### Video Transcript

Which of the following is the wrong
model to decompose 43?

There’s an interesting word in this
question: decompose. Do you know what it means? When something decomposes, it
breaks up or splits up. And so we use this word in math to
describe when we split up a number. So we could really read our
question as which of the following is the wrong model to break up the number 43? We’re given three models to choose
from, and each model contains two parts. Firstly, there’s a place-value
table where we can see a number has been modeled using 10s and ones blocks. And next to each one of these
tables is a part–whole model which shows us how the number of 43 has been split up
or decomposed.

This is an interesting question
really because we’re not being asked for the right answer here. The question asks us, which of the
following is the wrong model to decompose 43? In other words, which one is the
odd one out? Two of these models show different
ways to split up the number 43 and one of them doesn’t, and we need to find that
one. Let’s start then by looking at our
first model. In the tens part of our place-value
table, we can see four 10s. We know that four 10s have a value
of 40. This is where the number 40 comes
from in our part–whole model. We can also see three red ones
blocks. And we know, don’t we, that we can
split up the number 43 into four 10s or 40 and three ones.

If you were told to make the number
43 out of 10s and ones, this is probably the way you do it. So we know this first model is
correct. You know, we can use this first way
of showing 43 to help find other ways. If we look at the remaining two
models, we can see that there’s something similar about them. Instead of four 10s, they both have
three 10s. Something’s happened to one of the
10s. Well, if we just took away one of
the 10s like this, the number would stop being worth 43. It would actually be worth 33. We know that one 10s block is the
same as 10 ones. So if we’re going to get rid of one
of our 10s blocks, we need to exchange it for 10 ones. That’s better.

Now, instead of three ones, we have
another 10 ones, so we have 13 ones altogether. We can decompose 43 into 30 and
13. And if we look at our possible
answers, we can see that this is the same as the bottom model. By finding the two models that are
correct, we’ve identified the wrong one. It contains three 10s, which are
worth 30, but only four ones, which are worth four. And what do we get if we put 30 and
four together? This model shows 34 not 43. It’s almost as if the person that’s
made it has swapped the digits around. The wrong model to decompose 43 is
the one that shows three 10s and four ones, or 30 plus four.