Video Transcript
Have Liam and Isabella made the
same number using place value blocks?
In this question, two students,
Liam and Isabella, have made numbers out of place value blocks. And all this question asks us is,
are they the same number? Now, at first glance, we might say
no. Well, they certainly haven’t used
the same place value blocks, have they? Liam’s used a lot more tens, and
Isabella’s number contains two 100s blocks. Liam’s doesn’t. So we could look at these models
and say, “Wow! They’re not the same number at
all.”
But before we jump to the answer
no, perhaps we better look a little bit more closely at the actual numbers that
these students have modeled. Both numbers have been made out of
hundreds, tens, and ones. Liam’s number is made up of one
100. This has a value of 100. Then he’s used 12 10s, and 12 10s
have a value of 120, and finally four ones. And if we add together 100, 120,
and four, we get the number 224.
Now, what number has Isabella
made? We can see two 100s blocks, these
have a value of 200, two 10s blocks, which are worth 20, and then just like Liam
she’s used four ones. And 200 plus 20 plus four equals
224.
We can see that the answer to the
question is yes. Both Liam and Isabella have made
the number 224. But how can they do this? They’ve both used hundreds, tens,
and ones blocks. But they’ve used them in different
ways. Surely this makes a different
number. Well, this isn’t true. It’s possible to show the same
number but in different ways.
Isabella has modeled the number 224
the way that we would probably usually do this. We’d look at the digits in their
place value and we’d say we need to have two 100s, two 10s, and four ones. But as we said at the start, Liam
has less hundreds. Can you see what he’s done? Not only does Liam have one less
100, he’s actually got more tens. We know that 100 is the same as 10
10s. And Liam has swapped one of his
100s for 10 10s blocks. Both of the students have shown the
same number, but it’s just been broken up in different ways. The answer to the question is yes,
Liam and Isabella have made the same number.
