Video: Matching Equations to Word Problems Involving Multiplicative Comparison

Select the problem that can be solved by the equation 5 × 18 = 90. Noah is 18 years old. Sophia is 5 years older than Noah. How old is Sophia? Noah is 90 years old. Sophia is 5 times as old as Noah. How old is Sophia? Noah is 18 years old. Sophia is 5 times as old as Noah. How old is Sophia?

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Video Transcript

Select the problem that can be solved by the equation five times 18 equals 90. Noah is 18 years old. Sophia is five years older than Noah. How old is Sophia? Or Noah is 90 years old. Sophia is five times as old as Noah. How old is Sophia? Or finally, Noah is 18 years old. Sophia is five times as old as Noah. How old is Sophia?

In math, we’re often given problems and we need to sit down, read them carefully, and then decide what calculation or equation we need to use to find the answer. Well in this particular question, we’re working backwards. We start off by being given the equation. Five times 18 equals 90. So, we know what calculation we need to use to find the answer to the problem. But we just don’t know what the problem is. And we’re given three possible problems to choose from.

Let’s start off by taking a look at our equation. A useful way to think about problems and to represent calculations like this is using a bar model. And we could represent five times 18 by drawing a bar and splitting it into five equal parts, and each one of them would be worth 18. Our equation tells us that five 18s are 90. So, the total length of our bar model could be labelled 90. Now, let’s go through each of our possible problems and think about what we might do to find the answer. Perhaps we could draw a bar model for each one. When we find a bar model that matches our first bar model, we know we found the right answer.

In the first problem, we’re told Noah’s age, which is 18. And we’re also told that Sophia is five years older than Noah. And we’re asked how old is Sophia. Well, if Noah is 18 years old and Sophia is five years older, this means the answer to the problem needs to be solved by working out 18 plus five, five more than 18. This is not the equation we were looking for. Let’s try our second problem.

In this problem, Noah is 90 years old. So, let’s draw one bar that represents 90. And we’re told Sophia is five times as old as Noah. This means that we need to calculate the answer by finding five lots of 90. This is a similar sort of calculation to the one we’re looking at, but it’s going to give us a much larger number. In fact, perhaps in this problem Sophia and Noah are tortoises because the numbers are so large. We’ve only got one more problem to check. So, it seems like this one may be the correct answer.

We’re told Noah is 18 years old. This is very similar to the first problem. But instead of Sophia being five years older than Noah, we’re told that she’s five times as old as Noah. In other words, to calculates Sophia’s age, we need to work out five lots of 18. This is the bar model we’re looking for. And to find the answer to this problem, we’d work out five multiplied by 18 and find the answer of 90. Sophia’s age is 90 years old.

Instead of starting with a problem and then working out the calculation, in this question we started with a calculation and were asked to find a problem that fitted it. The problem that can be solved by the equation five times 18 equals 90 is the one that reads: Noah is 18 years old. Sophia is five times as old as Noah. How old is Sophia?

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