say twelve
and one of the factors is four
that is pretty simple to figure out in your head that uh... that will be three
so the comparison here is that
twelve is three times bigger than four
that we take another
example let's say thirty
and let's say one of the factors is five
then we know that that's a six
so then the comparison
is that
thirty is six times bigger than five
but really we expect more at the fifth grade level
what happens if it's a more difficult scale factor
it seemed like the pattern was that all you have to do is divide to get the
scale factor and that's pretty much true
as we saw for example ...
with twelve being the the product one factor being a four
it ended up being three times bigger
so we take something that's maybe a little bit tougher let's say
ninety-six
and let's see let's compare that one of the factors is six
if we do the division we come out with sixteen
but of course would have to go through the actual process of doing the dividing
so now the comparison is that ninety-six
is sixteen times bigger than six
the whole idea a scale factors is that it's actually a ratio of the product
and one of the pairs of the factors
so if we look
at it algebraically
and let's ... let this statement be
that one factor times the comparison that we want to make which should be the
other factor
is equal to your product
if we do
a little bit of algebra
and do this
and of course we have to do it to both sides of the equation
and so this simplifies
to this expression
where the comparison is really just
the result of taking your product
and dividing it by the factor that you want to make a comparison to
so with this in mind
saying that relationship of the comparison being the
product compared to the factor that's really important for two reasons
first that lays a foundation for proportional reasoning
the scale factor tells you the relationship
and the second most important thing here is that
and is very applicable at this grade level
is that it enables students to figure out the scale factors
that are not whole numbers
so for example
let's say the product is
nine
and the factor is a six
now that it
that is not a whole number comparison
but if we do a little bit a simplification
and consider that... the ratio of nine to six
that will simplify let's see we can divide them both by three
that will simplify it to be over two
which
as a mixed number
would be one and a half
so then the comparison would be that
nine
is one and a half
times bigger
than six
if we were to do another example
let's say we reverse it and we're comparing
six
to nine
so that if we do some simplification
is so simple five to overthrow use the comparison here is that six
is two-thirds is as big as nine