## Detailed Solution for Word Problem of the Day

### INTRODUCTION

### Ok, I think most of you have chewed on this problem long enough so now it's time for the solution. Keep in mind that learning the math concept is what we are after. Remember, we are not only interested in whether or not our students can simply solve a particular word problem. Instead what we really want, is to know that they understand the underlying math concept that is presented *in* the math problem.

### That's why the word problems that I post up on MathEdge.com are not just random problems. Rather, these problems are thoughtfully chosen & crafted to target specific math skills. And the detailed solution that accompany each problem are there to spark dialog around the problem and the underlying math concepts. I see way too many *"solutions"* to math problems where only the *"answer"* is given. I propose a different approach for your students: Let's understand & interpret the solution, let's give it life... in this way math becomes more real, more relevant, and more enjoyable.

### Thanks.

### Discussion

**There are two questions that are asked in the word problem. The first question is ***"what fraction of the cupcakes did Ray have left over?" *

*"what fraction of the cupcakes did Ray have left over?"*

### To answer this question requires a fundamental understanding of fractions. We essentially need to add together the fractional parts that were given to us then subtract that total from the *whole.*

*...Ahhh* but your students asks *"what whole?" *Then you respond *"the whole unknown".*

### What? Yes that's right, we do not need to know how many cupcakes were baked in order to answer the first question. We only need to know the *parts *(which were already given to us). Here is an insightful way to put it to your students: If I said *"I have a tray of Oreo cookies, and I gave half of them to my friend. What part do I have left over?"* Their answer will undoubtedly be *"the other half"*.

### See what I mean?

### We did not need to know the actual quantity of cookies to answer the question that was asked. The same concept applies to this problem. We were asked what *fraction* of the cupcakes were left over.

### With all this in mind, the solution looks like this.

(click image below to enlarge)