This paper proposes an approach to teaching algebra in the first year of high school using the Portugol programming tool to solve problems in the workbook of the structured teaching system of the state of Mato Grosso, Brazil. The study aims to demonstrate the direct link between algebra and programming, while also introducing an essential skill for the future. The use of Portugol allows students to better visualize and understand algebraic concepts, making learning more dynamic and engaging. In addition, the experience promotes greater participation in the classroom, arousing students’ interest in mathematics and programming.

This dissertation focuses on approaching financial mathematics in a contextualized way in the classroom and recognizing the importance of mathematical modeling in financial life as crucial, as it allows practical situations, such as financing, to be translated into mathematical language.  To this end, this work aimed to carry out a comprehensive study of financial mathematics, from basic concepts such as percentages, simple and compound interest, to a detailed explanation of the mathematical models that make up the SAC and PRICE amortization systems. It also sought to promote understanding of these contents by solving problem situations in the classroom, contextualizing their relevance to the students' daily lives. Based on the methodological assumptions of bibliographical and qualitative research, according to Marconi and Lakatos (2003) and Gil (2002), the data was produced through detailed explanations of the content covered and the application of contextualized activities in a private school. This process was carried out with two 1st year high school classes, located in a municipality in the north of the state of Mato Grosso. After the theoretical part of each stage of financial mathematics, the test was divided into two stages. In the first stage, seven questions were asked about percentages, simple interest and compound interest; in the second stage, five more questions were asked about the SAC and PRICE amortization systems. In addition to administering the test, at the end there was a dialog between the students and the teacher about the experience, which led to debates and pleasant exchanges of ideas about the content studied. By presenting the concepts of financial mathematics in a contextualized way and related to the students' lives, the learning process became significantly more engaging and effective. This approach facilitated not only the theoretical understanding of the content studied, but also its practical application. The contextualization of the topics allowed the students to see the relevance of what they were learning and how this knowledge could be applied in real situations. In this way, contextualization aroused students' interest in studying mathematics. As a result, financial education was enriched, better preparing students to deal with financial issues in the future and refining financial mathematics, generating tools that allow students to make informed decisions.

The main objective of the research described here was to develop a meaningful, engaging and playful teaching material on the topic of “prime numbers”. The material, intended for students in Basic Education, was developed based on theoretical and practical aspects present in the literature in the area. The research methodology adopted initially consisted of an exploratory bibliographic review, with the objective of gathering the theoretical framework necessary for the development of the proposed material. With the theoretical framework in hand, the almanac “Leãozito: The Mysteries of Prime Numbers” was created. In addition, a software (for Windows) capable of performing primality tests using the Sieve of Eratosthenes and Brute Force methods was designed and implemented in the C/C++ programming language. The software, called Primus, is intended to provide real-time feedback to students and teachers about the primality of numbers of interest. The software is also capable of generating lists of prime numbers and composite numbers. Once the almanac was in hand, it was used in 7 high school classrooms at the São Vicente de Paula State School in Sinop, Mato Grosso. The impressions of the 143 participating students about the material were collected through an evaluation questionnaire. The data were analyzed from a qualitative point of view, according to the content analysis recommended by Bardin (2016), and from a quantitative point of view, using Descriptive and Inferential Statistics. The analyses were effective in validating the material, given its acceptance. It can be inferred from the research that the implementation of innovative methodologies can significantly improve student engagement and their understanding of the topic.

This thesis presents the development of a didactic sequence involving the mathematical content of trigonometric ratios, using the “GeoGebra” software. The main objective of the thesis is to provide a dynamic and attractive didactic sequence for students, making them interested and involved in the proposed activities. The objective of the sequence was to contribute to the students' learning process as an introduction to trigonometry content, as well as to assist mathematics teachers in teaching trigonometry. The didactic intervention happend at Escola Estadual Jardim Universitário, in Alta Floresta city, in a $2º$ year high school class and was developed in the first two-months period of $2024$. The evaluation of the thesis was supported by qualitative research, using as an instrument of Data collection, observation and sessions focused on students' attitudes towards developing the proposed activities. The sequence was structured into five activities, one introductory, three teaching trigonometric ratios and one evaluative. During the activities we encountered some difficulties and some surprises, however we managed to conclude with a positive result. We managed to get students to be active in class, asking questions, questioning and solving activities, things that did not happen in previous math classes.

