# A.11 and *A.9 - Curve of Best Fit

A.11    The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models.  Mathematical models will include linear and quadratic functions.

A.9  The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions.

Bloom's Level:  Create

### BIG IDEAS

• I can make accurate predictions about future events, make millions of dollars, predict the end of the world, and always cheer for the winning team.
• I will describe relationships between variables using graphical models, be able to predict values and outcomes, and determine whether relationships are linear or non-linear.

### UNDERSTANDING THE STANDARD

• The graphing calculator can be used to determine the equation of a curve of best fit for a set of data.
• The curve of best fit for the relationship among a set of data points can be used to make predictions where appropriate.
• Many problems can be solved by using a mathematical model as an interpretation of a real-world situation.  The solution must then refer to the original real-world situation.
• Considerations such as sample size, randomness, and bias should affect experimental design.

·  Data and scatterplots may indicate patterns that can be modeled with an algebraic equation.

·  Determining the curve of best fit for a relationship among a set of data points is a tool for algebraic analysis of data.  In Algebra I, curves of best fit are limited to linear or quadratic functions.

·  The curve of best fit for the relationship among a set of data points can be used to make predictions where appropriate.

·  Knowledge of transformational graphing using parent functions can be used to verify a mathematical model from a scatterplot that approximates the data.

·  Graphing utilities can be used to collect, organize, represent, and generate an equation of a curve of best fit for a set of data.

·  Many problems can be solved by using a mathematical model as an interpretation of a practical situation.  The solution must then refer to the original practical situation.

·  Data that fit linear y = mx + b and quadratic y = ax2 + bx + c
functions arise from practical situations.

·  Rounding that occurs during intermediate steps of problem solving may reduce the accuracy of the final answer.

·  Evaluation of the reasonableness of a mathematical model of a practical situation involves asking questions including:

­  “Is there another linear or quadratic curve that better fits the data?”

­  “Does the curve of best fit make sense?”

“Could the curve of best fit be used to make reasonable predictions?”

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

A.111  Write an equation for a curve of best fit, given a set of no more than twenty data points in a table, a graph, or real-world situation.

·  A.9Determine an equation of a curve of best fit, using a graphing utility, given a set of no more than twenty data points in a table, a graph, or a practical situation.

A.112  Make predictions about unknown outcomes, using the equation of the curve of best fit.

·  A.92   Make predictions, using data, scatterplots, or the equation of the curve of best fit.

A.113  Design experiments and collect data to address specific, real-world questions.

·  A.9Solve practical problems involving an equation of the curve of best fit.

A.114  Evaluate the reasonableness of a mathematical model of a real-world situation.

·  A.9Evaluate the reasonableness of a mathematical model of a practical situation.

### KEY VOCABULARY

curve of best fit, outcome, reasonableness, sample size, randomness, bias

Updated: Oct 27, 2017