Question Video: Comparing Three-Digit Numbers Represented by Place Value Blocks Mathematics • 2nd Grade

Have Liam and Isabella made the same number using place value blocks?

02:59

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.

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