Uma ferramenta didática para ajudar na fixação dos conceitos introdutórios de análise combinatória

Humans, as well as some animals are born gifted with the ability to perceive quantities. The needs that came from the evolution of societies and technological resources make the the optimization of such counting methods necessary. Although necessary and useful, there are a lot of diculties in the teaching of such methods.In order to broaden the range of available tools to teach Combinatorial Analysis, a owchart is presented in this work with the goal of helping the students to x the initial concepts of such subject via pratical exercises

Uma proposta alternativa para o ensino progressões relacionadas a funções

Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

O estudo das funções quadráticas e sua relação com o cotidiano

Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited

Sistema de numeração posicional e a lógica da divisão de inteiros

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Probabilidade no ensino médio

This thesis aims to show teachers and students in teaching and learning in a study of Probability High School, a subject that sharpens the perception and understanding of the phenomea of the random nature that surrounds us. The same aims do with people who are involved in this process understand basic ideas of probability and, when necessary, apply them in the real world. We seek to draw a matched between intuition and rigor and hope therebyto contribute to the work of the teacher in the classroom and the learning process of students, consolidating, deepening and expaning what they have learned in previous contents

Função Afifim: Teoria e aplicações

In this work we present a proposal to contribute to the teaching and learning of affine function in the first year of high school having as prerequisite mathematical knowledge of basic education. The proposal focuses on some properties, special cases and applications of affine functions in order to show the importance of the demonstrations while awaken student interest by showing how this function is important to solve everyday problems

Um estudo dos sistemas de amortizações SAC e francês no ensino médio apoiado na construção de planilhas Eletrônicas

The aim of this work is to provide a text to support interested in the main systems of amortization of the current market: Constant Amortization System (SAC) and French System, also known as Table Price. We will use spreadsheets to facilitate calculations involving handling exponential and decimal. Based on [12], we show that the parcels of the SAC become smaller than the French system after a certain period. Further then that, we did a comparison to show that the total amount paid by SAC is less than the French System

Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

Área e volume da esfera

In this dissertation, we present a study on the teaching of volume of the sphere and the area of spherical surface. On this topic, a quali-quantitative was taken survey with the objective of identifying how these topics are addressed. For this, we made 14 questions to 30 teachers of Natal and the results of this survey are presented and discussed. After that, we present alternative ways to derive the formulas of the volume of a sphere and the are of a spherical surface

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

Equações de segundo grau e mudança de variáveis

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom

Desenvolvendo e gerenciando compostagem de resíduos sólidos urbanos: para geração de renda e repasse de tecnologia à acrevi

Nowadays, as well as in the past decades, the dumping of biodegradable organic waste in landfill is common practice in Brazil, as well as in most parts of the world. Nevertheless due to its rapid decomposition and release of odors, this practice hamper’s the operation and implementation of a recycling system. These facts encouraged our research to find an efficient system for the management of organic waste, not only for the use of official workers responsible for managing these wastes, but also for non-governmental institutions. The Recycling for Life Community Association – ACREVI (Associação Comunitária Reciclando para a Vida), together with the municipal authorities of Mossoró-RN, Brazil, have assumed the social role of collecting and recycling solid waste produced by most of the local population. However, it was observed that the organic waste it collected was not receiving any treatment. This present work aims to make compost with mixed waste (green waste and organic household), and then do chemical analysis of the material in view to use the waste as organic fertilizer. The objective being: to share the knowledge acquired by putting it into a very simple language accessible to people with little education. The experiment was conducted at ACREVI, Mossoró (RN), and the compost was obtained following the method "windrow", forming three cells (I, II, III) with conical shape, dimensions of 1.6 meters and 2.0 meters in diameter for cells I and II, and 1.0 meters high and 2.0 meters in diameter for cell III. The process was accompanied by analysis: CHN elemental, a variation of cell temperature, humidity, pH, TKN, bulk density, nutrients and heavy metals. Stabilized organic compounds reached the C/N ratio of 10.4/1 cell I and 10.4/1 in the cell II in the cell, showing how good soil conditions, with potential to improve the physical properties of any soil and pH acid soils, has presented the cell III at the end of the process the C/N 26/1, is a high ratio may be associated with the stack size III, thus changing the optimal conditions for the occurrence of the process. The levels of heavy metals in the analyzed compounds were lower than those established by the SDA normative instruction, Nº 27, of 5 June, 2006. The use of pruning trees and grass are used in small-scale composting, while generating a quality compost in the final process, it also created an important condition for a correct sizing of the composting piles. Under the studied conditions it is not advisable to use cells with a height of 1.00 m in height and 2.00 m in diameter, as these do not prevent the rapid dissipation of heat and thus can not be a good product at the end of composting. The composting process in the shed of the association and the preparation of the primer enabled the development of an alternative technology to generate income for members of ACREVI.

