Video: Writing Two Subtraction Sentences to Represent the Same Subtraction Model

Write a subtraction sentence that matches the model. Which of the following is another subtraction equation for the model? [A] 8 − 5 = 4 [B] 8 − 4 = 4 [C] 5 = 8 − 4 [D] 8 − 3 = 5

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Video Transcript

Write a subtraction sentence that matches the given model. Three equals five take away two. Five equals eight take away four. Three equals eight take away five. Five take away three equals eight. Or eight equals three take away five. Which of the following is another subtraction equation for the model? Eight take away five equals four. Eight take away four equals four. Five equals eight take away four. Or eight take away three equals five.

This question is all about the model that we can see in the picture. So, let’s spend some time looking at it and seeing what’s going on. To begin with, we’ve got a line of cubes. Let’s count how many we’ve got altogether. One, two, three, four, five, six, seven, eight. So, the whole line of cubes contains eight cubes, but we can see that it’s then split up. Can you see that it’s been broken off? So now we’ve got a group of green cubes and a group of red cubes. Let’s count how much we’ve got in each part.

We’ve got one, two, three green cubes and one, two, three, four, five red cubes. You know, we could draw a part–whole model here to show what’s going on. The whole line of cubes, as we’ve said already, is eight. But then, when it’s broken into two parts, the part of green cubes is worth three and the part of the red cubes is worth five. Five and three are two parts that go together to make eight.

Now we’re asked to write a subtraction sentence that matches this model. Now before we do that, what do you think is being taken away? Do you think the green cubes are being taken away and we’re left with the red cubes? Or do you think the red cubes are being taken away and we’re left with the green cubes? It might be hard to see just by looking at the picture, but there are some things we do know. Firstly, we know that number of cubes that there are in the whole amount is eight. So, our subtraction is definitely going to include the number eight, isn’t it?

Can you see any subtractions that don’t include the number eight? Well, this first one doesn’t, does it? We’ve got a three, a five, and a two. Let’s cross off this subtraction; it can’t be right. Something else we know about our model is that it contains three green cubes and five red cubes. So, we know our subtraction is going to include the numbers eight, three, and five. Are there any answers that don’t include these numbers? Well, if we look at the second one, we can see that there is a five and an eight, but there isn’t a three. So, again, we know straightaway this isn’t going to be the correct answer.

So, we’ve got three possible choices. Let’s have a look at them. The first subtraction says three equals eight take away five. This is interesting. It starts with the answer, doesn’t it? Often, we’ll have a subtraction where we’ll say something take away something equals something. Well, this subtraction is the other way round. Something equals something take away something. Let’s read it carefully. Three equals eight take away five. In other words, three is what’s left if we start with eight and we take away five. It looks like this matches the model, doesn’t it? Three green cubes are what’s left over if we start with eight cubes and we take away the five red cubes.

And if we quickly look at the other two subtractions, we can see they don’t actually make sense. If we start with five and then take away three, how can we have eight? That’s a bigger number. And the last subtraction doesn’t make any sense at all. Eight is what’s left over if we start with three and then take away five. I think we can cross this one through, don’t you? So, the subtraction that matches our model is three equals eight take away five.

In the second part of the question, we’re asked which of the following is another subtraction equation for the model. Let’s do exactly what we did last time. Remember, we’re looking for a subtraction that includes the numbers eight, three, and five because this is the whole and the two parts that we’re talking about. The first subtraction contains an eight and a five, but not a three. The second one we don’t have either of the two parts that we’re looking for. We’ve just got two fours. In the next subtraction, we’ve got a five and an eight again, but not a three. And so, the only subtraction that matches our model, which shows that three and five go together to make eight, is the last one.

This time, it’s as if we’ve taken away the green cubes, isn’t it? Eight cubes subtract three green cubes leaves us with five red cubes. In the model, it wasn’t very clear whether we were taking away the red or the green cubes. But one thing we did know is that we had eight cubes to start with, and we split it into three and five. And that’s how we know that the subtraction sentence that matches the model is three equals eight take away five. But we can also say eight take away three equals five.

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