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.
Standard TypeMichigan State Math Standards
Use the number line to place, compare, and order decimals to the hundredths. Use estimation and an algorithm based on place value to add decimals to hundredths. Use the number line to place, compare, order, and add decimals to the hundredths.
Match visual models to the numbers they represent in fraction and decimal format. Solve problems with decimal fractions. Match visual models to the numbers they represent in fraction and decimal format.
Use visual models and equations to solve problems involving multiplying and dividing fractions. Use models & equations to solve problems involving multiplying and dividing fractions.
Use visual models, repeated addition, and multiplication to solve problems with equal sized groups. Compare the strategies to see which one is most efficient. Use visual models, addition, & multiplication to solve problems with equal sized groups.
Use estimation and visual models to solve problems involving adding fractions with unlike denominators. Solve problems involving adding fractions with unlike denominators.