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Usando uma malha quadriculada formada por quadrados congruentes, um professor sombreou a palavra LUA.
Considerando cada quadradinho da malha como unidade de área, a região sombreada tem área igual a:
A imagem a seguir mostra a embalagem de uma pizza com a forma de um prisma octogonal.
Esse prisma possui um total de arestas igual a:
Texto: É brincando que se aprende
O professor Pardal gostava muito do Huguinho, do Zezinho e do Luizinho e queria fazê-los felizes. Inventou, então, brinquedos que os fariam felizes para sempre, brinquedos que davam certo sempre: uma pipa que voava sempre, um peão que rodava sempre e um taco de beisebol que acertava sempre na bola. Os três patinhos ficaram felicíssimos ao receber os presentes e se puseram logo a brincar com seus brinquedos que funcionavam sempre.
Mas a alegria durou pouco. Veio logo o enfado. Porque não existe nada mais sem graça que um brinquedo que dá certo sempre. Brinquedo, para ser brinquedo, tem de ser um desafio. Um brinquedo é um objeto que, olhando para mim, me diz: “Veja se você pode comigo!”. O brinquedo me põe à prova. Testa as minhas habilidades. Qual é a graça de armar um quebra-cabeça de 24 peças? Pode ser desafio para uma criança de 3 anos, mas não para mim. Já um quebra-cabeça de 500 peças é um desafio. Eu quero juntar as suas peças! Para isso, sou capaz de gastar meus olhos, meu tempo, minha inteligência, meu sono.
Qualquer coisa pode ser um brinquedo. Não é preciso que seja comprado em lojas. Na verdade, muitos dos brinquedos que se vendem em lojas não são brinquedos precisamente por não oferecerem desafio algum.
Que desafio existe numa boneca que fala quando se aperta a sua barriga? Que desafio existe num carrinho que anda ao se apertar um botão? Como os brinquedos do professor Pardal, eles logo perdem a graça. Mas um cabo de vassoura vira um brinquedo se ele faz um desafio: “Vamos, equilibre-me em sua testa!”. Quando era menino, eu e meus amigos fazíamos competições para saber quem era capaz de equilibrar um cabo de vassoura na testa por mais tempo. O mesmo acontece com uma corda no momento em que ela deixa de ser coisa para se amarrar e passa a ser coisa de se pular.
Laranjas podem ser brinquedos? Meu pai era um mestre em descascar laranjas sem arrebentar a casca e sem ferir a fruta. Para o meu pai, a laranja e o canivete eram brinquedos. Eu olhava para ele e tinha inveja. Assim, tratei de aprender. E ainda hoje, quando vou descascar uma laranja, ela vira brinquedo nas minhas mãos ao me desafiar: “Vamos ver se você é capaz de tirar a minha casca sem me ferir e sem deixar que ela arrebente”.
Para um alpinista, o Aconcágua é um brinquedo: é um desafio a ser vencido. Mas um morrinho baixo não é brinquedo porque é muito fácil – não é desafio. Ao escalar o Aconcágua, ele está medindo forças com a montanha ameaçadora! Pelo desafio dos picos, os alpinistas arriscam as suas vidas, e muitos morrem. Parodiando o Riobaldo: “Brincar é muito perigoso...”.
Há brinquedos que são desafios ao seu corpo, à sua força, à sua habilidade, à sua paciência. E há brinquedos que são desafios à inteligência. A inteligência gosta de brincar. Brincando, ela salta e fica mais inteligente ainda. Brinquedo é tônico para a inteligência. Mas se ela tem de fazer coisas que não são desafio, ela fica preguiçosa e emburrecida.
