In the 1980s, A&W, an American restaurant chain, unveiled a new menu item– a third of a pound burger meant to rival McDonald’s popular Quarter Pounder. After creating an expensive marketing campaign and a fan-fare filled roll-out, the A&W’s third pound burger failed. It was only after soliciting feedback from their focus groups that A&W executives began to understand why. The American public believed the third pound burger to be smaller than McDonald’s quarter pound burger. Misunderstanding the four in one-fourth to be larger than the three in one-third caused Americans to believe that A&W was cheating them out of their money by charging a price for the burger that did not equal the value.
This story speaks volumes about how fractions are perceived by students and adults alike. It’s imperative that our students learn to understand fractions in the same way that they understand numbers in other forms. For this reason, today’s activity will focus on comparing fractions by reasoning about their sizes.
This activity addresses the following Common Core State Standard for Math:
3.NF.A.3.D- Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Specifically, this activity addresses comparing fractions by reasoning about their size. Development of this skill begins with a conceptual model. When presented with a variety of visual fractions, students begin to understand that the more pieces the whole is partitioned into, the smaller the value of each piece.
Here’s an example:
This is a great visual to pose the question “What do you notice?” and then chart the students’ responses on chart paper. After exploring with fractions for enough time, students will begin to make connections and discover the relationships between fractional parts.
It’s important to actual have students build a fraction wall with fraction tiles or have them create their own with markers or colored pencils. This way, they have a reference tool they can refer back to so that they continue to reason and make conjectures about the size of various fractions.
From the model, students develop the idea that the smaller the denominator, the larger the part and vice versa. Students can also make connections about the relationships between fractional parts, such as two one-eighth pieces equal one one-fourth piece.
This is also a good time to explore comparing fractions with the same numerator. For example, four-fifths is greater than four-sixths because equal parts that are each one-fifth are larger than equal parts that are each one-sixth.