Exploring Rational Numbers in Middle School

• Main Author: Boudoin, Robyn Jasmin
• Other Authors: Madden, James
• Format: Others
• Language: en
• Published: LSU 2015
• Subjects: Mathematics
• Online Access: http://etd.lsu.edu/docs/available/etd-11162015-003712/

The move by the state of Louisiana to fully implement the Common Core State Standards (CCSS) from 2013 -2014 school year on and to align all state mandated tests to the CCSS has caused teachers to change the way they teach and how they deliver content. The overall most crucial new part of the CCSS in Mathematics is the emphasis on the Standards for Mathematical Practice. In order to illustrate the meaning of the Mathematical Practice Standards, non routine problems must be used that allow students and teachers to dig deeper and practice their mathematical habits of mind. Rational numbers provide an almost ideal playground to practice the standards. In my thesis I will define rational numbers and discuss their representation as decimals both terminating and repeating. I will look briefly at the history of rational numbers, what role the Egyptians played in the history and how they used unit fractions. I will also look at two exploratory problems that can be discussed in a middle school mathematics class in order to illustrate the Mathematical Standard Practices as required by the CCSS. In the first exploration students will investigate properties of Egyptian unit fractions. The second exploration will focus on investing the periods of the decimal representation of rational numbers and their connection to the distribution of the prime numbers.