Uma abordagem no ensino de frações baseadas em atividades para o 6º ano do ensino fundamantal

The objective of this work if constitutes in creation a proposal for activities, in the discipline of mathematics, for the 6th year of Elementary School, that stimulates the students the develop the learning of the content of fractions, from the awareness of the insufficiency of the natural numbers for solve several problems. Thus, we prepared a set with twelve activities, starting by the comparison between measures, presenting afterward some of the meanings of fractions and ending with the operations between fractions. For so much, use has been made of materials available for use in the classroom, of forma ludic, for resolution of challenges proposed. Through these activities, it becomes possible students to recognize the necessity of using fractions for solve a amount larger of problems

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

Análises estratigráfica e estrutural da Seção Rifte (Valanginiano ao Barremiano) na área do levantamento sísmico 3D de baixo vermelho, Bacia Potiguar emersa

Baixo Vermelho area, situated on the northern portion of Umbuzeiro Graben (onshore Potiguar Basin), represents a typical example of a rift basin, characterized, in subsurface, by the sedimentary rift sequence, correlated to Pendência Formation (Valanginian-Barremian), and by the Carnaubais fault system. In this context, two main goals, the stratigraphic and the structural analysis, had guided the research. For this purpose, it was used the 3D seismic volume and eight wells located in the study area and adjacencies. The stratigraphic analysis of the Valanginian-Barremian interval was carried through in two distinct phases, 1D and 2D, in which the basic concepts of the sequence stratigraphy had been adapted. In these phases, the individual analysis of each well and the correlation between them, allowed to recognize the main lithofacies, to interpret the effective depositional systems and to identify the genetic units and key-surfaces of chronostratigraphic character. The analyzed lithofacies are represented predominantly by conglomerates, sandstones, siltites and shales, with carbonate rocks and marls occurring subordinately. According to these lithofacies associations, it is possible to interpret the following depositional systems: alluvial fan, fluvio-deltaic and lacustrine depositional systems. The alluvial fan system is mainly composed by conglomerates deposits, which had developed, preferentially in the south portion of the area, being directly associated to Carnaubais fault system. The fluvial-deltaic system, in turn, was mainly developed in the northwest portion of the area, at the flexural edge, being characterized by coarse sandstones with shales and siltites intercalated. On the other hand, the lacustrine system, the most dominant one in the study area, is formed mainly by shales that could occur intercalated with thin layers of fine to very fine sandstones, interpreted as turbidite deposits. The recognized sequence stratigraphy units in the wells are represented by parasequence sets, systems tracts and depositional sequences. The parasequence sets, which are progradational or retrogradational, had been grouped and related to the systems tracts. The predominance of the progradation parasequence sets (general trend with coarsening-upward) characterizes the Regressive Systems Tract, while the occurrence, more frequently, of the retrogradation parasequence sets (general trend with finning-upward) represents the Transgressive System Tract. In the seismic stratigraphic analysis, the lithofacies described in the wells had been related to chaotic, progradational and parallel/subparallel seismic facies, which are associated, frequently, to the alluvial fans, fluvial-deltaic and lacustrine depositional systems, respectively. In this analysis, it was possible to recognize fifteen seismic horizons that correspond to sequence boundaries and to maximum flooding surfaces, which separates Transgressive to Regressive systems tracts. The recognition of transgressive-regressive cycles allowed to identify nine, possibly, 3a order deposicional sequences, related to the tectonic-sedimentary cycles. The structural analysis, in turn, was done at Baixo Vermelho seismic volume, which shows, clearly, the structural complexity printed in the area, mainly related to Carnaubais fault system, acting as an important fault system of the rift edge. This fault system is characterized by a main arrangement of normal faults with trend NE-SO, where Carnaubais Fault represents the maximum expression of these lineations. Carnaubais Fault corresponds to a fault with typically listric geometry, with general trend N70°E, dipping to northwest. It is observed, throughout all the seismic volume, with variations in its surface, which had conditioned, in its evolutive stages, the formation of innumerable structural features that normally are identified in Pendencia Formation. In this unit, part of these features is related to the formation of longitudinal foldings (rollover structures and distentional folding associated), originated by the displacement of the main fault plan, propitiating variations in geometry and thickness of the adjacent layers, which had been deposited at the same time. Other structural features are related to the secondary faultings, which could be synthetic or antithetic to Carnaubais Fault. In a general way, these faults have limited lateral continuity, with listric planar format and, apparently, they play the role of the accomodation of the distentional deformation printed in the area. Thus, the interaction between the stratigraphic and structural analysis, based on an excellent quality of the used data, allowed to get one better agreement on the tectonicsedimentary evolution of the Valanginian-Barremian interval (Pendência Formation) in the studied area

Petrologia dos granitóides brasilianos associados à zona de cisalhamento Remígio-Pocinhos(PB)

