How many times have you divided a sandwich, cookie, or cupcake between two children only to hear them utter those dreaded words? If one cookie is divided into “halves,” can one half really be bigger than the other?
Welcome to what I like to call Misconceptions About Fractions 101. Even before your child enters school, they have already been exposed to many scenarios involving fractions, however, their understanding of fractions is usually incomplete. To complicate matters even further, students have already learned that multiplying whole numbers results in a larger whole number, but now we teach them that multiplying two fractions results in a smaller fraction! Is it any wonder that around the time when computations involving fractions occur in third grade, many children begin experiencing difficulty in math?
So aside from measuring ingredients for recipes, slicing pizza, and cutting sandwiches into equal parts, why do we really need to learn about fractions?
Recent research suggests that understanding the concept of fractions is the basis for all higher-level mathematics; from algebra to physics to chemistry. Understanding fractions is not about memorizing complex rules or teaching students to “multiply by the reciprocal” when dividing. Understanding fractions is about learning how numbers relate to one another and being able to identify fractional parts on a number line.
Since a basic tenet of classroom instruction is to build upon a child’s prior knowledge, often times a teacher may first have to clarify misconceptions and ideas a student has about fractions before proceeding with formal instruction. Students need to have a conceptual understanding of what numerators and denominators mean beyond the traditional definition of the numerator being the number on the “top” and the denominator the number on the “bottom.” Teachers at Posnack use fraction bars that correspond to Singapore Math bar models to help students understand equal parts of a whole number, and to identify the relationship between the numerator and denominator. By using fraction bars or bar models as opposed to the traditional “pizza” model, students are better able to visualize the problem and make the connection between the concrete and the abstract.
Singapore Bar Models are used for more than just solving fraction problems. Beginning in second grade, students are learning how to solve a variety of word problems using the model drawing strategy. Parent workshops will be held during the month of October to share with you the ways in which you can help your child use model drawing strategies to solve problems by developing algebraic thinking skills.
In the meantime, can you solve the following fraction problems? Send me your answer as a “comment” along with how YOU solved this problem. I look forward to seeing many of you at the upcoming workshops – the dates and times will be announced later this week.
EX #1 (Grades 3-5): Terra’s monthly allowance is $48. She puts ½ of her allowance into savings and gives ¾ of the remaining money to a local charity. How much money does Terra have left for herself each month?
EX #2 (Grades 6-8): When Erin and Amy went shopping, they started with a total of $91. Amy spent $25 and Erin spent 3/5 of her money. At that point, Amy realized her remaining money was 3 times Erin’s remaining money. How much money did Amy have when she started shopping?