Algebra II
Standard
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| Skills (Note:
none listed for science standards)
|
Teacher
Strategy
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Student
Tasks or Scientific Investigation/Experimentation
|
Assessment
or Scientific Application/Assessment
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Resources
and Technology
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The California Mathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
25. Students use properties from
number systems to justify steps in
combining and simplifying functions.
Skills (Note: none listed for science standards)
Teacher Strategy
Review Standards #21,22,23,and 24.Review functions,especially functions of the form f(g(x)) and g(f(x)). Look at sequences of numbers which are written in terms of variables.Have students simplify them to determine if they are arithmetic or geometric series.
Ask students to recall the associative, commutative,and distributive properties.Discuss how these properties are applied to the mathematics they have been doing with functions.
Review complex numbers.Have students explore arithmetic and geometric series involving complex numbers.
Use the Sets of Numbers graphic below to discuss number systems and which properties can be applied in combining and simplifying each set of numbers and,especially,functions.
The bracketed letters represent alpha notation frequently used to represent the respective set.
Student Tasks or Scientific Investigation/Experimentation
Explain how to determine whether a set of numbers is a sequence or a series.Give examples. Explain how to determine whether a series is arithmetic or geometric.Give examples.
Assessment or Scientific Application/Assessment
Give three examples of real-world applications
of geometric sequences,such as successive
reductions of a graphic on a copier.Explain the
application and use reasonable numbers to
describe the sequence.In what real-world applications would you need
to find the sum of a geometric series?Describe
two such series.SAT average mathematics scores in Santa Clara
County for the years 1988 through 1997 are:
538,537,539,539,545,545,542,546,
550,and 555.Analyze and describe these
data.Are these numbers a sequence or a series?
Can you predict the 1998 scores based on this
information?Can you predict the 2000 scores?
If you can,do it.If not,explain why not.
Resources and Technology
Resource:The Write Tool to Teach Algebra by V.Gray.(book)This hands-on model for introducing writing and critical thinking into the algebra curriculum contains specific instructions,writing activities,reproducibles, and assessment suggestions.104 pages. Grades 7-12.ETA,Vernon Hills,Illinois ([email protected]) Technology:Tangible Math:Algebra Animator by LOGAL software,Inc.for 7th-12th grade is rated “Desirable ” by the California Instructional Technology Clearinghouse. (Floppy disk,Macintosh,Windows)Students may examine one-to-one and many-to-one functions;compare and contrast motion defined by a constant,linear,quadratic, cubic,rational,exponential,and logarithmic functions.It is an excellent tool to teach graphing skills,compare various graphs, prepare tables,find points of intersections, and connect graphing and equations to real- life situations and word problems.(This software also supports Standards #13,#15, and #24.) Resources & Technology
This page is taken from the Santa Clara Office of Education.