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 California Mathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
18. Students use fundamental counting
principles to compute combinations
and permutations.
Skills (Note: none listed for science standards)
Teacher Strategy
Combination:A selection of items regardless of order.Permutation:An arrangement of items in some specified order.Since order does matter with permutations,a greater number of arrangements is possible. Teach students the concept of factorials and ask them to make their own definition.If n is a positive integer,the expression n!is defined as n!=n(n -1)(n -2)(n -3)…(1).[Note:0!is defined to be 1.]
Given the digits 1,2,3,4,5,and 6 how many four-digit numbers can be made if it is okay to repeat a digit?Ask them to explain how they solved this problem.
Repeat the problem with none of the digits repeating.
Student Tasks or Scientific Investigation/Experimentation
Give students dice and ask them to determine
number of outcomes,number of outcomes with
an even number,odd number,etc.Ask students to make up specific problems in
permutations and combinations with the dice.Have students work in a group and find a
situation where four types of counting problems
are involved.Ask them to write a short
paragraph describing such a problem.
Assessment or Scientific Application/Assessment
Give students various problems where counting
and use of the formulas and common sense are
involved.
Resources and Technology
Resource:“Pennant Fever ” unit from the third
year textbook of the Interactive Mathematics
Program ™ ((IMP ™)deals with combinations
and permutations.Contact Key Curriculum
Press at 1-800-995-MATH for ordering
information.Books on Pascal ’s Triangle are a good resource
for studying combinations.About Teaching Mathematics — A K-8 Resource
by Marilyn Burns,Math Solutions Publications,
1992.Even though this book says K –8,many
if not all of the activities are appropriate for
high school students.Technology:Sensei High School Math by
Broderbund Software,Inc.for 8th-12th grade
(Algebra,Calculus,and Geometry)is rated
Desirable by the California Instructional
Technology Clearinghouse.(Floppy Disk,
Macintosh)Algebra is designed to
complement Algebra 1 and 2.The programs
may be used to introduce topics or show
examples to the entire class,or used with
small groups or individuals for independent
study,practice or remediation.
This page is taken from the Santa Clara Office of Education.