Content Area: Math

 

Index: 4.4A Grade 12 CPI 4

 

Standard: 4.4 - Data Analysis, Probability, and Discrete Mathematics

 

Strand: A - Data Analysis

 

Cumulative Progress Indicator: 4 -  The student will estimate or determine lines of best fit (or curves of best fit if appropriate) with technology, and use them to interpolate within the range of the data.

 

Grade: 12

 

Sample Activities:

 

·        Students conduct an experiment where they suspend a weight on a string from a hook in the doorway. They swing their homemade pendulum and time how long it takes for it to swing 10 times. They had performed this experiment in 8th grade and used the median-median line fit method to model the data. In this revisitation of the problem, the teacher insists they use very short lengths and very long lengths in addition to various ones in between. When the data is graphed, it becomes apparent that the data is not linear and would fit a quadratic curve better. (The median-median line, available on many calculators which have statistics capabilities, is found by dividing the data points on the x-y plane into three equal sets, grouped by x-value, finding a single point for each set whose coordinates are the medians of the respective coordinates of the points in the set, connecting the first and third points by a straight line, and shifting this line 1/3 of the way toward the second point. See Contemporary Precalculus Through Applications.)

 

·        Students perform an Introductory Physical Science experiment where water is cooled by adding ice cubes and stirring. A Calculator Based Lab temperature probe is attached to a graphing calculator which is programmed to gather the data. Students (or each group of students) link their calculators to the original one to transfer the data to their calculators. They use the statistics functions to perform a quadratic fit, an exponential fit, and a logarithmic fit, and use the function graph capabilities to determine which is the best model.

 

·        Students work through the What's My Line unit described in the Keys to Success in the Classroom chapter of the Framework. They use median median and regression lines to estimate the height of a person whose thigh bone was found in a dig.

 

·        Additional Framework Activities