Algebra II
Standard
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| Skills (Note:
none listed for science standards)
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Teacher
Strategy
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Student
Tasks or Scientific Investigation/Experimentation
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Assessment
or Scientific Application/Assessment
|
Resources
and Technology
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The California Mathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
21. Students apply the method of
mathematical induction to prove
general statements about the
positive integers.
Skills (Note: none listed for science standards)
Teacher Strategy
Principle of Mathematical Induction:Let P(n)be a predicate that is defined for integers n,and let a be a fixed integer.Suppose the following two statements are true:
Now the inductive hypothesis is the supposition that P(k)is true.This supposition can be used to show that P(k +1)is true because P(k +1)is an equation,and the truth of an equation can be shown in a variety of ways.One of the most straightforward is to transform the left-hand side into the right-hand side using algebra and other known facts and legal assumptions.
Mathematical Induction is used to check conjectures about the outcomes of processes that occur repeatedly and according to definite patterns,such as sequences.
Student Tasks or Scientific Investigation/Experimentation
Assessment or Scientific Application/Assessment
Explain Mathematical Induction in your own words and use an example problem that you solve with it.
Resources and Technology
Resource:Discrete Mathematics with
Applications by Susanna S.Epp,Wadsworth
Publishing Company,1990,Belmont,
California.Chapter 4 “Sequences and
Mathematical Induction ” goes into depth on
this subject with a variety of examples
including coins,dominoes,and the story of
the young Carl Friedrich Gauss and his
summing of the numbers one through one
hundred.This is an excellent resource for
Mathematical Induction.Advanced Mathematical Concepts by Merrill.
ISBN 0 —02-824315-3.
This page is taken from the Santa Clara Office of Education.