This paper presents a collection of Experimental Activities of the Mathematics Curricular Component (CC) of the 9th grade of Elementary School (EF), in line with the contents contained in the Structured Material adopted by the State Department of Education - SEDUC/MT. Two methodologies were used to obtain the data: interviews with teachers of the Mathematics CC of the 9th grade of Elementary School of the 9 urban schools of the municipality of Alta Floresta, State of Mato Grosso, and bibliographic research. The purpose of this paper, which contains 18 (eighteen) Experimental Activities, is to help Mathematics teachers make the CC more attractive, demystify it as difficult to understand and consequently collaborate with the improvement of Mathematics indexes in the State of Mato Grosso. For this purpose, an Educational Resource was prepared, in the form of a Booklet, which will be disseminated and made available to teachers.

This work reports a research involving students of the second year of High School in a public school in the municipality of Sinop-MT, in which the Mathematics teacher proposes an activity developed in the classroom involving Mathematical Modeling contextualized as an active methodology through theory of Learning Curves. Such theoretical contributions were inserted so that the activities of games such as the game of Cards, Puzzles, Rings and the online game Tap Tap Dash presented themselves as a real situation performed by the students, connecting such games to contents present in the curriculum of Basic Education mathematics, through Mathematical Modeling, transforming these activities into a teaching and learning environment. The activities were planned in such a way that the students participated actively, from data collection to the analysis and interpretation of models that describe learning curves using the mathematical software Geogebra. As a result, we came to the conclusion that the environment provided by Mathematical Modeling was able to make students learning meaningful. This is justified through the students speeches and also through the experience we had with this research, so that we could see that Modeling associated with the use of technologies in the classroom boosts students learning by motivating them and instilling in them curiosity, generating more dynamic and effective learning.

This dissertation presents a didatic sequence for learning Mathematics, using photovoltaic panels as a topic of study. We will briefly discuss the importance of using active methodologies such as Project Based Learning (ABProj) and Mathematical Modeling, which bring significant benefits to the studentes, allowing them to develop skills and competencies needed to meet the challenges of today's world, while making the process of learning mathematics more engaging and meaningful. A mathematical modeling work was carried out with a central theme related to photovoltaic panels with the objective of modeling the angle of inclination of the plates' installation, for the maximization of the luminous energy flux and thus obtain higher energy production. Based on the model developed, didactic sequences and activities are proposed to be used in elementary and high school. In this sense, this work proposes through Project Based Learning (ABProj) and Mathematical Modeling, that the student uses mathematics in a concrete and satisfactory way, enabling analysis, discussion, construction of concepts and formulation of ideas through the resolution of everyday problems, contributing to meaningful learning.

This work is the result of a didactic action experienced in the Professional Master's Program in Mathematics in National Network - Profmat of UNEMAT - Campus of Sinop. The present study involves students in the third year of high school at a state public school in the municipality of Sorriso, in the state of Mato Grosso, in which the Mathematics teacher proposes an activity developed in the classroom involving Financial Education. In which the proposal is based on meaningful learning in order to contribute to the student's training and that they collaborate in the organization of family budgets, specifically in the acquisition of assets, which can be a property, adding their financial resources in purchases of products and services in a way conscious. Family budget control assists in making financial decisions, contributes to reducing debt and to the possibility of acquiring goods. Studying Financial Education allows students to acquire knowledge about financial concepts and products, developing in them an awareness that unplanned actions can subsequently impact their quality of life. From this perspective, the work aims to elaborate and experiment with a pedagogical proposal, using Financial Mathematics for students of the 3rd year of High School, from a state school in the city of Sorriso in the State of Mato Grosso. The research will be qualitative participant, using a case study and methodologically will be worked through a guideline problem that will involve the acquisition of a consumer good chosen by the students, which may be the acquisition of a property or a consumer good that requires the student needs to research the best way to acquire this good, leaving it to the discretion of the group of students what will be researched, presenting situations that involve the budget and family expenses, thus encouraging the habit of saving to be able to invest in the achievement of goals, specific knowledge about interest rates for real estate financing and develop a critical view on which is the best investment.

The present work starts from a personal quest to try to understand how to teach and how to make learn those who in some way in my opinion should be better taught in this country. I am referring here to the indigenous peoples for being the first Brazilians who lived here when the country is said to have been "discovered", after this fact the life of freedom of the indigenous peoples was transformed, in goals that were never theirs. Today more than half a millennium they still live the goals set by other peoples and to maintain their cultures, traditions and preserve nature, they need knowledge that goes beyond the ethnic knowledge that their ancestors passed on to them from generation to generation. To obtain this knowledge, it is sought in other cultures to learn new languages and new knowledge, within this mathematics is present with all its rules and concepts and that for a majority of people becomes complicated to learn, even when it is taught in the very language in which we were raised. The present work presents a research of the action-research type, where it is proposed to know and test better how to do the act of teaching and learning indigenous students who attend urban schools, where their culture, customs and language of origin are not taken into account. These are steps and processes that are applied and observed the income of the respective students, to describe in this work the results obtained. For this, it was necessary to study the problems of school learning for students of ordinary schools, that is, of non-indigenous students and compared to the learning processes of the indigenous people in question here.

