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!!