Classroom Sneak Peek # 4 - Model with Mathematics

The past couple of weeks I began blogging about the 8 Mathematical Practices from the Common core.  I finished Mathematical Practice # 1, Mathematical Practice # 2, and Mathematical Practice #3.  This week the focus is on CCSS Mathematical Practice #4 - Model with mathematics..  I'll address what this looks like in the classroom, what students will be doing, what teachers will be doing, and the most important, the type of questions teachers will be asking.  Dan Meyer was at ESSDACK where he worked with middle and high school teachers to discuss what this "modeling with math" looks like at that level.

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.

What does this really look like?  The chart below is a work in progress.  I've designed this with the expertise of many classroom teachers.  If you have other ideas, please don't hesitate to email me and share your expertise as well.  If you are interested in using this process with your staff, read What Do The Common Core Standards Look Like in the Math Classroom.

Mathematical Practice: Model with mathematics.

Student Actions:	Teacher Actions:	Open-Ended Questions:
Apply math concepts to real-world problems (may include community or school problems) Write equations to go with a story problem. Take risks and make predictions. Use estimation as a way of predicting. Use a variety of math tools and can easily flow between different tools (formulas - graphs - problem - function tables - number lines) Change course and the tool being used, if it doesn't work for them. Draw conclusions. Question if their prediction and/or solution makes sense.	Provide real-world problems for students to solve daily (story problems, school, or community problems) Explicitly connect the equation that matches the real-world problem. Facilitate discussion about what the symbols or variables mean in the equation. "Why are we writing the equation 57 + ___ = 97 After reading, before solving a problem, have students predict what the answer should be about. What would be a logical answer. Facilitate discussions about what the problem is asking and what might be logical answers. Provide opportunities for students to go back and forth between different math tools. Function tables, flow charts, Venn diagrams, number lines, 200 charts, etc. should be readily available and students familiar with all the possible tools. Monitor student work as they solve, asking them if this tool is going to help solve the problem and how. Require students to make sense of the problem and if the solution is reasonable.	How might you represent what the problem is asking? How does the equation you wrote match the problem? What tools have we used (number line, function table, etc.) that might help you to organize the information from the problem? Why do you believe your estimation is a good estimation? How is this tool/strategy helping you to solve the problem? What else might you try? What might be a good estimate? Would a larger number or smaller number make more sense? How might a picture or math tool help you solve the problem?