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.
Instead of promoting tricks, we can “Think CRA” and build a solid foundation for fraction comparison THINKING!
It is then imperative that we consider methods of building an 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 experiences 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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