Modeling Oscillating Systems: Mathematics Component Content Standards

## NCTM: students will be enabled to

• Use mathematical models to represent and understand quantitative relationships

“High school students should be able to develop models by drawing on their knowledge of many classes of functions—to decide, for instance, whether a situation would best be modeled with a linear function or a quadratic function—and be able to draw conclusions about the situation by analyzing the model. Using computer-based laboratories (devices that gather data, such as the speed or distance of an object, and transmit them directly to a computer so that graphs, tables, and equations can be generated), students can get reliable numerical data quickly from physical experiments. This technology allows them to build models in a wide range of interesting situations”

• Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

“In grades 9–12 students should gain a deep understanding of the issues entailed in drawing conclusions in light of variability. They will learn more-sophisticated ways to collect and analyze data and draw conclusions from data in order to answer questions or make informed decisions in workplace and everyday situations. They should learn to ask questions that will help them evaluate the quality of surveys, observational studies, and controlled experiments. They can use their expanding repertoire of algebraic functions, especially linear functions, to model and analyze data, with increasing understanding of what it means for a model to fit data well. In addition, students should begin to understand and use correlation in conjunction with residuals and visual displays to analyze associations between two variables. They should become knowledgeable, analytical, thoughtful consumers of the information and data generated by others.
As students analyze data in grades 9–12, the natural link between statistics and algebra can be developed further. Students' understandings of graphs and functions can also be applied in work with data.”

• Create and use representations to organize, record, and communicate mathematical ideas;
• Select, apply, and translate among mathematical representations to solve problems;
• Use representations to model and interpret physical, social, and mathematical phenomena.

“High school students should be able to create and interpret models of more-complex phenomena, drawn from a wider range of contexts, by identifying essential features of a situation and by finding representations that capture mathematical relationships among those features. They should recognize, for example, that phenomena with periodic features often are best modeled by trigonometric functions and that population growth tends to be exponential, or logistic. They will learn to describe some real-world phenomena with iterative and recursive representations.”

## Maryland: Core Learning goals

### Goal 1 Functions and Algebra

The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra.
Expectation 1.1
The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

Indicator 1.1.1
The student will recognize, describe, and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.
Indicator 1.1.2
The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

Expectation 1.2
The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

Indicator 1.2.4
The student will describe how the graphical model of a non-linear function represents a given problem and will estimate the solution.

## Maryland Content Standards

### Knowledge of algebra, patterns and functions

Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving patterns and functional relationships.

### Process of communication

Students will demonstrate their ability to organize and consolidate their mathematical thinking in order to analyze and use information, and will present ideas with words, symbols, visual displays, and technology.

### Process of connections

Students will demonstrate their ability to relate and apply mathematics within the discipline, to other content areas, and to daily life.