Algebra II
Standard
|
| Skills (Note:
none listed for science standards)
|
Teacher
Strategy
|
Student
Tasks or Scientific Investigation/Experimentation
|
Assessment
or Scientific Application/Assessment
|
Resources
and Technology
|
|
The CaliforniaMathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
5. Students demonstrate knowledge of
how real and complex numbers are
related both arithmetically and
graphically. In particular, they can
plot complex numbers as points in
the plane.
Skills (Note: none listed for science standards)
Teacher Strategy
Have students plot the graph of y =x2 and y =x –1 and ask for their point of intersection. They should not intersect and students should tell you that x =y is not defined for negative values of y.Talk about –1 and introduce i for imaginary. Talk about how every number has a real and an imaginary point. Explain to the students that when a graph of a trinomial crosses the x-axis,this is sometimes referred to as the roots of the equation.Have them sketch the graph and find the roots of
y =(x+1)2 –4
y =(x+1)2
y =(x+1)2 +4Graph three does not have real roots but does have imaginary ones.
Explain to the students the complex number plane where the real numbers are on the x-axis and the imaginaries are on the y-axis.Have students plot numbers such as 2+i,3,–4,etc. on the plane.
Student Tasks or Scientific Investigation/Experimentation
Have students explore different graphs and determine if there are solutions,imaginary solutions or no solutions.
Have students plot various real and imaginary numbers on a complex-number plane.
Assessment or Scientific Application/Assessment
Given various graphs students need to determine
if the roots are real or imaginary.Given various points students should be able to
graph them on a complex number plane.True or False?
• Every real number is a complex number..
• Every imaginary number is a complex number..Show where each lies on the complex
coordinate plane.
• real numbers
• pure imaginary numbers
Resources & Techn
Resources and Technology
Have students explore on the graphing calculator if the graphs of y =and
Fractals for the Classroom:Introduction to Fractals and Chaos,NCTM
This page is taken from the Santa Clara Office of Education.