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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?" 

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)

The Second Question

Now that the first question has been answered, guess what... it can be used to answer the second question.  The second question is meant for your students to apply the information from the first question to answer the second question.  Now note that this problem could have been given without the first question.  We could have just jumped right into the second question, but then the underlying concept involving fractions may have been missed.  We've got to make sure we know that our student are understanding fractions because these same concepts are going to show up over and over again... guaranteed.  So it's much better to master them now.

So now if we know that 1/6 of the cupcakes were left over, then all we need to do is take 1/6 of 450 to get the answer to the second question.

1/6 of 450 is 75.

The beauty of this problem is that if we say Ray baked a different number of cupcakes, then all we need to do is recalculate 1/6 of that new amount to answer the second question.  

Try  giving your students a few values or better yet, have them generate a few values of their own choosing. 

How did your students approach solving this problem? Were they initially confused then later "got it" or did they already have fractions mastered ans was able to easily understand the concepts? What are other observations you noticed?

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