Content Area: Math

 

Index: 4.3D Grade 12 CPI 2

 

Standard: 4.3 - Patterns and Algebra

 

Strand: D - Procedures

 

Cumulative Progress Indicator: 2 -   The student will select and use appropriate methods to solve equations and inequalities

·        Linear equations – algebraically

·        Quadratic equations – factoring (when the coefficient of x² is 1) and using the quadratic formula

·        All types of equations using graphing, computer, and graphing calculator techniques

 

Grade: 12

 

Sample Activities:

 

·        Students are asked to find the solutions to 2x = 3x^2. Some students use a spreadsheet to develop a table of values. Once they find an interval of length 1 which contains a solution, they refine their numbers to develop the answer to the desired precision. Other students graph both y = 2x and y = 3x^2 using graphing calculators or computers and use the trace function to determine where they intersect. Other students graph the function y = 3 x^2 - 2x and use the trace function to find the zeroes. Other students enter the function in their graphing calculator and check the table of values.

 

·        As a portion of a final assessment, students are given one opportunity to place a cup which is supported 6 inches off the ground in such a position as to catch a marble rolled down a ramp. They perform the roll without the cup to locate the point where the marble strikes the ground. They measure the height of the end of the ramp above the ground and the distance from the point on the ground directly beneath the end of the ramp to the point where the marble struck the ground. They generate the quadratic function which models the path of the marble. Several students use different methods to ensure they have the correct function. Then they decide where they will have to place the cup by substituting 6 for the function value and determining the corresponding x value. Students solve the equation using the quadratic formula, and the trace function on a graphing calculator, and proceed to place the cup and roll the ball only when the solutions produced by all of the methods agree.