### 4 — Model With Mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.

Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. 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, possibly improving the model if it has not served its purpose.

### Illustrations

In elementary school, students begin to think about how numbers and operations can describe the world. Deciding which operations apply to a particular context, and why, is an import step toward being able to do increasingly more sophisticated modeling problems in later grades: 3.OA Analyzing Word Problems Involving Multiplication

In order to model with mathematics, students need to make simplifying assumptions about a context. It is important for students to have opportunities to do this in very familiar contexts before they are asked to do the more complex task of making such assumptions (based on appropriate research) for unfamiliar or scientifically complex contexts, as they will be asked to do in high school: 7.RP Sale!

Full-blown modeling tasks require many different skills, including sifting through information and deciding what is relevant, interpreting graphs, locating information needed to solve a problem, and making simplifying assumptions. Students need opportunities to work on this skills a few at a time as well as in concert: N-Q Ice Cream Van