Fractions. Did that make your stomach hurt? :-)
Many people often view fractions as being completely separate from whole numbers. Within Common Core, students should be making connections with what remains true about whole numbers and what might be unique to fractions. For example, the number 4 could also be represented as 16 fourths or 4/1. Recognizing these representations as being equivalent is an important understanding for students.
In the 2010 issue of NCTM's Teaching Children Mathematics, Wendy S. Bray and Laura Abreu-Sanchez describe in their article "Using Number Sense to Compare Fractions" how they have introduced fractions to third-grade students. They recommend using circles when introducing fractions. Their reasoning for using circles rather than other area models is that the missing piece is evident.
This was a BIG a-ha moment for me when I read this article. For many years, I have introduced fractions by having students build a fraction kit based on lessons from Marilyn Burns. What I had not considered was that the students would need to know the size of the whole in order to think about the relative size of the fractions we built. Because the lesson always started from the whole (a strip of paper) and we then began to divide the strips into pieces, it was evident to most students that 1/2 was represented by half of a strip of paper. However, this was only because the students had seen the initial strip of paper. I love that using a circle allows students to use intuition and think more deeply about fraction sense.
From using the circle, the students branched out to other representations with fractions - such as area models, number lines, and linear models. By continuing to use these representations to explore different ideas about fractions - such as determining whether a fraction was more or less than one-half - students were able to connect their understanding with the symbols used to represent the fractions.
More about fractions coming later..... In the meantime, this is a great article to get you started with teaching fractions!
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