Fractions as Part-Whole concept

Fractions as Part-Whole concept is the most commonly used example to teach fractions to children [1].

A fraction represents one or more parts of a geometrical figure which has been divided into some EQUALLY-SIZED pieces. [2]

Example 1	Example 2
Are the red parts in the circle the same fraction as the yellow parts in the rectangle? What is the fraction in both cases?

Susan J. Lamon in her book [2] stresses the importance of 5 points in the part-whole idea:

1. Part does not mean just one piece but can be more pieces
2. The size of the parts can change but all the parts must remain equal
3. In the mathematical language we use the fraction symbols (e.g. 1/2, 2/4, or 7/5 etc..) to represent the idea
4. The two numbers (e.g. 1 and 2, 7 and 5 etc..) are an ordered couple. By ordered we mean that writing 1 and then 2 is NOT the same as writing 2 and then 1.
   When we write 2 "over" 4 we mean "2 EQUAL parts out of 4 of the same EQUAL parts" ("two forths") and we write it 2/4.
5. The number and size of the fractions depends on how we divide the whole, or expressed in another way, how we unitize it. So the two numbers in the ordered couple can be different but the fraction is the same 2/4 = 4/8 i.d. an "half" or "one half".

Some common errors in fractions as part whole concept:

1. The numbers "up" and "down" (or numerator and denominator) in a fraction are not separate values, but ONE number called rational number ( that you can digit in a calculator as an integer or a decimal number).
   
   
2. The below picture DOES NOT SHOW 3/4 GREEN, BUT 1/2 GREEN
   
   
3. 1/6 is NOT smaller than 1/60 (because 6 is smaller than 60)
   
   
4. 1/2 + 1/2 is NOT = 2/4!

Source:

1 Elementary and Middle School Mathematics: Teaching Developmentally (7th Edition)

2. Teaching Fractions And Ratios For Understanding: Essential Content Knowledge And Instructional...

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