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Unit 4: Modeling and Using Tools (MP4 and MP5)

# 4.1 Introduction to Modeling with Mathematics (MP4)

“Modeling” is mathematizing a situation (which includes structuralizing, idealizing, and making assumptions) or making use of a given or constructed model by interpreting or validating it in relation to the context. Modeling is important because it links classroom mathematics and statistics to everyday life. MP4, “Model with mathematics,” directly addresses this practice. Modeling within mathematics is a broad standard that includes within its definition a wide range of mathematical problems. The Program for International Student Assessment (PISA) rubric defines modeling problems on a continuum of four different levels, shown below.

Level 0 problems are purely computational or context is unnecessary for solving them.

Level 1 problems are directly translatable from a context. An example is a simple word problem from which students can formulate an equation.

Level 2 problems use models and modify them to satisfy changed conditions. Such problems allow students to study patterns and relationships between quantities, and represent these patterns and relationships using words, numbers, symbols, and pictures. These can be problems that have multiple solution strategies, but usually have only one correct solution.

Level 3 problems have no predetermined solution. Such problems require students to make assumptions about the context, develop strategies to solve them, check their answers, present results, and possibly revise their solution strategies and begin the process over again.