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My students love these things

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I also am guilty of teaching invert and multiply in my seventh grade classroom.  Since it was a skill that was already supposed to be taught,  I did not spend the extra instructional time reteaching the division conceptually.  I personally notice students having a hard time recognizing that a fraction division problem is asking me to divide.  Drawing a model is the only way the problem makes sense.   When I taught sixth grade math, my students would only "keep change flip" when the problem was not a word problem, otherwise they drew a model.  What I find most difficult is bridging the gap between the concrete representation and the algorithm.

-Mallory

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I agree that students need real-world context and manipulatives to successfully understand fractions.  Using manipulatives give students that extra visual they need to understand fractions as well as assist with dividing and comparing them.  I believe students need multiple opportunities to see fractions in different ways which will increase their ability to use fractions in many ways.

Lakeya

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I often find myself  reteaching the “invert and multiply” method that was taught in fourth through sixth grade, but after having completed the assigned readings for this week, we can see now how this is not the most effective and beneficial choice.  According to Van de Walle, Karp, and Bay-Williams (2013), they suggest using conceptual examples and models that build on students’ prior knowledge of division with whole numbers.  By implementing one of their methods (measurement, partitive, sharing the whole and repeating fraction) students will have a better understanding and really know why they are breaking certain numbers apart.

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In order to teach “invert and multiply,” students must have a highly developed form of number sense that entails an ability to identify the numerical value associated with small quantities.  If students have a poor number sense, it directly interferes with learning algorithms because it prevents students from using strategies to verify if their solution to the problem is reasonable.  Often many students do not understand why dividing fractions produces a larger answer.  It is through the use of real-world contexts and manipulatives that students will find success when moving from using models to reasoning with fractions.

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You made an excellent point when you said that students do not understand why dividing fractions give them larger numbers. They need to have the understanding of what it means to divide by a fraction, like if they were asked to divide six by 1/2, it means 'how many 1/2's are there in six. Using the picture model will help them to see how it works :)

Thanks!
-Elise