Armando eats 1/8 of his box of chocolates in the morning and ¼ of his box of chocolates in the afternoon. Did Armando eat more chocolate in the morning or the afternoon? How do you know?

Comparing fractions <groan> you know that your students will come in with all sorts of “tricks” and misconceptions up their sleeves. But, never fear, because if you can predict it, you can prevent it. If you know your student will think that an eighth is larger than a third because 8 is bigger than 3 we just need to be sure that you are being strategic in your instruction and getting out ahead of these predictable misconceptions.

These common errors, so often, are born out of the idea that students are handed numbers and asked to reason with them. They draw from what they know the best. And in this case, students have spent the vast majority of their primary years working with whole numbers. When third grade rolls around and students are asked to compare these fractions it is entirely understandable that they draw on their knowledge of whole number comparisons. Who could blame them?

It is then imperative that we consider methods of building understanding of fractions and comparison for students before they overgeneralize and draw their own “connections” that are doing little more than building confusion. Using the concrete, representative, abstract model for instruction you can build understanding in the concrete and representative stages and slowly fold in opportunities for abstract thinking. Students will then have anchors in their concrete and representative work to pull from rather than drawing on whole number generalizations.

The concrete, representative abstract (C-R-A) model calls for instruction to be built from concrete hands-on experiences, linked to visual representations and ultimately these experience allow students to generalize their understanding through purely numeric or mental work.

So what, exactly, will the C-R-A framework look like at each step of the way? Follow me into the next three posts of this comparing fractions series. We will look to the 3rd and 4th grade fraction comparison standards and the most effective and efficient ways to promote understanding.

Post 1: The Math Spot Compares Fractions- Introduction
Post 2: The Math Spot Compares Fractions- Comparison Tools
Post 3: The Math Spot Compares Fractions- Representative Models
Post 4: The Math Spot Compares Fractions- Abstract Thinking

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