If your students
are struggling with adding and subtracting fractions with unlike denominators,
the problem could actually be with:

-understanding of
how to compose and decompose fractions.
Can they add and subtract fractions with LIKE denominators, first? Do they show understanding and flexibility of
this concept, or do they only know that they have to add the numerators and not
why?

-fluency with
multiples and the multiplication times tables.
Multiples are the basic patterns on which equivalent fractions
work. If students are struggling to
skip count or to work with basic multiplication facts, they will inevitably get
stuck on this one step of the process.
If they have to stop and think about think about a multiplicaion fact,
they tend to lose the larger picture of the problem they are working on and are
much more likely to make errors and lose their place completely. The more familiar students are with multiples,
the easier it will be for them to quickly recognize the lowest common multiple,
or lowest common denominator, for any two fractions.

-understanding
fraction equivalency. In order to add or
subtract fractions with unlike denominators, we have to be able to convert one
or both of them to an equivalent fraction, and we have to understand why that
works in order to fully apply it.
Students need a solid understanding of how equivalent fractions are
formed and the patterns they create, so that they can fluently generate and
recognize equivalent fractions.

-fluency
generating equivalent fractions. This is
a step where students will get stuck if they cannot form equivalent fractions
quickly and accurately.

-understanding of
concepts of fractional size and being able to use benchmarks and estimation to
judge whether or not their answer is reasonable. This is important for making sure their
answers makes sense and realizing when they’ve made a mistake, so they can
correct it.

If students are
adding and subtracting mixed numbers with unlike denominators, they’ll also
need strong:

-understanding of
improper fractions, mixed numbers, and how they relate to each other. Students should be able to move fluently
between the two, and should have a strong understanding of how they are
connected. If students lack basic
conceptual understandings for improper fractions and mixed numbers,
manipulating them and working with them will be very difficult for them.

-fluency and
understanding converting between improper fractions and mixed numbers. Converting is not always necessary for
addition or subtraction, but it offers students another option for how to solve
the problem, and another strategy for working efficiently.

If your students
are struggling with adding and subtracting fractions with unlike denominators,
it’s possible that the breakdown is in one or more of these areas. Do a quick assessment to find out which
one(s) and provide students with support to strengthen their conceptual
weaknesses and practice in areas where they need to become more fluent. Students who are strong in all of these areas
will be able to add and subtract fractions with unlike denominators fairly
easily. It’s a difficult concept, but if
you break it down, the pieces are much more manageable for our students.

Happy (fraction) Teaching!!

Christine Cadalzo