More Problem Contexts

Chapter 7 continues the discussion of ratio and proportion problem contexts, with a specific emphasis on understanding why problem context and the meaning of quantities are vitally important considerations for classroom planning and instruction. In this chapter, we see how the same problem type can be cast in different contexts. This chapter also includes discussion of other ratio and proportion contexts such as similarity, scale factors, measurement monetary conversions, probability and sampling. This chapter discusses the ratio and proportion problem contexts, with a specific emphasis on the importance of instructionally focusing on the meaning of the quantities in different ratio and proportion contexts such as similarity, scale factors, slope, measurement, monetary conversions, probability and sampling. Measurement conversions involve changing the size of a unit of measure using a conversion factor. This is different from a scale factor, which results in a larger or smaller quantity or size. The Common Core State Standards for Math standards focus on two aspects of using sampling to make inferences about a whole population. First, the understanding that the relationship between a characteristic found in a random sample of the whole population is proportional to finding that characteristic in the whole population. Second, validity of the inference made from the sample depends upon how representative the sample is of the population as well as the size of the sample.