The CaCCSS expects mathematically proficient students to be able to 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, 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.
In order for teachers to produce students capable of applying mathematics in the ways described above, they will need to engage students in tasks that require critical thinking and problem solving, Critical thinking and problem solving are skills that can be taught, however, in our current era of accountability, many teachers abandon the teaching of these skills in favor of test preparation. These resources are intended to provide teachers support in making the needed enhancements and changes in instruction.