#### Math - 2017-18

# 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.9The student willcollectandanalyzedata,determinethe equation of the curve of best fit in order tomake predictions, andsolvepractical problems, using mathematical models of linear and quadratic functions.

**Bloom's Level:** Create

*Adopted: 2009*

### 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* = *ax*^{2}
+ *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.11_{1} **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.9_{1 }**Determine**
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.11_{2} **Make
predictions** about unknown outcomes, using the equation of the curve of best
fit.

·
A.9_{2 }**Make predictions**, using data,
scatterplots, or the equation of the curve of best fit.

A.11_{3} **Design**
experiments and **collect** data to
address specific, real-world questions.

·
A.9_{3 }**Solve**
practical problems involving an equation of the curve of best fit.

A.11_{4} **Evaluate**
the reasonableness of a mathematical model of a real-world situation.

·
A.9_{4 }**Evaluate**
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*