Louisiana Curriculum Framework Content Strand:  G  Grade Level:  10

CURRICULUM
INTEGRATION:       Measurement, Right Triangles, Algebra

TIME FRAME:          Two class periods

MATERIALS:            Protractor, ruler

STUDENT
GROUPINGS:          One to two

POSSIBLE
OBSTACLES
TO STUDENT
LEARNING:            Lack of familiarity with ruler

                                     examples

                                    arithmetic series  0, 2, 4, 6, 8, 10, 12, etc. (add 2 to get next)
 
                                    geometric series  1, 2, 4, 8, 16, 32, 64, etc. (multiply by 2 to get next)

                                ARITHMETIC MEAN
                                 Have students select two numbers in the arithmetic series that have
                                 one number between them, such as 4 and 8. Direct students to find
                                 arithmetic mean (a.m.) first using computation method, i.e.,
                                (4+8)/2 = 6.  Then allow students to come up with a way to show
                                 visually that 6 is the a.m. of 4 and 8. A suggested representation is:
 

                                        ________
                           4                    arithmetic mean
                    ____________     (half-way
                               6                  between)
                                        ________________
                                                                      8
 
                          GEOMETRIC MEAN

                           Begin same way as before, by selecting two numbers with one between,
                                 such as 2 and 8. Guide students through computation method, as shown:

                                        2 : x  as  x : 8
                    2 / x  =  x / 8
                    16     =   x^2
                      4     =   x
                                 Then take students step-by-step through construction of geometric mean