Fraction talks developed as a way to use the Number Talk routine to target fractions. A growing body of fraction talks are available at fractiontalks.com.
I’ve created a writeup below for how to use fraction talks, as well as a collection here which are ideal for introducing fraction talks to students early in their understanding of fractions, and then continuing in slowly increasing levels of difficulty.
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After processing whether or not if the green shaded region of the first example is 3/4 or 3/8, an interesting follow-up question to pose is “What is 3/4 the correct answer to?” [3/4 of a 1/2 piece or 3/4 x 1/2]. Consider then posing the question to the class, “Is 3/4 of a half piece the same as having 3/8 of the whole piece?” [Write out the equation, 3/4 x 1/2 = 1/8 x 1] “Is that true or false?” I have been experimenting adding the “x 1” to help students – and the adults with whom I do p.d. – that one way to envision multiplication of fractions is through the re-unitizing of the first mathematical expression [3/4 of a 1/2 piece or 3/4 x 1/2] to the whole unit [x 1]. The area shaded green to the unit of one-half is compared [=] to the unit of the whole [x 1]. The eye just shifts from unitizing it from the one unit to the other. The area does not change; just the unit referent. This work grows out of my using some materials from Susan Lamon (2015).
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Great thought, James. Changing the unit is a fantastic way to extend and deepen the conversation.
HI Jim! Happy to see your name here and eager to share ideas about fraction talks with the teachers I work with.
RCA