Percentages and Milk Fat

• # Percentages and Milk Fat

The Milk Fat problem provides a rich context for looking into students’ understanding of percentages as well as the complexity of these problems.
Percentages have proven to be a challenging concept in school mathematics. At the surface, a percentage is merely a rational number, representing a ratio between a number and 100. At the conceptual core, however, a percentage is sensitive to the context, making sense with respect to a network of related quantities. In our effort to engage our students in the conceptual exploration of rational numbers, we noticed a milk bottle label (see fig. 1) and posed a few questions about the use of percentages in this context. Simple as it is, the milk label gave us a meaningful lens to explore the dynamics of percentage use in context. In this article, we analyze the Milk Fat problem and the diverse responses of our students (in this case, prospective elementary teachers) because their responses relate to perspectives of additive and multiplicative reasoning and literacy. We further discuss the impact of intervention and the persistence of additive reasoning. We invite our readers to try the problem with their own audiences.