Video Transcript
Write the following number in
expanded form: 1384 equals what. 4000 plus 800 plus 30 plus one,
1000 plus 300 plus 80 plus four, 1000 plus 300 plus 40 plus eight, or 3000 plus 100
plus 80 plus four.
We know that we can express numbers
in lots of different ways. In this question, we’re given a
four-digit number. And the way that it’s written in
the question we’d say is it’s in digit form. We’ve just got those four digits
written: one three eight four. And our question asks us to write
this number in a different way. We need to write it in expanded
form. We know when something expands, it
gets bigger or it opens up. And if we want to write a number in
expanded form, we need to take that number and open it up into its different
parts. A four-digit number is made up of
thousands, hundreds, tens, and ones. And so we need to split up our
four-digit number into four parts.
We could sketch a part–whole model
to help us here. Perhaps, we ought to call it a
part, part, part, part–whole model. To begin with, let’s write our
whole number, 1384. Let’s begin by looking at our first
digit, one. Is it worth one, 10, 100, or
1000? Well, if we think of the four
places that make up a four-digit number, we know that the first digit is the number
of thousands that we have. And if there’s a one in the
thousands place, this has a value of 1000.
Now, if we pause for a moment to
look at our possible answers, we can see that they are four different additions. They show a number of thousands
added to a number of hundreds plus a number of tens and a number of ones. Now, as we’ve seen already, the
thousands digit in our number is one, and this has a value of 1000. So, can you see which answers might
be correct here? It’s not the first addition because
that begins with 4000. And we know it’s not the last
edition either; that begins with 3000. But it could be either of the other
two answers.
Let’s carry on splitting up our
four-digit number. And we’re on to the second digit,
three. Now, this digit is in the hundreds
place, and three 100s have a value of 300. But can you see if we go back to
our two possible answers, both of them show 300 being added. In fact, the only difference
between them is the number of tens that are being added and the number of ones. So, let’s finish off expanding the
tens and ones in our number. In the tens place, we have the
digit eight. And we know that eight 10s have a
value of 80. And then, finally, in the ones
place we have the digit four.
And so, by looking at our
part–whole model, we can say that the number 1384 can be split into 1000, 300, 80,
and four. And so we can see the answer. We’ve expanded a four-digit number
into its thousands, hundreds, tens, and ones. And we’ve written these as an
addition, just the same as writing the number in expanded form. 1384 is the same as 1000 plus 300
plus 80 plus four.