Todo conhecimento científico começa com um desafio: um enigma a ser decifrado! A natureza desafia: “Veja se você me decifra!”. E aí os olhos e a inteligência do cientista se põem a trabalhar para decifrar o enigma. Assim aconteceu com Johannes Kepler (15711630), cuja inteligência brincava com o movimento dos planetas. Assim aconteceu com Galileu Galilei (1564-1642), que, ao observar a natureza, tinha a suspeita de que ela falava uma linguagem que ele não entendia. Pôs-se, então, a observar e a pensar (ciência se faz com essas duas coisas, olho e cérebro!) até que decifrou o enigma: a natureza fala a linguagem da matemática! E até hoje os cientistas continuam a brincar o mesmo brinquedo descoberto por Galileu.
Aconteceu assim também com um monge chamado Gregor Johann Mendel (1882-1962). No seu mosteiro havia uma horta onde cresciam ervilhas. Os outros monges, vendo as ervilhas, pensavam em sopa. Mas Mendel percebeu que elas escondiam um segredo. E ele tanto fez que acabou por descobrir o segredo que nos revelou o incrível mundo da genética. E não é esse mesmo jogo que faz a criança que está começando a aprender a ler? Ela olha para as letras-ervilhas e tenta decifrar a palavra que elas formam. Tudo é brinquedo!
Rubem Alves
https://institutorubemalves.org.br/wp-content/uploads/2018/08/2002.12.17.pdf
Texto: É brincando que se aprende
O professor Pardal gostava muito do Huguinho, do Zezinho e do Luizinho e queria fazê-los felizes. Inventou, então, brinquedos que os fariam felizes para sempre, brinquedos que davam certo sempre: uma pipa que voava sempre, um peão que rodava sempre e um taco de beisebol que acertava sempre na bola. Os três patinhos ficaram felicíssimos ao receber os presentes e se puseram logo a brincar com seus brinquedos que funcionavam sempre.
Mas a alegria durou pouco. Veio logo o enfado. Porque não existe nada mais sem graça que um brinquedo que dá certo sempre. Brinquedo, para ser brinquedo, tem de ser um desafio. Um brinquedo é um objeto que, olhando para mim, me diz: “Veja se você pode comigo!”. O brinquedo me põe à prova. Testa as minhas habilidades. Qual é a graça de armar um quebra-cabeça de 24 peças? Pode ser desafio para uma criança de 3 anos, mas não para mim. Já um quebra-cabeça de 500 peças é um desafio. Eu quero juntar as suas peças! Para isso, sou capaz de gastar meus olhos, meu tempo, minha inteligência, meu sono.
Qualquer coisa pode ser um brinquedo. Não é preciso que seja comprado em lojas. Na verdade, muitos dos brinquedos que se vendem em lojas não são brinquedos precisamente por não oferecerem desafio algum.
Que desafio existe numa boneca que fala quando se aperta a sua barriga? Que desafio existe num carrinho que anda ao se apertar um botão? Como os brinquedos do professor Pardal, eles logo perdem a graça. Mas um cabo de vassoura vira um brinquedo se ele faz um desafio: “Vamos, equilibre-me em sua testa!”. Quando era menino, eu e meus amigos fazíamos competições para saber quem era capaz de equilibrar um cabo de vassoura na testa por mais tempo. O mesmo acontece com uma corda no momento em que ela deixa de ser coisa para se amarrar e passa a ser coisa de se pular.
Laranjas podem ser brinquedos? Meu pai era um mestre em descascar laranjas sem arrebentar a casca e sem ferir a fruta. Para o meu pai, a laranja e o canivete eram brinquedos. Eu olhava para ele e tinha inveja. Assim, tratei de aprender. E ainda hoje, quando vou descascar uma laranja, ela vira brinquedo nas minhas mãos ao me desafiar: “Vamos ver se você é capaz de tirar a minha casca sem me ferir e sem deixar que ela arrebente”.
Para um alpinista, o Aconcágua é um brinquedo: é um desafio a ser vencido. Mas um morrinho baixo não é brinquedo porque é muito fácil – não é desafio. Ao escalar o Aconcágua, ele está medindo forças com a montanha ameaçadora! Pelo desafio dos picos, os alpinistas arriscam as suas vidas, e muitos morrem. Parodiando o Riobaldo: “Brincar é muito perigoso...”.
