Structures in Ratio and Rate Problems

Chapter 6 focuses on two basic structural elements of ratio and proportion problems: problem contexts and problem types. These two elements differ in important ways. We learn that ratio and proportion problems can have the same problem context while structured as different problem types with differing mathematical demands. This chapter also explains that ratio relationships can be part-to-part or part-to-whole. These relationships can be explicitly stated or implied from the information provided in a problem. This chapter focuses on two basic structural elements of ratio and proportion problems: problem contexts and problem types. It also explains that ratio relationships can be part-to-part or part-to-whole. These relationships can be explicitly stated or implied from the information provided in a problem. Even though all three problems involve the same context, constant speed, each represents a different problem type with differing mathematical demands that provide students opportunities to apply different strategies. The evidence in student solutions to ratio and proportional problems is categorized based on evidence of the use of multiplicative relationships between the quantities in ratios as well as the type of strategy used to solve the problem. In addition, ratio problems are classified based on whether the correct ratio referent was used to solve the problem. Buy/consume problems are generally easier for students than problems involving constant speed and density.