This work focused on the implementation of the "comics" teaching methodology and the Scratch software to create digital comics, in a second year high school class, in a public school. Initially, the intention was to strengthen mathematical concepts through this application. However, many students adopted a more expressive approach, focusing on storytelling. Although the project did not fully achieve its initial goal of improving students' understanding of mathematical concepts, as many students adopted a more expressive approach focused on storytelling, it generated several benefits. It provided a stimulus for students' creativity and the development of narrative, design and critical thinking skills. It allowed students to express feelings, particularly regarding test anxiety, suggesting the potential of the methodology to promote well-being in the classroom. This led me, as an educator, to rethink my teaching practice and realize the importance of not focusing exclusively on learning mathematical content, but also adopting a more humanistic perspective in the classroom. This application also encouraged project-based learning, which increased student engagement and motivation. The experience gave the teacher an opportunity to reflect on their teaching practices and find new ways to achieve pedagogical goals, including adjusting the focus of mathematics according to the students' interests. Additionally, by using Scratch, students have developed digital skills and 21st century competencies. In summary, this dissertation highlights the importance of innovative teaching methods and suggests that other similar experiences can be useful for educators who seek alternative teaching methods. The research also paves the way for greater integration of technology and mental health into the school curriculum.

Linear programming emerged from several contributions, still in the first half of the 20th century, and played an important role in the context of the second world war, enabling a better use of limited resources.Its use can occur in different sectors such as military, industry, commerce, education, health, etc.It is a mathematical optimization tool that aims to reduce the consumption of resources or increase the performance of services, subject to restrictions on the variables and relationships between them.The modeling of a linear programming problem considers that both the function to be optimized and the restrictions imposed have a linear behavior in each variable.One application of linear programming methods is Data Envelopment Analysis (DEA), which emerged at the end of the 1970s, through the work of Charnes and his fellow researchers, which provides a model for comparing companies, sectors, agencies, etc.itself, analyzing the individual efficiency of each unit (Decision-Making Unit - DMU), based on information on the level of use of inputs (inputs/imputs) and obtaining results or products (outputs/outputs).This work initially aimed at the elementary study of these two tools, in order to enable their computational implementation in relatively easy access software.Thus, in order to understand and apply the concepts studied, referring to the Simplex algorithm used to solve a Linear Programming (LP) model, as well as to enable the presentation of the method's iterations to future interested parties, the construction software was chosenof spreadsheets "'Calc"' which is part of the package "'LibreOffice"' and is distributed free of charge.For the implementation of the Simplex algorithm, the logic functions of this software were mostly used, making it possible to display each step of the algorithm and its iterations.At another time, the tool "'solver"', available by the software, was used, which allows, quickly and directly, the resolution of a LP model, from the input of information in a spreadsheet.With this, a spreadsheet was built, adapted to a DEA - CCR model focused on Imputs, through which it was possible to simulate applications, using educational indicators from ten states of the federation, finding reference units for each DMU analyzed, as well as desired levels of inputsthat lead to the established efficiency.The spreadsheet obtained, used as a simple analysis tool, can be important in the process of learning to use this method, in comparison with results presented in texts in the area, and in applications with a limited amount of inputs and products.

The study presented aims to identify the fraction learning objectives that make up the
activities of a collection of textbooks from the sixth to the ninth year of elementary
school and make use of them to prepare a complementary proposal that aims to
contribute to its improvement following the taxonomy of Bloom revised. The contents
related to the fraction were analyzed, as it is a topic addressed in various stages of
elementary school, in addition, research such as that of Silva (2005, p. 112), show the
difficulty of teachers in the early years in approaching this subject, stating that there is
a gap between the teacher's knowledge, content and way of teaching and learning.
Another factor is the poor performance of students in external assessments of the
Basic Education Assessment System – Saeb (Prova Brasil) in terms of fractions.
During the work, it was possible to perceive the importance of verifying which learning
objectives a textbook is meeting according to the revised Bloom taxonomy and if they
are in line with the intended skills in the National Common Curricular Base - BNCC.
Bloom's revised taxonomy was used as a reference for analyzing the activities included
in the selected book collection, which resulted in a report. In short, it was identified that
some dimensions of the cognitive process are not addressed while others appear in
greater numbers. It was proposed for each skill related to the theme, complementary
activities that contemplate all the dimensions of knowledge and the cognitive process
of Bloom's taxonomy. This work can be a methodological alternative for teachers in the
analysis of activities, collaborating with the learning process and that is in accordance
with the goals outlined by the teacher.

