FRACTIONS: MATH’S “TOWERS OF TERROR”

FRACTIONS: MATH’S “TOWERS OF TERROR”

Standard of Mathematical Practice No. 4 states that students need to be able to model with mathematics.  Modeling is practiced early in a child’s math career.  In kindergarten and first grade, students are taught to “draw” a model of their problems.  For example, Brody and his class went to the apple orchard.  Brody picked 3 apples and his friends, Harry and Monty, each picked 5 apples.  How many apples did they pick all together?  

In order to solve this addition problem, the students will make a model of the problem, by drawing a set of 3 apples and 2 sets of 5 apples.  These beginnings allow students to visualize their problems and how to solve them.  Being able to visualize is the first step to understanding fractions.  It has always amazed me how the creating parts of a whole can confuse otherwise mathematically savvy students and their adult homework help.  I have a friend that is able to calculate relatively well, but just freezes when fractions are involved.  I believe she would benefit from creating a “picture” when working with fractions.

Apple Problem Representation

 Once a new mathematician has his or her model, the calculation to 13 apples becomes more manageable, as the "calculator" can count the number of apples to reach the answer.

Some Practical Manipulative Ideas

Being able to create a model that represents the whole and its equal parts is as necessary to beginning fractions, as it was to begin adding and subtracting.  The models allow a student to see the interactions of the fractions with the whole.  It also allows the students to manipulate the fractions and gain an understanding in a concrete way.  This will also allow their understanding to move from the concrete to abstract.


As the saying goes, “A picture is worth a 1000 words.”  I believe a model representation of fractions would save a lot of heartache.