Math Error

…in this case there are at least three!

Consider the following two ways to solve the problem.

The first way is the way I learned to add fractions with different denominators some 15 years go.  This method teaches you to find a common denominator by either finding the LCM or by simply multiplying the denominators together then writing the equivalent fraction.  Then add and simplify if needed.

The second way was demonstrated by a student in class.  I find it rather interesting.  First you convert any mixed numbers into a fraction.  Then multiply each fraction by 1 (in terms of the second fraction’s denominator).   Then add and simplify if needed.

Let me brag on one of my students for a bit.  “K” is a very laid back student.  Most of his peers would not label him as a “thinker.” But I am! “K” has surprised me and the math coach several times so far this year.  Just when I think that he is not paying attention and daydreaming…wham! He comes up with a way of doing things that is much, much more simple than the way that I am trying to explain it.  He is a thinker.  Here is how he did the same problem in his head!  The drawings are my interpretation of his words as he was explaining how he did the problem.

Way to go “K” I am proud of you!  I bragged on you all day Monday and promised that I would blog about it.  Sorry it took so long to get around to it!

Readers, what creative ways can you come up with to solve this problem?