Great Examples of Mathematical Modeling
I travel to a lot of different states. Everywhere I go, everyone seems to be grappling with this idea of mathematical modeling. The New Math Common Core has placed a particular emphasis on Mathematical Modeling throughout. Whether or not you are aligning your curriculum to the CCSS, its explanation is revelatory. It states that:
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. …Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation…They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense…
Given this criteria, are your students mathematically proficient? Do they have a repertoire of models to make sense of their mathematical thinking. Here is a great resource with plenty of examples to get you started. I found this online from the publisher. These explanations of mathematical thinking are in the front of a great series of books on problem solving using bar diagrams. When I use these books I start with a grade level below the grade level I am teaching. I would even start at the beginning of the series so the students have a conceptual understanding and procedural fluency so when they get to the more difficult problems they have a strong foundation. See the resource page below of the different types of models and let me know what you think!