The Brasiliano Cycle in the Seridó Belt (NE Brazil) is regarded mostly as a crustal reworking event, characterized by transcurrent or transpressional shear zones which operated under high temperature and low pressure conditions. In the eastern domain of this belt- the so-called São José de Campestre Massif (SJCM), a transtensional deformation regime is evidenced by extensional components or structures associated to the strikeslip shear zones. The emplacement of the Neoproterozoic Brasiliano granitoids is strongly controled by these discontinuities. Located in the southern border of the SJCM, the Remígio-Pocinhos shear zone (RPSZ) displays, in its northern half, top to the SW extensional movement which progressively grade, towards its southern half, to a dextral strike-slip kinematics, defining a negative semi-flower structure. This shear zone is overprinted upon allocthonous metasediments of the Seridó Group and an older gneiss-migmatite complex, both of which containing metamorphic parageneses from high amphibolite to granulite facies (the latter restricted to the strike-slip zone), defining the peak conditions of deformation. Several granitoid plutons are found along this structure, emplaced coeval with the shearing event. Individually, such bodies do not exceed 30 km2 in outcropping area and are essentially parallel to the trend of the shear zone. Petrographic, textural and geochemical data allow to recognize five different granitoid suites along the RPSZ: porphyritic granites (Serra da Boa Vista and Jandaíra), alkaline granites (Serra do Algodão and Serra do Boqueirão) and medium to coarse-grained granites (Olivedos) as major plutons, while microgranite and aluminous leucogranite sheets occur as minor intrusions. The porphyritic granites are surrounded by metasediments and present sigmoidal or en cornue shapes parallel to the trend of the RPSZ, corroborating the dextral kinematics. Basic to intermediate igneous enclaves are commonly associated to these bodies, frequently displaying mingling textures with the host granitoids. Compositionally these plutons are made up by titanite-biotite monzogranites bearing amphibole and magnetite; they are peraluminous and show affinities to the monzonitic, subalkaline series. Peraluminous, ilmenite-bearing biotite monzogranites and titanite-biotite monzogranites correspond, respectivally, to the Olivedos pluton and the microgranites. The Olivedos body is hosted by metasediments, while the microgranites intrude the gneiss-migmatite complex. Being highly evolved rocks, samples from these granites plot in the crustal melt fields in discrimination diagrams. Nevertheless, their subtle alignment also looks consistent with a monzonitic, subalkaline affinity. These chemical parameters make them closer to the I-type granites. Alkaline, clearly syntectonic granites are also recognized along the RPSZ. The Serra do Algodão and Serra do Boqueirão bodies display elongated shapes parallel to the mylonite belt which runs between the northern, extensional domain and the southern strike-slip zone. The Serra do Algodão pluton shows a characteristic isoclinal fold shape structure. Compositionally they encompass aegirine-augite alkali-feldspar granites and quartz-bearing alkaline syenite bearing garnet (andradite) and magnetite plus ilmenite as opaque phases. These rocks vary from meta to peraluminous, being correlated to the A-type granites. Aluminous leucogranites bearing biotite + muscovite ± sillimanite ± garnet (S-type granites) are frequent but not volumetrically important along the RPSZ. These sheet-like bodies may be folded or boudinaged, representing partial melts extracted from the metasediments during the shear zone development. Whole-rock Rb-Sr isotope studies point to a minimum 554��10 Ma age for the crystalization of the porphyritic granites. The alkaline granites and the Olivedos granite produced ca. 530 Ma isochrons which look too young; such values probably represent the closure of the Rb-Sr radiometric clock after crystallization and deformation of the plutons, at least 575 Ma ago (Souza et al. 1998). The porphyritic and the alkaline granites crystallized under high oxygen fugacity conditions, as shown by the presence of both magnetite and hematite in these rocks. The presence of ilmenite in the Olivedos pluton suggests less oxidizing conditions. Amphibole and amphibole-plagioclase thermobarometers point to minimum conditions, around 750°C and 6 Kbars, for the crystallization of the porphyritic granites. The zirconium geothermometer indicates higher temperatures, in the order of 800°C, for the porphyritic granites, and 780°C for the Olivedos pluton. Such values agree with the thermobarometric data optained for the country rocks (5,7 Kbar and 765°C; Souza et al. 1998). The geochemical and isotope data set point to a lower crustal source for the porphyritic and the alkaline granites. Granulite facies quartz diorite to tonalite gneisses, belonging or akin to the gneiss-migmatite complex, probably dominate in the source regions. In the case of the alkaline rocks, subordinate contributions of mantle material may be present either as a mixing magma or as a previously added component to the source region. Tonalite to granodiorite gneisses, with some metasedimentary contribution, may be envisaged for the Olivedos granite. The diversity of granitoid rocks along the RPSZ is explained by its lithospheric dimension, allowing magma extraction at different levels, from the middle to lower crust down to the mantle. The presence of basic to intermediate enclaves, associated to the porphyritic granites, confirm the participation of mantle components in the magma extraction system along the RPSZ. This mega-structure is part of the network of Brasiliano-age shear zones, activated by continental collision and terrane welding processes at the end of the Neoproterozoic

