One of the primary works of the secondary mathematician is building functional fluency. NCTM describes “representation” as referring to both a process and a product. So mathematical representations include all the different ways that students depict their thinking as well as the processes they use to put their thinking into those forms. Representations have often been taught as an end in and of themselves, most as essential elements in supporting students’ understanding.
When students gain access to mathematical representations and the ideas they express they acquire a set of tools that significantly expand their capacity to model and interpret physical, social, and mathematical phenomena. The linear activity takes linear functions, with the same domain set, and represents them through verbal, tabular, graphical, symbolic, and set representations. There is also a contextual problem for each for the students to work through. There are six sets of cards, each with 6 representations with facilitation notes. The quadratic activity takes quadratic functions, with the same domain set, and represents them through verbal, tabular, graphical, symbolic, and set representations. There are six sets of cards, each with 5 representations with facilitation notes.
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