Há brinquedos que são desafios ao seu corpo, à sua força, à sua habilidade, à sua paciência. E há brinquedos que são desafios à inteligência. A inteligência gosta de brincar. Brincando, ela salta e fica mais inteligente ainda. Brinquedo é tônico para a inteligência. Mas se ela tem de fazer coisas que não são desafio, ela fica preguiçosa e emburrecida.
Todo conhecimento científico começa com um desafio: um enigma a ser decifrado! A natureza desafia: “Veja se você me decifra!”. E aí os olhos e a inteligência do cientista se põem a trabalhar para decifrar o enigma. Assim aconteceu com Johannes Kepler (15711630), cuja inteligência brincava com o movimento dos planetas. Assim aconteceu com Galileu Galilei (1564-1642), que, ao observar a natureza, tinha a suspeita de que ela falava uma linguagem que ele não entendia. Pôs-se, então, a observar e a pensar (ciência se faz com essas duas coisas, olho e cérebro!) até que decifrou o enigma: a natureza fala a linguagem da matemática! E até hoje os cientistas continuam a brincar o mesmo brinquedo descoberto por Galileu.
Aconteceu assim também com um monge chamado Gregor Johann Mendel (1882-1962). No seu mosteiro havia uma horta onde cresciam ervilhas. Os outros monges, vendo as ervilhas, pensavam em sopa. Mas Mendel percebeu que elas escondiam um segredo. E ele tanto fez que acabou por descobrir o segredo que nos revelou o incrível mundo da genética. E não é esse mesmo jogo que faz a criança que está começando a aprender a ler? Ela olha para as letras-ervilhas e tenta decifrar a palavra que elas formam. Tudo é brinquedo!
Rubem Alves
https://institutorubemalves.org.br/wp-content/uploads/2018/08/2002.12.17.pdf
The Question,relate to the contents of the Parâmetros Curriculares Nacionais (PCN).
One important issue to be considered in the teaching of a foreign
language is the impact of technology on society. The PCN
recognize that a foreign language is essential because:
The Question,relate to the contents of the Parâmetros Curriculares Nacionais (PCN).
The PCN state that the development of listening skills:
The Question,relate to the contents of the Parâmetros Curriculares Nacionais (PCN).
According to the PCN, while engaged in socio-interaction,
people make use of three types of knowledge to construct
meaning: systemic knowledge, world knowledge and knowledge
of text organization. One example which illustrates the
knowledge of text organization is the ability to:
The Question,relate to the contents of the Parâmetros Curriculares Nacionais (PCN).
One theoretical issue which serves as the basis for the PCN for
foreign languages is the socio-interactional nature of language
and language learning. This means that, when engaged in
discourse, speakers:
The Question,relate to the contents of the Parâmetros Curriculares Nacionais (PCN).
The PCN state that learning a foreign language helps the
educational process as a whole because:
Based on text 2, an adapted forum discussion, answer question below.
Teaching with no books
Dianne Bell
I have started teaching in a language school suggesting no books to teach except for some magazines. These show the framework what should be worked on, for example, countability and that’s it. When it was offered I accepted the job easily because it seemed challenging and at the same time simple but now I’m out of reliable materials. Please help me out in what ways I can find materials for all the suggested frameworks.
Comments
Mila Junior and Senior Teacher
Posted on 02/22/2015
What exactly are you supposed to be teaching (i.e., conversation, grammar, business English, etc.)? Can you give more examples of the “frameworks”? If there are no books or resources, it sounds like the school wants you to do conversation classes. These can be easy to prepare if you tell the students to come prepared with a topic to discuss. Then, you can assist them with keeping a conversation going, asking questions, giving opinions, etc.
Flore
Secondary Teacher
Posted on 01/07/2015
Hi, I think it really does depend on the students and the level you are teaching to. I have found a lot of online resources are useful, especially news articles. If you just type in “Free online English lessons” or something similar you are bound to find resources. I had to teach like that once. They give you a book with a list of what you should be teaching in each lesson but nothing else. The teacher has to make the lesson up out of thin air each time, and it’s pretty time-consuming.
