Video: Matching Additive Comparison Word Problems to Equations

Select the word problem whose answer is 52 − 11 = 41. [A] There were 11 fewer girls than boys at a summer camp. There were 52 boys. How many girls were there? [B] There were 11 more girls than boys at a summer camp. There were 52 boys. How many girls were there?

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Video Transcript

Select the word problem whose answer is 52 take away 11 equals 41. Is it, there were 11 fewer girls than boys at a summer camp. There were 52 boys. How many girls were there? Or is it, there were 11 more girls than boys at a summer camp. There were 52 boys. How many girls were there?

This question contains two word problems within it, but only one of the word problems has an answer equal to 52 take away 11 which equals 41. We need to find which word problem could be answered by using this number sentence. Now, one way to solve the problem could be to find the answer to both word problems. That way we can see which one equals 41.

Another method, and this is the one we’re going to use, is to use reasoning and to think for ourselves, how would we find the answer if we were to work this out? So, we don’t actually have to calculate the exact answer. We just need to think about how we’d get there. Let’s use bar models to help.

In both word problems, our starting point isn’t the number of girls, it’s the number of boys because we’re told the exact amount of boys that there are. We know there were 52 boys. So, let’s use this bar to represent our 52 boys. We’re also told that there were 11 fewer girls than boys at this summer camp. So, how can we represent this on our bar model? We need to draw a bar that shows 11 less than 52. So, the number of girls are shown in the pink bar. You might already have an idea of which operation you’d use to find out the answer with this problem. But let’s have a look at the second word problem.

There’s only one word different between this word problem and the first one, so we can start with 52 boys again. This time, we’re told, and this is the word that’s different, there were 11 more girls than boys. And so, we need to draw the unknown bar that represents girls in a different way this time. It needs to show 11 more than 52. In this bar model, we can see that the number of girls, which is the pink bar, the bar that we don’t know the value of, is 11 more than 52. If it’s 11 more than 52, then to find the value of the pink bar, the number of girls, we need to add 11 to 52.

And the opposite is true for the first word problem. There are 11 fewer girls than boys, so we start off with the number of boys and we take away 11 to find the number of girls. This is the word problem we’re looking for. This is the one whose answer is 52 take away 11 equals 41. So, there must be 41 girls on the summer camp. The word problem whose answer is 52 take away 11 equals 41 is, there were 11 fewer girls than boys at a summer camp. There were 52 boys. How many girls were there?

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