Mecanismos de alojamento de magmas granitóides :exemplo do plúton de Japi(RN)

This dissertation describes the igneous suites of the Japi granitoid pluton, intrusive in the Paleoproterozoic gneiss-migmatite complex of the eastern domain of the Seridó Belt, northeastern Brazil. Field relations show that the pluton is affected by strong deformation associated to the Brasiliano orogeny (known as the D3 phase) , with a NW-trending extensionalleft-hand senestral shear zone (the Japi Shear Zone, JSZ) bordering the intrusive body to the west. Four plutonic suites are found in the main pluton and as satellyte intrusions, besides Iate pegmatite and pink leucogranites. An alkaline granitoid suite, dominated by syenogranites bearing sodic augite (and subordinate hornblende), define a main elliptical intrusion. In its northern part, this intrusion is made up by concentric sheets, contrasting with a smaller rounded stock to the south. These granites display a pervasive solid-state S>L fabric developed under high T conditions, characterized by plastic deformation of quartz and feldspar. It is especially, developed along the border of the pluton, with inward dips. A regular magmatic layering is present sometimes, parallel to the tectonic foliation. The syntectonic emplacement as regards to the Brasiliano (D3) event is indicated by the common occurrence of dykes and sheets along transtensional or extensional sites of the major structure. Field relations attest to the early emplacement of the alkaline granites as regards to the other suites. A basic-to-intermediate suite occurs as a western satellyte body and occupying the southern tail of the main alkaline pluton. It comprises a wide variety of compositional terms, including primitive gabbros and gabbro-norites, differentiated to monzonitic intermediate facies containing amphibole and biotite as their main mafic phases. These rocks display transitional high-K calc-alkaline to shoshonitic affinities. Porphyritic monzogranite suítes commonly occur as dykes and minor intrusives, isolated or associated with the basic-tointermediate rocks. In the latter case, magma mingling and mixing features attest that these are contemporaneous igneous suites. These granites show K-feldspar phenocrysts and a hornblende+biotite+titanite assemblage, displaying subalkaline/monzonitic geochemical affinities. Both suites exhibit SL magmatic fabrics overprinting or transitional to solid-state D3 deformation related to the JSI. Chemical data clearly show that they are related to different parental magmas. Finally, a microgranite suite occurs along a few topographic ridges paralell to the JSI. It comprises dominantly granodiorites with a mineralogy similar to the one of the porphyritic granitoids. However, discriminant diagrams show their distinct calc-alkaline affinity. The granodiorites display an essencially magmatic fabric, even though an incipient D3 solid-state structure may be developed along the JSI. Intrusion relationships with the previous suites, as well as regards to the D3 structures, point to their Iate emplacement. All these suites are intrusive in a Paleoproterozoic, high-grade gneiss-migmatite complex affected by two previous deformation phases (D1, D2). The fabrics associated with these earlier events are folded and overprinted by the younger D3 structures along the JSZ. The younger deformation is characterized by NE-dipping foliations and N/NE-plunging stretching lineations. In the JSZ northern termination the foliation acquires an ENE orientation, containing a stretching lineation plunging to the south. Symmetric kinematic cri teria developed at this site confirms the transpressional termination of the JSZ, as also shown by orthorrombic quartz c-axis patterns. E-W-trending d extra I shear zones developed in the central part of the JSZ are interpreted as antithetic structures associated to the transtensional deformation along the JSZ. This is consistent with its extensional-transcurrent kinematics and a flat-and-ramp geometry at depth, as shown by gravimetric data. The lateral displacement of the negative residual Bouguer anomalies, as regards to the main outcropping alkaline pluton, may be modelized by other deeper-seated granite bodies. Based on numerical modelling it was possible to infer two distinct intrusion styles for the alkaline pluton. The calculated model values are consistent with an emplacement by sheeting for the northern body, as already suggested by satellyte imagery and field mapping. On the other hand, the results point to a transition towards a diapir-related style associated to the smaller. southern stock. This difference in intrusion styles may relate to intensity variations and transtensional sites of the shear deformation along the JSZ. Trace element and Sr and Nd isotopes of the alkaline granites are compatible with their derivation trom a more basic crustal source, as compared to the presently outcropping highgrade gneisses, with participation (or alternatively dominated by) of an enriched lithospheric mantle component. Like other igneous suites in the Seridó Belt, the high LlL contents and fractionated REE patterns of the basic rocks also point to an enriched mantle as the source for this kind of magmatism. Geochemical and isotope data are compatible with a lower crustal origin for the porphyritic granites. On the basis of the strong control of the JSZ on the emplacement of lower crustal (porphyritic and alkaline granites) or lithospheric mantle (basic rocks, alkaline granites or a component of them) magmas, one may infer a deep root for this structure, bearing an important role in magma extraction, transport and emplacement in the Japi region, eastern domain of the Seridó Belt

