Content Area: Math

 

Index: 4.1A Grade 8 CPI 6

 

Standard: 4.1 - Number and Numerical Operations

 

Strand: C - Estimation

 

Cumulative Progress Indicator: 6 -  The student will recognize that repeating decimals correspond to fractions and determine their fractional equivalents.

·        5/7 = 0. 714285714285…  =  0.

 

 

Grade: 8

 

Sample Activities:

 

·        Students investigate using simple equations to iterate patterns. For example, they use the equation y = x + 1 and start with any x-value, say 0. The resulting y-value is 1. Using this as the new x yields a 2 for y. Using this as the next x gives a 3, and so on, resulting in the sequence 1, 2, 3, 4, ... . Then students use a slightly different equation, y = .1x + .6, starting with an x-value of .6 and finding the resulting y value. Repeating this process yields the sequence of y-values .6, .66, .666, .6666, ..., which approximates the decimal value of 2/3.

 

·        Students explore the question of which fractions have terminating decimal equivalents and which have repeating decimal equivalents. They discover that the only fractions in lowest terms which correspond to terminating decimals are those whose denominators have only 2 and 5 as prime factors.

 

·        Students explore the question of which fractions have decimal equivalents where one digit repeats and learn that these are the fractions 1/9, 2/9, 3/9, ... . They generalize this to find the fractions whose decimal equivalents have two digits repeating like .171717 ... .