Fractions are a well-known bugaboo for both teachers and students, and Marian Small has done teachers a great favor in tackling how best to teach fractions in her book Uncomplicating Fractions to Meet Common Core Standards in Math, K-7. First, she has simply brought together all of the Common Core State Standards related to fractions in one place, where the authors of the standards decided to divide an already complicated topic across four different domains: Expressions and Equations, Geometry, Ratios and Proportional Relationships, Statistics and Probability, and The Number System. Small also includes standards related to decimals from Numbers and OperationsBase 10. She has organized the book by standard, integrating the mathematical practices standards where relevant, and presented Important Underlying Ideas, including common misconceptions, Good Questions to Ask, as well as a summary in each chapter. I particularly liked the Good Questions to Ask, although a few of them seemed a little too challenging for the given grade level. Questions are generally open-ended with multiple solutions that provide insight into students thinking. Not only are the questions themselves well designed for this purpose, they can serve as models for creating your own problems for assessing conceptual understanding. For example, for Grade 1, she recommends asking students to Draw a picture to show why someone might say one fourth can be more than one half. I might save such a question until Grade 2 or 3, but it does challenge students to think carefully about wholes, parts, and fractions.
Uncomplicating Fractions includes many examples of visual models of fractions, from pattern blocks to number lines to fraction towers. Small generally recommends following a teaching-learning sequence that begins with concrete materials and then moves to visual models and finally symbolic representations. This is the widely known approach proposed by Jerome Bruner, although he is not referenced in the book. Given the increased emphasis on the number line as a central representational model for fractions, it was a little surprising that Small did not include a sequence bridging between fraction strips and the number line. She may have made this choice because the book is developmental in its overall structure, and there is not a step-by-step sequencing of topics or representations within each chapter. Nevertheless, this is a very useful book, both as a reference for all the standards connected to fractions, and as a source of good, original ideas for assessing and representing them.