The study of functions is essential in the teaching and learning process, as it is an integrative content, which makes it possible to relate everyday activities with mathematical content, thus allowing the study of the behavior of phenomena both in everyday life and in other areas of knowledge. In this sense, this work aims to present some proposals for practical activities for teaching functions. Each activity (problem - situation) will be modeled through curve fitting and, for this purpose, this work suggests the use of GeoGebra, wxMaxima and Least Squares Method software. The suggested activities are: (i) to present some possibilities of mathematical models applied in civil construction; (ii) approximate the sine function in the interval of a by means of a polynomial function of degree five; (iii) find a quadratic function that represents the interdependence between space and time variables from an experimental activity called “Free Fall”; (iv) estimate the value of the gravitational acceleration at the place of application of the "Free Fall" activity and (v) estimate the maximum height reached by a ball, and the distance traveled by the ball in relation to the horizontal axis (ground) through of the “kicking a soccer ball” experiment. The teaching approach, on the use of the Least Squares Method, will be given so that the teacher is free to choose the best way to deal with the topic with the students, whether through an algebraic matrix treatment, linear systems or electronic spreadsheets, for example, according to the reality of each class.

This work was developed through a literature review to discuss new ways of exploring mathematics in high school, relating some problems as new technologies and with a theme linked to the environment. In order to present a complement in the teaching process, this work has as main objective to present to the teachers an attractive way to approach content. In this sense, a study on the main aspects of the BNCC, its origin and how its implementation contributes to the teaching process, a theoretical review follows with a presentation of a brief history of geometry, linking the origin of Euclidean Geometry to the emergence of Fractal geometry, finally are sets of four sets of activities divided by themes, all sets of activities about Fractal Geometry. As activities encompass an exploration of the GeoGebra software, the use from geometric drawing tools, use of tables, to the use of functions in determining fractal dimensions. A treatment of images of realities focused on the healthy environment. used as a motivational means for the study of different fields of mathematics.

This work deals with the application of Mathematics as fundamental tool for processing of images captured by satellite. In these terms, the objective of this work was to develop a free software that could carry out image fusion process via the IHS fusion method. Such software, implemented in C / C ++, was based on image rectification algorithm that incorporates collinearity equations (Projective Geometry). Therefore, changes were made in the referred algorithm and in collinearity equations in order to generate the referred software. In this case, the modified image rectification algorithm was used as a multispectral image resampling tool. The input images were from the Sino-Brazilian satellite CBERS 4. Multispectral images (R, G and B) from the MUX sensor - Regular Multispectral Camera, with 20 m spatial resolution, and panchromatic image from the PAN sensor - Multispectral and Panchromatic Camera, with a spatial resolution of 5 m, were used. Using the QGIS software, two cutouts were made on CBERS 4 images. The cutouts were used in tests and related to the regions of Ilha Solteira and Engenheiro Souza Dias (Jupiá) reservoirs, located between the states of São Paulo and Mato Grosso do Sul. The results (fused images), after being submitted through the contrast enhancement process, are defined as satisfactory, indicating research success.

This work describes a didactic proposal for the study of geometric concepts of areas of irregular flat figures, seeking to involve social and environmental issues surrounding the region in which the student is located. This is a bibliographical research, with which it subsidized the construction of a didactic path that makes it possible to achieve a more meaningful learning development. In this way, trying to contribute in the way of minimizing possible gaps that exist in the teaching and learning process of geometry, especially in the area of flat figures. In its development, research and image analysis of areas of our national territory is proposed, determining these areas through Pick's Theorem and thus comparing the results with the available legal records. Therefore, this work seeks to present contributions in the approach of the concepts that cover the referred theme and providing an awareness of the problems caused in recent times in our environment and in some regions. We believe that this proposal can provide students with not only memorizing concepts and using them mechanically, but also developing skills and abilities necessary for their socio-environmental and intellectual independence.