Jake
Science Educator
Posted on 11/22/2015
There are so many other resources out there for teachers to use, online and off, that teaching without textbooks is becoming more and more acceptable including websites, iPod lectures and field trips — that will encourage you to toss out your textbooks. Before you can toss out the textbook and replace it with technology tools, you’ll need to understand how your students — whatever their age — respond to and work with technology.
(Adapted from https://www.englishclub.com/)
Based on text 2, an adapted forum discussion, answer question below.
Teaching with no books
Dianne Bell
I have started teaching in a language school suggesting no books to teach except for some magazines. These show the framework what should be worked on, for example, countability and that’s it. When it was offered I accepted the job easily because it seemed challenging and at the same time simple but now I’m out of reliable materials. Please help me out in what ways I can find materials for all the suggested frameworks.
Comments
Mila Junior and Senior Teacher
Posted on 02/22/2015
What exactly are you supposed to be teaching (i.e., conversation, grammar, business English, etc.)? Can you give more examples of the “frameworks”? If there are no books or resources, it sounds like the school wants you to do conversation classes. These can be easy to prepare if you tell the students to come prepared with a topic to discuss. Then, you can assist them with keeping a conversation going, asking questions, giving opinions, etc.
Flore
Secondary Teacher
Posted on 01/07/2015
Hi, I think it really does depend on the students and the level you are teaching to. I have found a lot of online resources are useful, especially news articles. If you just type in “Free online English lessons” or something similar you are bound to find resources. I had to teach like that once. They give you a book with a list of what you should be teaching in each lesson but nothing else. The teacher has to make the lesson up out of thin air each time, and it’s pretty time-consuming.
Jake
Science Educator
Posted on 11/22/2015
There are so many other resources out there for teachers to use, online and off, that teaching without textbooks is becoming more and more acceptable including websites, iPod lectures and field trips — that will encourage you to toss out your textbooks. Before you can toss out the textbook and replace it with technology tools, you’ll need to understand how your students — whatever their age — respond to and work with technology.
(Adapted from https://www.englishclub.com/)
Read the following article and answer question based on the text.
Faced with the unprecedented stream of migrants fleeing war and trauma in the Middle East and North Africa, Europe needs to take clear-sighted action.
For its part, the UK has agreed to take 20,000 refugees, a significant portion of whom will likely be children and orphans according to report. One key aspect in ensuring their smooth settlement in the UK will be providing these refugees with language training.
Many Syrians are well-educated and many speak fluent English. Others, however, do not speak English well enough to function professionally within the UK. The issue of language is so fundamental to our lives that we often overlook it. Several multi-million pound training contracts have failed to be delivered on account of not addressing the language barrier. All the goodwill, financial backing, and technical expertise to deliver needed medical, economic, military,engineering, or navigational training may be present; but unless there is a shared language in which to impart that knowledge, little will be accomplished.
One of the biggest misconceptions about language is that if you “just go to the country,” you’ll pick it up. Many people believe that immersion will guarantee fluency; yet you may well know several immigrants who have been in this country for years and still only speak broken English. You might also know dozens of expats in various countries across the world who have failed to pick up the local languages of their host countries. Training and effort are both necessary.
Though not a guarantee of fluency, immersion is a wonderful opportunity. The first issue we need to address with respect to refugees is ensuring that those who come will actually be immersed. That is, that they will be welcomed as part of larger communities, and not simply join communities of other refugees. On the other hand, immersion is just an opportunity, and in order to take full advantage of it, training and education are required. In terms of refugees, we need to consider options for the provision of language training, whether by self-study, classroom instruction, private tuition, or some combination of the three.
The array of needs is staggering. In truth, every language learner has a different set of learning objectives, and will require different training to meet those objectives. Coordinating the actual needs with providers in different regions and accounting for different personal schedules and start dates is a significant challenge. It is, however, a challenge that must be addressed immediately, as proficiency in English will be a key enabler of success for refugees in this country.
