Multiplicative Reasoning LT

• Concrete Modelers with Equal Groups-Children to solve multiplication problems with very small numbers by making equal groups and counting all the objects. They also solve division problems by dealing out one or more objects at a time. (https://www.learningtrajectories.org/math/multiplying-dividing/concrete-modeler-x )

• Equal Groups with Parts and Whole-Predicts qualitatively the inverse relation between divisor and quotient in simple, concrete situations. Can re-assemble equal groups or parts to make the collection of the single whole as "n times as many (much)." (https://www.learningtrajectories.org/math/multiplying-dividing/parts-and-wholes-x )

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• Derived Facts

• Array

• Multiplicative Comparison

1) the conceptual principles and the development of the ideas underlying a concept;

2) representations, strategies and conceptions

3) meaningful distinctions, definitions and multiple models;

4) coherent structure – recognizing that there is a pattern in the development of mathematical ideas as a concept becomes more complex; and

5) bridging standards-understanding that there might be gaps between standards and knowing what underlying concepts are in between to bridge the gaps between the standards.