Grades 8-12 
Mathematics 
Algebra II 
Standard 21
Students apply the method of mathematical induction
to prove general statements about the positive integers.

 

Resources
Lesson Plans
Assessments
Algebra 2 
An Integrated Approach,  Larson/Kanold/Stiff, 1995,  
D.C. Heath and Company 

Section References 

Not addressed directly in the text. 

CA Exit Exam Web Site 

http:/www.chspe.com/ 
download.html 

Specific Textbook   
Web Sites    

http://www.glencoe.com/  
sec/math/prealg/mathnet/    

http://www.eduplace.com/  
links/    

http://www.eduplace.com/    

http://www.hmco.com/  
college/mathematics/  
index.html    

http://www.mcdougallittell  
.com/    

http://www.hmco.com/    

http://www.SRA-4KIDS.com/    

General Math   
Reference Sites    

http://www.learner.org/  
sami/view-category.php3  
?category=math    

http://www.score.k12.ca.us/    

http://henson.austin.apple  
.com/edres/curric.shtml    

http://school.discovery.com/  
schrockguide/index.html    

http://www.EDsOasis.org/    

http://www.math.com/    

http://www.nea.org/grants/  
free.html    

http://www.wcom.com/  
marcopolo/    

http://www.udel.edu/sine/    

http://dewey.chs.chico.k12  
.ca.us/math.html    

Free Stuff    

http://www.nea.org/  
grants/free.html    

State/National Math   
Ed Organizations    

http://www.nctm.org/    

http://www.cde.ca.gov/    

Calif. Dept. of Ed. Standards, Assessment, Ed. Reference.    

Calculator Reference Site    

http://www.ti.com/  
calc/docs/calchome.html  

Previously Published Data 

1.) Observe that: 

  • x - 1 = 1(x - 1)
  • x(x) - 1 = (x - 1)(x - 1)
  • x(x)(x) - 1 = (x(x) + x + 1)(x - 1)
Describe the pattern suggested by these factorizations. What do you think will happen in the case of x to the k - 1; where x is greater than or equal to 1? Justify your opinion by induction. 
2.) For each positive integer n, let P(n) be the formula: 

1(1) + 2(2) +...n(n) = n(n + 1)(2n + 1) 

          6
  • Write P(1). Is P(1) true?
  • Write P(k).
  • Write P(k + 1). 
    • Previously Published Data 

    1.) For each positive integer n, let P(n) be the inequality n(n) < 2 to the n  

  • Write P(5). Is P(5) true?
  • Write P(k)
  • Write P(k + 1) 
  • Is n(n) < 2 to the n true for all n > 5 
    2.) Prove by mathematical induction for all integers n is greater than or equal to 1: 1(1)(1) + 2(2)(2) + ...n(n)(n) = (n(n + 1)) ((n(n + 1)) 2 2 3.) Explain Mathematical Induction in your own words and use an example problem that you solve with it.     

    •