Fractions are one of the hardest mathematical concepts to teach students for several reasons. The biggest is that students often cannot conceptualize what a fraction is despite being surrounded by fractions in their everyday lives. While some students are quick to grasp what one-half of a gas tank is, four-sevenths of something is totally out of their understanding. There is nothing in their world to compare it to, so they don’t have the schema to make sense of what they are seeing or what is being represented by the fraction. Plus, fractions are often taught as just numbers without real world examples connected to them which makes it harder for students to understand. Additionally, students often find it difficult to remember what each part of a fraction is and what a fraction does. For example, students need to recognize that the numerator is the number of parts you have of a whole while the denominator represents the whole unit. Another aspect of fractions that is challenging for some students is the fact that there are so many rules involved in using them mathematically. For example, when you add fractions you must first find the common denominator but you don’t need to do that when multiplying or dividing fractions. So much to put together!
Yesterday, my goal as a tutor was to help my student conceptualize fractions. To make things fun while still driving the point home concretely, I brought in the makings of s’mores. Before breaking out the food, we went outside and played a few games of foursquare. We began by drawing out a large box with chalk on her driveway, which allowed me to teach the difference between a whole number and a fraction. Then, I had her divide the court first into halves and then into quarters which allowed me to kinesthetically teach how two halves and four quarters can equal a whole. With that basic information mastered, we went inside and used the food to drive home the point of what numerators and denominators are. The graham crackers were perfect for teaching fourths while the Hershey chocolate bar was great for teaching the more complex fractions of sixteenths. We began small with the graham crackers. I asked my student to write a number and a fraction to represent the graham crackers because I wanted her to see that one cracker equaled four fourths. Once she had grasped this concept, I had my student break the food into fractions to help her solve simple math problems that I posed to her. You could see her understanding grow with each tactile interaction with the food. Then, I introduced an extra large chocolate bar with twenty sections to allow us to complete problems with different denominators to show why you need to have a common denominator to add fractions. Finally, to ensure she thoroughly comprehended the material, I sent her out into her home to bring me examples of fractions in her everyday life. In the kitchen, she found a set of measuring cups. In the living room, we talked about how the number of window panes could be represented by fractions. In the end, we celebrated and reviewed her newfound understanding by noshing on the chocolate, Graham Crackers, and marshmallow and reviewing the material we had learned. It was a suitable reward for mastering a difficult concept.
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