Talking about financial mathematics and financial education in public schools, a topic that is rarely addressed in regular high school. Even though it is of great importance to any individual. Knowing that there is increasingly easier access to credit, whether through credit card, financing, overdraft, among others available on the market. The lack of knowledge of these items unbalances personal finance, enabling knowledge of basic math concepts such as percentage, simple and compound interest, interest rates, amortization and other relevant related to basic economics. These themes are of fundamental importance for the financial future of our young people, compromising their salaries by acquiring debts can compromise their planning, being aware in the present guarantees better periods for the future. To train citizens who are increasingly capable and aware of the risks of managing their earnings, making decisions that are increasingly clear and correct. The purpose of this study is to promote Teaching-Learning through Problem Solving by presenting a material that can contribute to the formation of the student, in addition to didactic work for the mathematics teacher, we seek through Problem Solving the structuring of a material that can help in the construction of knowledge about financial mathematics together with regular high school teachers, contributing and promoting content in the classroom. In addition to enabling a reading of the reality about financial mathematics, in order to develop a critical sense when we talk about decision-making in our financial life and nothing better than facing these decisions with a broader view. However, it is necessary to ensure that important concepts for a critical view of their reality and financial situation are developed so that students can analyze, plan and organize their financial lives.

This research focuses on Financial Education in Schools and seeks to explore the concepts of financial mathematics and financial education, in order to work them together through didactic sequences and presenting some models of household budgeting, a topic that we have already heard about, but which maybe we don't know what it really is, or we've never even made one. Our study has as main objective to investigate what knowledge a group of high school students, from a private school, in the city of Sinop-MT, has about Financial Education. The Common National Curriculum Base (BNCC) in 2017, brings them in their skills and abilities in elementary and high school, thus, our work will be a qualitative research, where we will work didactic sequences, involving problem solving and mathematical modeling, to thus we discuss the concepts of financial mathematics and financial education. We used as a guide for activities the financial education books at school, approved by the MEC and made available on the National Strategy for Financial Education (ENEF) platform, some activities were adapted according to the proposed content. We seek to discuss the importance of financial education at school, and the contents of financial mathematics, already covered by the teacher, such as Percentage, Simple and Compound Interest, then, through problem situations and models suggested by the teacher, we address issues about decision-making, organization , simulation of a budget, relevant issues to be able to improve the management of personal finances, seeking to develop a conscious consumption.

This work is linked to the Professional Master's Program in Mathematics in National Network – PROFMAT of the University of the State of Mato Grosso – UNEMAT, University Campus of Sinop, and aimed to understand how mathematical modeling is used in the study and description of the advancement of Covid-19 pandemic in Mato Grosso using the SIR model. This research sought to answer the following questions: how is the study of the dynamics of infectious diseases carried out using the SIR model? How to transpose the understanding of the SIR model and the infection dynamics caused by Covid-19 to high school students? To help reflect on these issues, the theoretical framework assumed includes notions about Mathematical Modeling and mathematical models based on authors such as Rodney Carlos Bassanezi, Maria Salett Biembengut, Jonei Cerqueira Barbosa, Dionísio Burak, João Frederico da Costa Azevedo Meyer, and many others; with an emphasis on the description of the modeling process, as well as on the strategies and difficulties in its adoption as a teaching methodology. In addition, part of the theoretical framework was intended to elucidate some concepts involving rate of change and differential equations, aiming to support the methods adopted in the study process of the SIR model and based on the contributions of Rodney Carlos Bassanezi and Wilson Castro Ferreira Junior, William E. Boyce and Richard C. DiPrima, James Stewart, among other authors. The research had a quali-quantitative approach being forwarded through a descriptive-explanatory study. The research object was the Covid-19 dynamics in Mato Grosso until the end of January 2021 and the data were collected from the interactive panel provided by the Mato Grosso State Health Department - SES/MT, which were organized in Excel spreadsheets. To model the data, the discretized SIR model implemented in Excel was used, and the infection parameter was obtained by minimizing the squared error function from the real data and the simulated data using the Solver tool. Three approaches were used to obtain the infection parameter: 36-day intervals with the addition of the previous intervals; 36-day intervals without adding the previous intervals; 7-day intervals without adding the previous intervals. The research findings show that in the dynamics of infection caused by Covid-19 through the SIR model, the population can be divided into three compartments: susceptible, infected and removed; where the objective is to identify the number of individuals that move from one compartment to another per unit of time. The adoption of different intervals in the square error minimization process proved to be very relevant for understanding the dynamics and favored different projections of peak and maximum infection values based on consolidated data up to the end of January. At the end of the study, a didactic proposal is made to be worked on with the students of the third year of high school based on mathematical modeling. The problem is initially generated by the teacher and the other steps will be conducted by the students.