## Science and Engineering Practices: Using Mathematics and Computational Thinking

In both science and engineering, mathematics—the study of numbers, quantities, and measurements—is extremely important. In fact, it’s at the core of the two fields. Mathematics is a tool for representing variables and their relationships, recording, organizing, and making sense of data, and helping scientists and engineers make predictions and test theories. A huge number of mathematical calculations are involved in building a sound bridge structure or engineering a car, to name just two examples!

Technology has transformed how science and engineers work. Using computers and other digital tools enhances the application of mathematics in science and engineering, and as a result, scientists and engineers have become increasingly dependent on computational thinking. Previously, analyzing a large data set would be a long and arduous task, but now a computer can do the same job in significantly less time, and engineers can easily digitally model their designs to scale.

Students are expected to use a range of digital tools in their science education, but it’s also important that they engage in computational thinking as a mindset—working through problems systematically and logically (just like a computer!).

## Obtaining, Evaluating, and Communicating Information: Progression

Primary School (K–2) |

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

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

4. Use quantitative data to compare two alternative solutions to a problem.

Elementary School (3–5) |

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

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

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

Middle School (6–8) |

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

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

3. Apply mathematical concepts and/or processes (such as ratio, rate, percent, basic operations, and simple algebra) to scientific and engineering questions and problems.

4. Use digital tools and/or mathematical concepts and arguments to test and compare proposed solutions to an engineering design problem.

High School (9–12) |

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

3. 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.

4. 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.).

## Grades K–2 Progression

Although in K–2, there are no performance expectations associated with this SEP, you should get your students comfortable with applying math and computational thinking in the science classroom. This can be achieved in a variety of ways. When collecting data, students can organize the information into spreadsheets or graphs—even if the data is very simple. You can also use tools such as rulers, thermometers, and timers in activities—this fun greenhouse effect experiment can help your students start to get used to using thermometers and this forces of friction activity can help your students get used to making measurements and recording data.

In upper elementary, students use mathematics and computational thinking to explain phenomena, and compare designs and find alternative solutions. Students must be given opportunities to apply mathematics to real-world science—make it fun and applicable to students’ lives! Track shadows across the ground as the Sun moves through the sky and plot the data into a graph, or carry out cooking activities like making a sourdough starter, and learn about bacteria while tracking how it develops and measuring its volume as it grows. It might also be helpful to try and match science activities to the content students are learning in math class.

## Grades 3–8 Progression

Starting in upper elementary and into middle school, students should be using a range of digital programs as part of their science education. Programs such as the NASA Sea Level Change Data Analysis Tool (DAT) can help students analyze large data sets, and digital simulation software such as PhET or Google Earth can enhance experiments and investigations. By middle school, students should be using complex mathematical concepts and representations to support scientific arguments and explanations.^{1} Math can be intimidating, even as students get older and more comfortable using it, so it’s important to find ways to make tricky concepts really fun and engaging. One way to do this is to set up simulations of real-world phenomena. Your students could pretend they’re biologists investigating the decline of a species—give them a data set of the population, a map of the area that the species lives in, and a description of the conditions in that area. Then, your students can appropriately analyze that data to gather evidence, present their findings, and, as an added bonus, see if they can use a digital tool to solve the problem!

## Learn More About Mathematics and Computational Thinking with Twig Science

Download our free printable *Mathematics and Computational Thinking *poster to serve as a reminder for your students that this practice is an important part of the process of scientific investigations.

To ensure that you hit the three dimensions of science learning, you need the support of a comprehensive 3-D science program. Twig Science is a phenomena-based science program that ensures all students have an interwoven understanding of Crosscutting Concepts, Science and Engineering Practices, and Disciplinary Core Ideas.