Content Area: Math

 

Index: 4.3C Grade12 CPI 2

 

Standard: 4.3 - Patterns and Algebra

 

Strand: C - Modeling

 

Cumulative Progress Indicator: 2 -The student will analyze and describe how a change in an independent variable leads to change in a dependent one.

 

Grade: 12

 

Sample Activities:

 

·        Students investigate the relationship between stopping distance and speed of travel in a car. The students gather data from the driver's education manual, graph the values they have found, note that the relationship is linear, and look for an equation that fits the data.

 

·        Students investigate the effect on the perimeters of given shapes if each side is doubled or tripled. They summarize their findings in writing and symbolically.

 

·        Students investigate how the area of a parallelogram changes as the length of the base is doubled, or the height is doubled, or both are doubled. They repeat the experiment for tripling and quadrupling each measurement. They discuss their findings and represent them symbolically.

 

·        Students compare two fare structures for taxis: one in which the taxi charges $2.75 for the first 1/4 mile and $.50 for each additional 1/4 mile, and one in which $4.25 is charged for the first 1/4 mile and $.20 for each additional 1/8 mile. They develop tables, graph specific points, and generate equations to describe each situation. They find which trips cost more for each fare structure and when both will result in the same cost.

 

·        Students investigate patterns of growth, such as compound interest or bacterial growth, with a calculator. They make a table showing how much money is in a savings account (if none is withdrawn) after one quarter, two quarters, and so on, for ten years. They represent their findings graphically, note that this is not a linear relationship (although simple interest is linear), and write an equation describing the relationship between the amount P deposited initially, the interest rate r, the number n of times that interest is paid each year, the number of years y, and the total T available at the end of that time period: T = (1 + r/n)ny(P).