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Curve Fitting

Web-based Resource

Curve Fitting

Grade Levels

10th Grade, 11th Grade, 12th Grade, 9th Grade

Course, Subject

Algebra I, Mathematics
Related Academic Standards
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  • Big Ideas
    Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
    Degree and direction of linear association between two variables is measurable.
    Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
    Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
  • Concepts
    Algebraic properties and processes
    Analysis of one and two variable (univariate and bivariate) data
    Functions and multiple representations
    Linear relationships: Equation and inequalities in one and two variables
    Linear system of equations and inequalities
    Polynomial functions and equations
  • Competencies
    Display, analyze, and make predictions using univariate and bivariate data.
    Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems.
    Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation.
    Use algebraic properties and processes in mathematical situations and apply them to solve real world problems.
    Write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques.
    Write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities.

Description

With your mouse, drag data points and their error bars, and watch the best-fit polynomial curve update instantly. You choose the type of fit: linear, quadratic, cubic, or quartic. The reduced chi-square statistic shows you when the fit is good. Or you can try to find the best fit by manually adjusting fit parameters.

 

PhET provides fun, interactive, research-based simulations of physical phenomena for free. We believe that our research-based approach- incorporating findings from prior research and our own testing- enables students to make connections between real-life phenomena and the underlying science, deepening their understanding and appreciation of the physical world.

To help students visually comprehend concepts, PhET simulations animate what is invisible to the eye through the use of graphics and intuitive controls such as click-and-drag manipulation, sliders and radio buttons. In order to further encourage quantitative exploration, the simulations also offer measurement instruments including rulers, stop-watches, voltmeters and thermometers. As the user manipulates these interactive tools, responses are immediately animated thus effectively illustrating cause-and-effect relationships as well as multiple linked representations (motion of the objects, graphs, number readouts, etc.)

To ensure educational effectiveness and usability, all of the simulations are extensively tested and evaluated. These tests include student interviews in addition to actual utilization of the simulations in a variety of settings, including lectures, group work, homework and lab work. Our rating system indicates what level of testing has been completed on each simulation.

All PhET simulations are freely available from the PhET website and are easy to use and incorporate into the classroom. They are written in Java and Flash, and can be run using a standard web browser as long as Flash and Java are installed.

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Full Course Content

Physics Education Technology
The Physics Education Technology (PhET) project at the University of Colorado produces fun, interactive simulations of physical phenomena that make bridges to the real world.

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