### Dimension 1: Practices

##### Using Mathematics and Computational Thinking

Below is the progression of the Science and Engineering Practice of Using Mathematics and Computational Thinking, followed by Performance Expectations that make use of this Science and Engineering Practice.

##### 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; statistically analyzing data; and recognizing, expressing, and applying quantitative relationships.

Mathematical and computational thinking at the K–2 level builds on prior experience and progresses to recognizing that mathematics can be used to describe the natural and designed world.

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.

Decide when to use qualitative vs. quantitative data.

Mathematical and computational thinking at the 3–5 level 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.

Create and/or use graphs and/or charts generated from simple algorithms to compare alternative solutions to an engineering problem.

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

Describe, measure, estimate, and/or graph quantities such as area, volume, weight, and time to address scientific and engineering questions and problems.

Organize simple data sets to reveal patterns that suggest relationships.

Mathematical and computational thinking at the 6–8 level builds on K–5 experiences and progresses to identifying patterns in large data sets and using mathematical concepts to support explanations and arguments.

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 (such as ratio, rate, percent, basic operations, and 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 problem.

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

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.

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.).

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

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.

Decide when to use qualitative vs. quantitative data.

Mathematical and computational thinking at the K–2 level builds on prior experience and progresses to recognizing that mathematics can be used to describe the natural and designed world.

## Using Mathematics and Computational Thinking

By combining mathematics with computational thinking, engineers and scientists are able to push the boundaries of what is possible. Engineers can apply scientific theories in a mathematical manner while scientists can utilise powerful information technologies created by engineers. This allows them to conduct extensive investigations and analyses and build complex models which would otherwise be difficult or even impossible. (NRC Framework, 2012, p. 65).

Students should use mathematics to visualize physical variables and their connections, as well as to make quantitative predictions. Mathematics also has vital applications in science and engineering such as logic, geometry, and calculus. Computers and digital tools can increase the power of mathematics by putting calculations on autopilot, approximating solutions for intractable problems, or examining sizeable datasets to discover underlying patterns.Students are expected to use laboratory tools connected to computers for observing, measuring, recording, and processing data. The NGSS performance expectations provide an overview of the critical mathematics skills necessary for understanding science; however, classroom instruction should seek to enhance students' knowledge in the use of mathematics and computational thinking. Computational thinking encompasses strategies such as data organization, algorithm creation and simulations used on both natural and man-made systems. Mathematics is a powerful tool that is essential for optimizing scientific learning, so it should be at the forefront of any science class.

GOALS

By grade 12, students should be able to

• Recognize dimensional quantities and use appropriate units in scientific applications of mathematical formulas and graphs.

• Express relationships and quantities in appropriate mathematical or algorithmic forms for scientific modeling and investigations.

• Recognize that computer simulations are built on mathematical models that incorporate underlying assumptions about the phenomena or systems being studied.

• Use simple test cases of mathematical expressions, computer programs, or simulations—that is, compare their outcomes with what is known about the real world—to see if they “make sense.”

• Use grade-level-appropriate understanding of mathematics and statistics in analyzing data.

National Academies of Sciences, Engineering, and Medicine. 2012. A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas. Washington, DC: The National Academies Press. https://doi.org/10.17226/13165.

Last updated:

August 1, 2023 at 12:28:48 PM

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