Have you ever considered
why we round the way we do?
You know, you probably remember
the trick or the rhyme,
five or higher, round up.
Four or lower stays the same,
but what does stay the same even mean?
Round higher?
Higher what?
It doesn't make any sense, right?
This video is going to look
at a very conceptual way
to explain rounding.
We're going to do that
using base 10 blocks.
So let's first take a
look on the number line.
Let's say we're rounding the
number 63 to the nearest 10.
I want to imagine a scenario
where you owe me $63.
You borrowed it to buy a
really expensive shirt.
This is out of my price range,
but you get the picture.
So you show up at my
house and you owe me $63,
and you say, "I only have $10 bills."
I'm rounding to the nearest 10,
which tells me that you
only have $10 bills.
You didn't bring any ones.
I'm like, "Ugh, this is so like you
"to not show up with exact change,
"but have no fear, we're going to round."
So what we're going to do is
we're going to draw a number line,
but we're going to hop or
jump on the number line 10.
I have to you think about
what are the two tens
that this is between?
And if you build the number
63 with your base 10 blocks,
you can see that you've got six
rods and three cubes, right?
Or six tens and three ones.
So I'm thinking that you
could show up at my house
with either $60 or six tens,
or you could show up $70.
Those are your two options, 'kay?
Now since this is a number line,
let's put what's in the very middle.
So between 60 and 70 would be 65,
so I'm going to go ahead and
mark that just like that.
That's the halfway point.
Now I'm given the number 63,
and I need to see which
side would it be on.
Now I could put my little tick marks,
but I'm just sort of
estimating at this point.
So I know that 63 is going
to go on the left side here
or this side of it.
So I'm going to put 63 there,
and now, I can see, I can
ask myself the question,
"Is 63 closer actually
physically on the number line
"to 60 or to 70?"
Well, it's super easy to
see that it's closer to 60.
Okay, cool, let's try another one.
Now you can see I've got
round 78 to the nearest 10.
Again, you borrowed $78 from me.
You show up at my house.
Let's draw a number line showing
what are the two options you
can show up at my house with.
So you can show up with $70
or $80.
Again, I can make my middle mark here
and know that that is 75.
I'm going to plot 78.
Is it going to go on
this side or this side?
It's going to go on this
side, maybe right about there,
and now, I can ask myself,
"Is it closer, is 78 closer
to 70 or closer to 80?"
Again, I can see it's closer to 80.
Now you might be thinking, "Okay,
"but what if I change this
and it's no longer 78,
"but now it's 75?
"Now what do I do?"
Well, that's a good question
because technically,
if I put 75 on here,
it's equidistant from 70 and 80, right?
We've got a problem.
Well, it turns out that just
like in order of operations
where mathematicians around
the world agree to do
certain operations in a certain order,
the same goes with rounding.
So there's this rule that
if it falls in the middle,
we're going to go ahead and round up,
which is why we get the rule
five or higher, round up.
Four or lower stays the same,
and the problem with just
teaching children those rules
is that they don't see the
conceptual point in this,
and when we get to decimals
and we're rounding to
tenths and hundredths,
it really becomes a problem.
This is a great strategy to allow children
to make their own rules.
After they do this a
certain number of times,
they're going to be able to
come up with that on their own,
and that is better for putting it
into their long-term memory
and really making sure they understand.
That's how you round using a number line,
and you can use your base
10 blocks to prove that.
I hope you found this video helpful.
