| Summary: | There is a consensus that 21st century citizens need competencies such as flexibility, creativity, critical thinking, taking different perspectives, and considering multiple solutions for which number sense and mental calculation flexibility play a crucial role. Number sense implies to know numbers and its relations with two central characteristics: (i) progressive development throughout schooling; (ii) global character, implying knowledge about numbers and operations and their flexible use in making mathematical judgments and solving problems. Mental calculation flexibility involves to know how to use dynamically number sense, number patterns and being attentive to problem characteristics to achieve a solution, which, in turn, depends on students’ knowledge of numbers and operations and their relations and how they are able to create a network of number relations. This chapter discusses those interrelations based on relevant literature and illustrated by data from Portuguese elementary school. Through data analysis of excerpts of students’ resolutions of open tasks and the respective discussion, the data illustrates the relevance of constructing number relations and how the teacher’s role, particularly the teacher’s actions in whole class discussion, can create a classroom environment conducive to the development of both number sense and flexibility in calculation.
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