Question Video: Distinguishing Multiplicative from Additive Comparison in Word Problems Mathematics • 4th Grade

Jacob started training to join the basketball team. In the first week, he scored a total of 23 baskets. In the second week, he scored 12 more baskets than in the first week. Should I add or multiply to find the number of baskets he scored in the second week? Why? [A] because “a total of” tells us to use addition [B] because “12 more” tells us to use multiplication [C] because “a total of” tells us to use multiplication [D] because “12 more” tells us to use addition [E] because “12 more” tells us to use subtraction

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Video Transcript

Jacob started training to join the basketball team. In the first week, he scored a total of 23 baskets. In the second week, he scored 12 more baskets than in the first week. Should I add or multiply to find the number of baskets he scored in the second week? Why? Because “a total of” tells us to use addition. Because “12 more” tells us to use multiplication. Because “a total of” tells us to use multiplication. Because “12 more” tells us to use addition. Or because 12 more tells us to use subtraction.

Questions like this are really interesting because they’re not asking us to find the answer; they’re asking us how we would find the answer. So we don’t have to work any answers out to our calculation here. We just need to work out what the calculation is. To begin with, let’s read that word problem once again. And as we do, we could sketch a bar model to help us understand what we need to do. So, firstly, we’re told that Jacob started training to join the basketball team. In the first week, he scored a total of 23 baskets. So we could draw a bar to represent week one. And we’ll label it 23 to represent all those baskets he scored in week one.

But it seems that Jacob’s training pays off, doesn’t it, because we’re told that in week two, he scored 12 more baskets than in the first week. How could we show the idea of 12 more than 23 on our bar model? Well, we could draw an extra bar labeled 12. Those are the 12 more that he scored. And then we could draw a new bar that covers all of this length. And this is the number of baskets that Jacob scores in the second week. Now, as we’ve said already, we’re not asked to find out how many baskets Jacob scores in the second week. We’re just asked how we would do this. Should we add or multiply? Well, we can see by looking at our bar model, can’t we, that the length of the second bar is worth 23 plus 12 more. We’re going to need to add to find the answer, aren’t we?

And then comes a really important question: Why? How do we know that we need to add and not multiply? What is it about the problem that we were given that shows us that we need to add to find the answer. We’re given five possible explanations here. Now perhaps the first time we read through these, it might have sounded a little complicated, but we can get rid of some of these answers straight away because we’ve already decided we need to add to find the answer. We don’t need to use multiplication, so we can cross through this sentence. And we know this sentence is wrong, too. And we definitely don’t need to use subtraction, do we? So we’re only left with two possible answers.

And the only difference between these answers are two little phrases. Did we see the words “a total of” in the question and thought to ourselves, oh, we need to use addition? Or did we see the phrase “12 more” and that’s what told us we needed to use addition? Well, firstly, we know that finding the total of something does mean that we need to use addition. But when we go back to the question and look at how those words are used, we’re just told in the first week he scored a total of 23 baskets. In other words, this was the amount he scored in week one. It’s got nothing to do with us finding the answer to the question, has it? It’s just saying that was the whole amount.

Now, if we find the phrase “12 more,” we can see that this is all about comparing the two weeks together, isn’t it? In week two, he scored 12 more than in the first week. This is where we find our answer, and this is how we know we need to use addition. In this question, we didn’t solve a word problem. We just thought about how we would solve it. To begin with, we used a bar model to work out that we needed to add to find the number of baskets that Jacob scored in the second week. And we know we need to add because “12 more” tells us to use addition.

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