ABSTRACT
This chapter illustrates the range of problem contexts students encounter while developing understanding and fluency when multiplying and dividing. It focuses on how the context of multiplication and division problems influences the difficulty of problems. To understand and describe distinctions between different multiplication and division contexts, researchers use the term semantic structures. The chapter summarizes the multiplication and division contexts that students encounter as they develop the understanding, flexibility, and fluency that are expected in the CCSSM. It discusses different problem contexts and their semantic structures for equal groups, equal measures, measurement conversion, multiplicative comparisons, multiplicative patterns, area, volume, and unit rates. The chapter reflects on the degree to which your instruction or your math program varies the problem contexts consistent with the demands of the grade level. It focuses on the fact that understanding problem contexts involves focusing on the meaning of the problem situation, including the quantities in the problem, how the quantities interact, and the units.
