criteria for success. Science and Pre-K–2 Condensed 3–5 Condensed 6–8 Condensed Engineering 9–12 Condensed Practices Practices Practices Practices Practices Mathematical and Mathematical and Mathematical and Mathematical and computational 5. Using Mathematics computational thinking computational thinking computational thinking in thinking in 9–12 builds on pre-K–8 and Computational in pre-K–2 builds on in 3–5 builds on pre-K–2 6–8 builds on pre-K–5 and experiences and progresses to Thinking prior experience and experiences and experiences and using algebraic thinking and progresses to progresses to extending progresses to identifying analysis, a range of linear and In both science and recognizing that quantitative patterns in large data sets nonlinear functions including engineering, mathematics can be measurements to a and using mathematical trigonometric functions, mathematics and used to describe the variety of physical concepts to support exponentials and logarithms, and computation are natural and designed properties and using explanations and computational tools for statistical fundamental tools for worlds. computation and arguments. analysis to analyze, represent, and representing physical mathematics to analyze model data. Simple computational variables and their data and compare simulations are created and used relationships. They are alternative design based on mathematical models of used for a range of tasks solutions. basic assumptions. such as constructing Decide when to use Decide if qualitative or simulations; solving equations exactly or qualitative versus quantitative data are approximately; and quantitative data. best to determine recognizing, expressing, whether a proposed and applying object or tool meets quantitative criteria for success. relationships. Use counting and Organize simple data Use digital tools (e.g., Create and/or revise a numbers to identify sets to reveal patterns computers) to analyze computational model or Mathematical and and describe patterns that suggest very large data sets for simulation of a phenomenon, computational in the natural and relationships. patterns and trends. designed device, process, or approaches enable designed worlds. system.
criteria for success. Science and Engineering Practices Pre-K–2 Condensed Practices 3–5 Condensed Practices 6–8 Condensed Practices 9–12 Condensed Practices 5. Using Mathematics and Computational Thinking In both science and engineering, mathematics and computation are fundamental tools for representing physical variables and their relationships. They are used for a range of tasks such as constructing simulations; solving equations exactly or approximately; and recognizing, expressing, and applying quantitative relationships. Mathematical and computational approaches enable Mathematical and computational thinking in pre-K–2 builds on prior experience and progresses to recognizing that mathematics can be used to describe the natural and designed worlds. Mathematical and computational thinking in 3–5 builds on pre-K–2 experiences and progresses to extending quantitative measurements to a variety of physical properties and using computation and mathematics to analyze data and compare alternative design solutions. Mathematical and computational thinking in 6–8 builds on pre-K–5 experiences and progresses to identifying patterns in large data sets and using mathematical concepts to support explanations and arguments. Mathematical and computational thinking in 9–12 builds on pre-K–8 and experiences and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. Decide when to use qualitative versus quantitative data. Decide if qualitative or quantitative data are best to determine whether a proposed object or tool meets criteria for success. Use counting and numbers to identify and describe patterns in the natural and designed worlds. Organize simple data sets to reveal patterns that suggest relationships. Use digital tools (e.g., computers) to analyze very large data sets for patterns and trends. Create and/or revise a computational model or simulation of a phenomenon, designed device, process, or system.