| Summary: | We investigate how the algorithms of the division of natural numbers are approached in didactic books of Mathematics of the initial years of elementary school, we mapped activities in which they are approached; and we analyze the use of division algorithms in partition and quotation situations. Were analyzed a total of 104 proposed division activities in six collections, randomly chosen, approved by the PNLD of 2016. With a quantitative-qualitative approach, we use as the analytical method of activities the thematic analysis procedures. The data show that more than 84% of the activities explores the process of the conventional algorithm. We identify the absence of activities that address the algorithms in the 1st and 2nd years. The algorithms of the division begin to be explored from the 3rd, usually by means of exact division, and long processes involving successive estimation and subtraction. Some collections present activities that stimulate the construction of arguments and reflection on the strategies used with the use of alternative algorithms by the students, as well as reflection on the decimal numbering system.
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