Question Video: Adding and Subtracting Multidigit Numbers to Solve Word Problems

Ethan and Anthony are competing in a video game. Ethan scores 3,700 points. Anthony scores 300 points less than Ethan. How many points does Anthony score? How many points do they score altogether?

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Video Transcript

Ethan and Anthony are competing in a video game. Ethan scores 3,700 points. Anthony scores 300 points less than Ethan. How many points does Anthony score? How many points do they score altogether?

This problem describes Ethan and Anthony, who are playing a video game. The first piece of information we’re given is Ethan’s score. We’re told that he has 3,700 points. And then we’re told Anthony’s score, or rather we’re told something about Anthony’s score. We’re told that Anthony scores 300 points less than Ethan.

Now, we’re given a bar model, and this helps us to see the relationship between these two boys’ scores. The bar that represents Ethan’s score is labeled 3,700. And although the bar representing Anthony’s score isn’t filled in yet — we don’t know it — we can see that it’s 300 less than Ethan’s. And we’ve got two questions to answer. And the first one asks us, how many points does Antony score?

Now, as we’ve said already, his score is 300 less than 3,700. We’re going to need to subtract to find the answer. But it’s the sort of calculation we could do quickly in our heads. We know that 700 take away 300 would leave us with 400. So 3,700 take away 300 is going to leave us with 3,400.

In the final part of our problem, we’re asked, “How many points do they score altogether?” What’s their overall total? Now, if we’d have been asked this right at the start, we might have said to ourselves, well, we can’t find the overall score. Because to do that, we’d need to know what Anthony’s score was, and we don’t know that. In other words, we’d have recognized this as being a two-step problem. First, we’d have needed to find out Anthony’s score, and then we’d be able to add the two together. But because we’ve already calculated Anthony’s score, we’ve done the first part of this two-step problem. We just now need to add the two boys’ scores together.

If we were to sketch another bar model just to show what we need to do here, it might look like this. We need to add together 3,700 and 3,400. Both our numbers have a three in the thousands place. And so the total of our thousands is 6,000. Then we just need to add the hundreds. Now, we know that 700 plus 300 would be the same as 1,000. So 700 plus 400 will be 100 more than this. It’s going to equal 1,100. And if we add together our 6,000 with this 1,100, we can see that the boys’ total score is 7,100.

We’ve solved the two parts of this problem by using bar models to help us. They showed us we needed to subtract to find the first part and then add for the second. The number of points that Anthony scores is 3,400 points, and the number of points they score altogether is 7,100 points.

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