Question Video: Decomposing Two-Digit Number into Tens and Ones Using Place Value and Cherry Models | Nagwa Question Video: Decomposing Two-Digit Number into Tens and Ones Using Place Value and Cherry Models | Nagwa

# Question Video: Decomposing Two-Digit Number into Tens and Ones Using Place Value and Cherry Models Mathematics • Second Year of Primary School

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

03:29

### 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.

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