Síntese, sinterização e caracterização de ferrita de níquel

In this work we obtain nickel ferrite by the combustion synthesis method whcih involves synthesising in an oven at temperatures of 750oC, 950oC and 125oC. The precursors oxidizing used were nickel nitrate, ferric as an oxidizing and reducing urea (fuel). After obtaining the mixture, the product was deagglomerated and past through a 270 mesh sieve. To assess the structure, morphology, particle size, magnetic and electrical properties of nanoparticles obtained the samples were sintered and characterized by x-ray distraction (XRD), x-ray fluorescence spectroscopy (FRX); scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), vibrating sample magnetometer (MAV ) and electrical permittivity. The results indicated the majority of phase inverse spinel ferrite and Hematite secondary phase nickel and nickel oxide. Through the intensity of the distraction, the average size of the crystallization peaks were half-height width which was calculated using the Scherrer equation. From observing the peaks of all the reflections, it appears that samples are crystal clear with the formation of nanoparticles. Morphologically, the nanoferritas sintered nickel pellet formation was observed with three systems of particle size below 100mn, which favored the formation of soft pellets. The average size of the grains in their micrometric scale. FRX and EDS showed qualitatively the presence of iron elements nickel and oxygen, where through quantitative data we can observe the presence of the secondary phase. The magnetic properties and the saturation magnetization and the coercive field are in accordance with the nickel, ferrite where the curve of hysteresis has aspects of a soft material. Dielectric constant values are below 10 and low tangent loss

Evolução termocronológica do sistema de falhas Senador Pompeu-CE

The region of the Senador Pompeu Shear Zone (SPSZ), in the North Tectonic Domain of the Borborema Province (BP), has its recent history associated with to South Atlantic Ocean formation event at the Jurassic. A lot of geologics models have discussed about crustal axis elevation in local scale and large scale (Borborema Province), relative to importants regionals tectonics directions of it. The identification and the relationship among this surfaces, stepped in many topographyc levels by tectonics mecanisms, is dificult because of the erosion process on it. Over there, sedimentary deposits is complex and it has not biostratigraphyc record in continental deposits. The analysis metodology on apatita fission-track, in the region of the SPSZ, purpose the more knowledge about morphotectonics mecanisms of the area and the impruvement of its morphotectonics models. For this, it was moleled the age and thermal history of the 11 apatites samples collected on both sides of this shear zone, taking relationships among other results of the thermochronology studies in the BP. Based on the thermal studies in this search, the region of the BP developed on two distint cooling events, separated for one period of relative stabilited. The first episode occur between 130 and 90 M.y., has been began when the samples cross the 120°C isoterm for last time and fineshed at 70°C. The second moment of the cooling process was began about 30 M.y., when the temperature was 90°C, from this to the equlibrium with present surface temperature at 30°C. Some evidences indicated a relacionship between thermal episodes and uplift events of the regional relief. The fundaments of the interpretation was based mainly on comparatives studies among results of the thermochronology analysis and geologics studies about BP. Nóbrega et al.(2005), e.g., on studies about the Portalegre Shear Zone, got similar results on SPSZ, with some details relative to local tectonic activity. Morais Neto et al. (2000) interpreted two importants cooling events in the BP based on their regional studies, that can be associated to regional uplift events. When Assine (1992) studied the stratigraphyc sequences of the Araripe Basin, in the south of Ceará state, conclude that the abrupt return to continentals condictions from the last sedimentar sequency (albiano-cenomaniane) indicate a regional uplift of the NE region of the Brazil at the 100 M.y., in the Albiano Intermediate/Superior. This ages are compatible to termal model of the SPSZ. This two periods of the thermal history of the BP are completely registered in the apatites samples just one age groups of the fission-track, that it is the most ancient age groups. This one suggest it has happened in response to heating before 75 M.y and it has erased the last report of the first moment relief evolution of the BP. The NNE-SSW and E-W structure reativation can have created ideal condictions for heating and local elevations of the geothermal gradients. The equilibrium between the apatites temperatures of this groups and the regionais temperatures took place about 50 M.y., when the samples of the two ages groups had a simillar evolution to present surfaces temperatures

Análise caracterização da dinâmica da Foz do Rio Apodi, região de Areia Branca/RN, com base na cartografia temática multitemporal de produtos de sensores remotos

The study area islocated in the northern cost of Rio Grande do Norte State, preciselyin a west zone of Apodi-Mossoró River, inclunding Tibau City, Grossos City and part of Mossoró City. Geologicaly, this area is composed by rokcs of Potiguar basin, represented by Cretaceous, Tertiary and Quaternary sediments. This area is characterizer by the intense action of cosatal processes (eolic and costal tranports, generalized erosion, alteration in the sediments balance and coast modification), reponsable for it´s morfological instability, also the antropic interference, where the iol industry is located, next Mossoró City, and also the salt exploration industry and the tendency of expantion of shrimp cultivation. This report had as objective the multitemporalgeoenvorimentalmonitoring of the region by recognizingin the field and analizingimages of orbital sensors of diferents years of last four decades. This analisys was achieved by Digital Images Procesing (DIP) thecnics, com subsidized, in a GIS, the preparion of Thematic Maps of natural resources (Geology, Geomorphology and Use & Ocupatios of Earth) and the Envorimental Sensivity to Oil Spilling, main objective os this project. Such technics constitute important tools of envoriment monitoring and maneging, indicating tendencies of antropic of natural growing, making possible the apropiated planning of development of the region, where the steps can be indicated minimized possibles envorimental impacts caused by antropics interferencies on the region, mainly those related to industrial activities, and oil industry above all. Researchs of this nature are very important to the analisys and ordered manegements of use and ocupation of coastal places