Elementary school teachers are challenged with a logical presentation of operations on fractions to elementary school age students. Some strategies teach factor based short cuts first and then lead into general cases. Some start with the general cases first. I propose that the general techniques should be taught first with an emphasis on the proper pattern of the solution. The technique outlined in this solution has been successfully applied in a tutoring environment with many students who were struggling with operations on fractions.
I would first explain that problems related to solving fractions have four levels of difficulty/understanding.
The first level is to understand an "all case" approach that works with any fraction.
The second level requires recognition of fractions that can use a short cut method which requires that the student applies the concept of factors.
The third level requires reducing the final answer to simplest form, which also requires the application of factors.
The fourth level involves solving problems of mixed numbers.
Then, I would return to level one and give the following explanation:
For addition, use the pattern:
a/b + c/d = a*d/b*d + b*c/b*d. I would show the pattern with arrows pointing to the numbers in the first expression and how those ...
Elementary school teachers are challenged with a method of teaching the addition, subtraction, multiplication and division of fractions. Decisions of whether to start with short cut methods and expand to all-case methods or begin with all-case and then proceed to short cut methods are typical of teachers approaching this subject. Another decision that needs to be made concerns the teaching of reduction of fractions to simplest form. Where and when should this topic be taught.
This solution outlines a classic method of starting with all-case methods of teaching the four operations on fractions, with additional opinions on how to proceed with the additional topics. The method shown in this solution has resulted in great success in tutoring many students who were struggling to learn their operations on fractions.