ABSTRACT
This chapter focuses on other underlying structures of multiplication and division problems that have been shown to influence the difficulty of problems, as well as the strategies students use to solve them. Engineering a problem means to alter the structures to elicit developing understandings, as well as common errors and misconceptions. The chapter explores the influence each of the following has on student solutions: the magnitude of the factors; the presence of powers of 10 and multiples of powers of 10 and having more than two factors in a problem. To explore the impact of the magnitude of factors on solutions, researchers suggest giving students contextual problems where the factors are single digits and then changing the factors to multidigit numbers while the context remains the same. The chapter illustrates how problems can be engineered to focus on student understanding of multiplication by powers of 10 and multiples of powers of 10.
