In this work, we approach the theme Polynomials that is inserted in the curriculum of the third
grade of High School. In general, this topic is reserved to be presented to the student in the fourth
quarter of the school year. Thus, due to the large volume of content proposed, this important topic
often ends up being exposed inefficiently. In order to provide support material to the teacher and
to provide the student with interest / motivation for the theme, we present several applications,
involving from nature and day-to-day problems, more elaborated themes such as higher order
arithmetic progressions to themes more advanced features such as polynomial interpolation
and curve fitting. In addition, as an increase in the support material for teachers, we propose
a methodology involving polynomial interpolation, more precisely, the Lagrange interpolation
formula. The methodology is divided into 5 (five) classes, each with its specific objective, for
example, in the third class, we propose an activity related to the construction of symmetrical
figures using the Lagrange polynomials.
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