Mapeamento digital de análogos a reservatórios petrolíferos: exemplos para depósitos fluviais da Unidade Açu-3 - Bacia Potiguar

In the current work are presented the results about the study of digital mapping of analogs referents the fluvial oil reservoirs in the Açu Formation. With the regional recognizing in the south corner of Potiguar Basin was selected a area of 150 Km square in the west of Assu city. In this area was chosen the outcrops for the digital mapping and from the data fields and remote sensors were done the depositional architectural for the fluvial deposits, which it was named coarse meandering fluvial systems. In the deposits were individualized 3 (three) fluvial cycles, which they was separated by bounding surface of fifth order. Such cycles are preferentially sandy, with fining-upward sequence finished in flood plain deposits. Inner of the sandy levels of the filling channels were characterized least cycles, normaly incomplete, constituted by braided sandy bodies and bounding surfaces of fourth order. In the mapped area was chosen a outcrop with great exposition, where it was possible to see tipical deposits of filling channel and was in this outcrop that was done the digital mapping. In this outcrop was used diverse technics and tools, which they integrated sedimentological, altimetric (GPS, Total Station), LIDAR (Light Detection and Ranging), digital photomosaic of high resolution and of the inner geometries (Ground Penetration Radar) data sets. For the integrating, interpretation and visualization of data was used software GoCAD®. The final product of the outcrop digital mapping was the photorealistic model of part of the cliff (or slope) because the observed reflectors in the radargrams were absents. A part of bar oblique accretion was modeled according to GPR gride of 200x200 meters in the alluvial Assu river probable recent analog. With the data of inner geometries was developed the three-dimentional sedimentary architectural, where it was possible characterize sand sheet deposits and many hierarchy of braided channels. At last, simulations of sedimentary geometries and architectures of the Potiguar Basin Fluvial Reservoirs were done with PetBool software, in order to understand the capacity of this program in simulations with a lot of numbers of conditioning wells. In total, 45 simulations was acquired, where the time and the channel numbers increase in relation of the conditioning wells quantity. The deformation of the meanders was detected from the change of simulated dominion dimensions. The presence of this problem was because the relationship between the simulated dominion and the width of the meander

Petrologia do plúton granitico serra verde, porção lestre do domínio seridó

The study area is located at the eastern-central portion of the Seridó Belt, on the interface between the Seridó Group Metasediments and the crystalline basement rocks of the Caicó Complex (RN). Petrographic and geochemical data allow us to define aspects related to the genesis and evolution of the Serra Verde Pluton magmas, which composes the goal of this dissertation The Serra Verde Pluton is a stock with outcropping area of about 25 km², which is intrusive into metasedimentary sequence and the basement gneisses. The pluton intrusion is sintectonic to the Brasiliano event, elongated along the NE direction, developing a cornue geometry. The rock is a monzogranite mainly composed by K-feldspar, plagioclase and quartz, which usually compose more than 85% of the modal analisys. The main mafic mineral is the biotite, while amphibole, sphene, epidote, opaque minerals, allanite, zircon and apatite occur as accessory minerals. It features still a latemagmatic paragenesis composed by chlorite, granular epidote, carbonates and muscovite, developed through the percolation of late CO2 and H2O rich fluids. Chemically, the Serra Verde Pluton rocks may be classified as metaluminous, of calc-alkaline affiliation, sometimes showing trondhjemític characteristics, with high Na2O (>4,5%), Sr (>400ppm) and Ba (>800ppm) and low K2O (≤3,0%), MgO (<1,0%), TiO2 (<0,5%), Rb (<90ppm), Y (≤16ppm) and Zr (≤13ppm). Micropetrographic evidences (mineral assembly and microtextures) indicate that the magma evolution occurred in moderated to high fO2 conditions, above the FMQ buffer. Thermo-barometric data obtained by minor elements geochemistry and the CIPW data, suggest a final/minimal pressure crystallization for the Serra Verde Pluton samples of about 3 to 5 kbar, liquidus temperature around 800o C, solidus temperature between 680o and 660o C. This data is compatible with those observed by many authors for the Neoproterozoic granites of the Seridó Belt. The group of analyzed data (Petrographic, microtextural and geochemical), suggests that the dominant process of the generation and evolution of the Serra Verde Granite magma was the fractional crystallization, probably from basement quartz-dioritic and tonalitic orthogneisses source