Grades 12 Fraction Bars Teacher's Guide
.....................Introduction.......................  
Lessons 19 of this guide are for grade 1 and lessons 117 are for grade 2. The first six lessons use only whole numbers and colors to describe fraction concepts. Such a period in which students use oral and meaningful descriptions before the introduction of fraction symbols is strongly recommended, as noted by this NCTM Standards 2000 statement: "Fraction symbols, such as 1/4 and 2/3, should be introduced only after children have developed the concepts and oral language necessary for symbols to be meaningful and should be carefully connected to both models and oral language." >>>>>>>>>>>>>>>>>>>>>>>>>>>> NCTM Standards 2000, page 57 The lessons in this guide have been designed to provide a gradual connection from whole numbers to fractions. The relationships and concepts arise naturally out of the activities and games and students are encouraged to describe their reasoning orally in words that make sense to them. Here are some examples of how this is done in this guide. (1) The language for verbal descriptions of wholes and parts of wholes is natural and nonthreatening. 

(2) In the first few lessons a pair of whole numbers is used to describe the number of parts in a whole and the number of shaded parts by using Double Boxes. Later this is modified by removing the boxes and leaving just the line between the two numbers, as suggested by the following illustration. 

(3) In the early lessons the language avoids fraction names and terminology. For example, the fraction 3/4 can be called "3 over 4" or "3 out of 4", and rather than initially using the terms numerator and denominator these are referred to as the top number and the bottom number. Another means of achieving a connection from whole numbers to fractions and a nonthreatening learning environment is through the use of games and activities. These will motivate students to learn specific ideas and to develop a positive attitude toward learning fractions. By the time fractions are introduced in Lesson 7, the use of these new numbers will be meaningful to students. 

The first graders in this photo are playing the game FLIP. They each place their bar next to the other player's, and the student with the bar having the greater shaded amount wins the two bars.  
The Fraction Bars program successfully uses manipulatives, diagrams, and oral language to develop readiness for fraction symbols and concepts of fractions in grades 1 and 2. The philosophy of presenting activities with concrete models before introducing fractions and their terminology is consistent with recommendations in the Standards: "Representing numbers with various physical materials should be a major part of mathematics instruction in the elementary school grades. … As students gain understanding of numbers and how to represent them, they have a foundation for understanding relationships among numbers." >>>>>>>>>>>>>>>>>>>>>>>>>> NCTM Standards 2000, page 33
