Fraction Concepts

Concepts that must be understood:

• Fractions are Part of a Whole
• Ratios
• Division

Three categories of models:

• Area
• Length
• Quantity or Set

Partitioning is dividing a shape into equal – sized pieces.  This can be done with counters (or any other object that are similar) by dividing the total number of counters into smaller groups of equal numbers.  If the students are working with a specific shape they simply divide that shape into equally sized parts.

Iteration means to look at and discover how many parts compare to the whole.  The best way to help students with fractions in this way is to get them use to thinking of fractions as how many of what.  The “what” is the denominator and the “how many” is the numerator.  Iteration can be done with strips of paper.  Give them a strip of paper and tell them what part of a whole it is.  Then have them find other parts of the whole as well as mixed number fractions based on the strip they were given.

Estimating Fractions

Some ways I can help support student’s development of estimation with fractions are asking them daily questions that forces them to look at fractions of the whole class and estimate a part of the class.  I could ask, for example, what fraction of our class is wearing jeans today?  Another way is to draw pictures with parts of the picture shaded.  Then ask the students to estimate what fraction is either shaded or un-shaded.

Equivalent Fractions

Two equivalent fractions are two ways of describing the same amount using different-sized fractional parts.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7^th ed.). Boston, MA: Pearson.