Video: Investigating Division and the Distributive Property Using Array Models

Daniel is using this model to help him divide by splitting 24. Which expression has been covered? 24 ÷ 4 = (_) + (4 ÷ 4) = 5 + 1 = 6

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Video Transcript

Daniel is using this model to help him divide by splitting 24. Which expression has been covered? 24 divided by four equals what plus four divided by four, equals five plus one, equals six.

The first sentence in this problem tells us that Daniel is using this model to help him divide. And we’re told that the number that he’s dividing is 24. Let’s take a moment and look at the model that Daniel’s using. Here he has an array of 24 balloons. We call it an array because the layout of the balloons is in rows and columns.

Now the division that Daniel’s working out is 24 divided by four. And we know this for two reasons. Firstly, we can see it in his calculations. And secondly, we can see that the array has been split into four rows. We can see some dotted lines have been drawn to help split 24 into four.

But Daniel hasn’t just split the whole block of 24 into four straight away. He’s done something before he’s divided. If we looked to the right of the diagram, we can see that he split up the number 24. On the left, there are 20 blue balloons. And on the right, there are four orange balloons. Why might he have done this?

Let’s imagine the sort of things that Daniel may have been thinking. He could’ve thought to himself, “Well, I don’t know how to work out 24 split into four, but I do know how many fours there are in 20 and also how many fours there are in four; I could split 24 into 20 and four and then divide each of those into four.” And so this is what he’s done.

The first thing he does is divide 20 by four. And we can see from his working out that this is the expression that’s been covered. There’s a question mark. The missing expression is 20 divided by four. 20 divided by four equals five. We can see five balloons in each row. Then Daniel works out four divided by four. And he divides his column of four orange balloons into four equal parts, which is one. There’s one orange balloon in each row.

So the answer to 24 divided by four is the answer to 20 divided by four plus four divided by four. Five plus one equals six. If we count the number of balloons in each row, we can see that there are six. The missing expression is 20 divided by four.

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