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Detailed Solution for Word Problem of the Day

DETAILED SOLUTION

There are several ways to solve this problem. Depending on the objectives, one way isn't necessarily better than the other.  However, we are not only training our students to be proficient in math.  We are also training them to be great thinkers.  And, to be a great thinker, your students need to be able to identify and take appropriate "intelligent shortcuts" when necessary.  This problem illustrates one example of when it is appropriate to take an intelligent shortcut.  

The quickest way to solve this problem is to realize that since 4/9 of the students are boys, then the remaining students, 5/9, are girls. Since we need to find out how many more girls there are than boys, we need to subtract 4/9 from 5/9 which leaves 1/9. That part can be done mentally. We're not finished yet, but this is the intelligent shortcut I was talking about. Realizing this will save valuable time when compared to solving the problem in a different way.  

Why do I call this an intelligent shortcut?  Consider this, most of your students will take some sort of standardized test.  These tests have time constraints, so these students must complete the exam in a limited amount of time.  The test creators know this.  Test questions are introduced into these types of exams to determine not only if a student can get the correct answer, but to also determine how quickly the answer was determined. Great companies like Apple and Google hire great thinkers.  

 With all this in mind, below is the solution:

(click image below to enlarge)

Compare and Contrast

The other way to solve this problem without any shortcuts is to:

Calculate 4/9th of 801 which is 356

Then subtract 356 from 801 which is 445

Then calculate the difference between 356 and 445  which is 89

You still arrive that the correct solution, but notice the number of steps and time involved! Not to mention the opportunity to make an arithmetic error!  A student that is solving the problem this way certainly understands the steps needed to calculate the answer -- which is definitely good -- however this student may not realize the "intelligent shortcut" that can be taken.  The realization that a shortcut is available usually only becomes apparent after a full understanding of the concepts associated with fractions is mastered.

 

More Compare & Contrast

Do you remember how s-l-o-w computers use to be?  Do you notice how fast they are now?  This is a direct result of various applications of intelligent shortcuts.  Engineers are constantly finding ways are doing things faster... faster computations, faster calculations, faster everything.  The examples are endless.  Intelligent shortcuts are at play here.  

Encourage intelligent shortcuts where appropriate.

Here is a fun exercise for your students.  Ask them to "compare & contrast" the different approaches to solving this problem.  Then please let us know your experience in the forum below. What are other observations you noticed?

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