Journal Article: Reason Why When You Invert and Multiply

In the article "Reason Why When You Invert and Multiply", Tina Cardone discusses the importance of children understanding why inverting and multiplying is used when dividing fractions. This relates to the mathematical practice #7 about making use of structure. Students must understand the structure division and fractions separately first, before applying them together. The author discusses various way to go about dividing fractions. Her examples include both dividing whole numbers by fractions as well as dividing fractions by fractions. After one example Cardone (2015) says,  "In this case, students discover that multiplying by the reciprocal is the equivalent of getting the common denominator and dividing the numerators." This clearly relates to mathematical practice #7 because it shows the need for students to use and understand math structures. Students tend to just memorize rules and strategies, but that is not always helpful to their learning. Many rules are forgotten or misinterpreted as students move through their math career. Understanding structure will help them to achieve higher.

Cardone, Tina. (2015). Reason why when you invert and multiply. Mathematics Teaching in the Middle School.