Using Mathematics and Computational Thinking

Using algebraic thinking and analysis for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions.

K-2 3-5 6-8 9-12
Mathematical and computational thinking in K–2 builds on prior experience and progresses to recognizing that mathematics can be used to describe the natural and designed world(s).

• Decide when to use qualitative vs. quantitative data.

• Use counting and numbers to identify and describe patterns in the natural and designed world(s).

• Describe, measure, and/or compare quantitative attributes of different objects and display the data using simple graphs.

• Use quantitative data to compare two alternative solutions to a problem.
Mathematical and computational thinking in 3–5 builds on 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.

• Decide if qualitative or quantitative data are best to determine whether a proposed object or tool meets criteria for success.

• Organize simple data sets to reveal patterns that suggest relationships.

• Describe, measure, estimate, and/or graph quantities (e.g., area, volume, weight, time) to address scientific and engineering questions and problems.

• Create and/or use graphs and/or charts generated from simple algorithms to compare alternative solutions to an engineering problem.
Mathematical and computational thinking in 6–8 builds on K–5 experiences and progresses to identifying patterns in large data sets and using mathematical concepts to support explanations and arguments.

• Use digital tools (e.g., computers) to analyze very large data sets for patterns and trends.

• Use mathematical representations to describe and/or support scientific conclusions and design solutions.

• Create algorithms (a series of ordered steps) to solve a problem.

• Apply mathematical concepts and/or processes (e.g., ratio, rate, percent, basic operations, simple algebra) to scientific and engineering questions and problems.

• Use digital tools and/or mathematical concepts and arguments to test and compare proposed solutions to an engineering design problems
Mathematical and computational thinking in 9- 12 builds on K-8 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.

• Create and/or revise a computational model or simulation of a phenomenon, designed device, process, or system.

• Use mathematical, computational, and/or algorithmic representations of phenomena or design solutions to describe and/or support claims and/or explanations.

• Apply techniques of algebra and functions to represent and solve scientific and engineering problems.

• Use simple limit cases to test mathematical expressions, computer programs, algorithms, or simulations of a process or system to see if a model “makes sense” by comparing the outcomes with what is known about the real world.

• Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m3 , acre-feet, etc.).

Introduction to SEP5: Using Mathematics and Computational Thinking

from NGSS Appendix F: Science and Engineering Practices in the NGSS

Modeling can begin in the earliest grades, with students’ models progressing from concrete “pictures” and/or physical scale models (e.g., a toy car) to more abstract representations of relevant relationships in later grades, such as a diagram representing forces on a particular object in a system. (NRC Framework, 2012, p. 58)

Models include diagrams, physical replicas, mathematical representations, analogies, and computer simulations. Although models do not correspond exactly to the real world, they bring certain features into focus while obscuring others. All models contain approximations and assumptions that limit the range of validity and predictive power, so it is important for students to recognize their limitations.

In science, models are used to represent a system (or parts of a system) under study, to aid in the development of questions and explanations, to generate data that can be used to make predictions, and to communicate ideas to others. Students can be expected to evaluate and refine models through an iterative cycle of comparing their predictions with the real world and then adjusting them to gain insights into the phenomenon being modeled. As such, models are based upon evidence. When new evidence is uncovered that the models can’t explain, models are modified.

In engineering, models may be used to analyze a system to see where or under what conditions flaws might develop, or to test possible solutions to a problem. Models can also be used to visualize and refine a design, to communicate a design’s features to others, and as prototypes for testing design performance.

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