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The first take-away that I had from this article was exactly number sense is. Number sense is the construction of a set of relationships that happen between the three worlds in mathematics. The three world are quantities, counting, and formal symbols. For students to be able to successfully gain number sense, they need opportunities to discover and construct the relationships between the three worlds at a more complex level. Being able to master these relationships and use them in learning and teaching math, causes both the teacher and the students to have more deeper connections to mathematics. Having this connection, especially the younger the student, will cause them to understand math at a level that is needed once the material starts to get harder and more complex.
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The first instructional principle was, rich-activities for making connections. This instructional principle is where students are exposed to the three distinct worlds of math (quantities, counting, and formal symbols) and how they are connected. The second instructional principle was, exploring and discussing concepts. In this instructional principle, students explore the concepts of math and then turn around and discuss those concepts learned in a social context. The last instructional principle was, ensuring an appropriate sequence of concepts. In this instructional principle, students are exposed to concepts in a grade-appropriate manner that allows them to grow instead of being too complex for the

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