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