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Decomposing Fractions : The Role of the Denominator


Adding fractions using the area model and tape diagramI absolutely love teaching fractions! It just makes sense to me, but I realize that I am in the minority when it comes to teaching fractions. I have taught elementary and middle school math and one common issue that many of the students have is understanding the role of the denominator. I have learned that  students cannot have a real conceptual understanding of fractions until they understand the role of the denominator or the unit fraction. I did not always teach fractions this way. It was the implementation of the Common Core Standards that made me rethink how I was introducing and teaching fractions to my students. Anchor chart for decomposing fractionsAlthough I am considered a veteran teacher I like learning more effective teaching strategies that will help my students to better understand concepts like fractions. In August 2007, I left elementary school to teach 6th grade math at a middle school. At that time adding fractions with unlike denominators was 6th grade skill. I was shocked when most of the students that I taught did not understand that the denominator never changed when converting improper fractions to mixed numbers. Most of them understood that they had to find common denominators to add, but when the fractions were added and created an improper fraction they understand when a fraction had a denominator of 3 it didn’t matter if you converted the fraction to an improper fraction the denominator stayed the same. When I think about this situation I wish I knew then what I know now, because I could’ve have taught a mini lesson on decomposing fractions. After I returned to elementary school to teach 4th grade math, I noticed when adding fractions and the 2 fractions equaled 1 whole, I would ask my students what does it mean when the numerator is the same as the denominator? They could tell me that is was 1 whole but when they had to apply this concept most of them were always confused or left it as is. Decomposing improper fractionsDecomposing fractions such as 3/3 into units of 1/3 was a life saver for me after returning to elementary school. This method gave the students the conceptual understanding that they needed to understand that 3/3 is the sum of 1/3 + 1/3 + 1/3 where each unit has a denominator of 3 and it does not change even when they are added .  This was progress for the teacher and the students! After teaching them to decompose fractions in different ways such as 2/3 + 1/3 = 3/3 it was a natural process for them to make the jump to converting improper fractions to mixed numbers. I also applied this concept to the fraction wheels that I used before I discovered decomposing fractions, because the students had to be able to apply this concept to any fraction situation. The beauty of using this method to teach fractions is that is can be used to add fractions, convert fraction to mixed numbers and multiply fractions. It’s not just a different way of teaching it’s a different way of thinking!