(Adapted from Aaron Ralby http://www.blogs.jbs.cam.ac.uk/ socialinnovation/2015/11/16/)
Read the following article and answer question based on the text.
Faced with the unprecedented stream of migrants fleeing war and trauma in the Middle East and North Africa, Europe needs to take clear-sighted action.
For its part, the UK has agreed to take 20,000 refugees, a significant portion of whom will likely be children and orphans according to report. One key aspect in ensuring their smooth settlement in the UK will be providing these refugees with language training.
Many Syrians are well-educated and many speak fluent English. Others, however, do not speak English well enough to function professionally within the UK. The issue of language is so fundamental to our lives that we often overlook it. Several multi-million pound training contracts have failed to be delivered on account of not addressing the language barrier. All the goodwill, financial backing, and technical expertise to deliver needed medical, economic, military,engineering, or navigational training may be present; but unless there is a shared language in which to impart that knowledge, little will be accomplished.
One of the biggest misconceptions about language is that if you “just go to the country,” you’ll pick it up. Many people believe that immersion will guarantee fluency; yet you may well know several immigrants who have been in this country for years and still only speak broken English. You might also know dozens of expats in various countries across the world who have failed to pick up the local languages of their host countries. Training and effort are both necessary.
Though not a guarantee of fluency, immersion is a wonderful opportunity. The first issue we need to address with respect to refugees is ensuring that those who come will actually be immersed. That is, that they will be welcomed as part of larger communities, and not simply join communities of other refugees. On the other hand, immersion is just an opportunity, and in order to take full advantage of it, training and education are required. In terms of refugees, we need to consider options for the provision of language training, whether by self-study, classroom instruction, private tuition, or some combination of the three.
The array of needs is staggering. In truth, every language learner has a different set of learning objectives, and will require different training to meet those objectives. Coordinating the actual needs with providers in different regions and accounting for different personal schedules and start dates is a significant challenge. It is, however, a challenge that must be addressed immediately, as proficiency in English will be a key enabler of success for refugees in this country.
(Adapted from Aaron Ralby http://www.blogs.jbs.cam.ac.uk/ socialinnovation/2015/11/16/)
Read the following article and answer question based on the text.
Faced with the unprecedented stream of migrants fleeing war and trauma in the Middle East and North Africa, Europe needs to take clear-sighted action.
For its part, the UK has agreed to take 20,000 refugees, a significant portion of whom will likely be children and orphans according to report. One key aspect in ensuring their smooth settlement in the UK will be providing these refugees with language training.
Many Syrians are well-educated and many speak fluent English. Others, however, do not speak English well enough to function professionally within the UK. The issue of language is so fundamental to our lives that we often overlook it. Several multi-million pound training contracts have failed to be delivered on account of not addressing the language barrier. All the goodwill, financial backing, and technical expertise to deliver needed medical, economic, military,engineering, or navigational training may be present; but unless there is a shared language in which to impart that knowledge, little will be accomplished.
One of the biggest misconceptions about language is that if you “just go to the country,” you’ll pick it up. Many people believe that immersion will guarantee fluency; yet you may well know several immigrants who have been in this country for years and still only speak broken English. You might also know dozens of expats in various countries across the world who have failed to pick up the local languages of their host countries. Training and effort are both necessary.
Though not a guarantee of fluency, immersion is a wonderful opportunity. The first issue we need to address with respect to refugees is ensuring that those who come will actually be immersed. That is, that they will be welcomed as part of larger communities, and not simply join communities of other refugees. On the other hand, immersion is just an opportunity, and in order to take full advantage of it, training and education are required. In terms of refugees, we need to consider options for the provision of language training, whether by self-study, classroom instruction, private tuition, or some combination of the three.
The array of needs is staggering. In truth, every language learner has a different set of learning objectives, and will require different training to meet those objectives. Coordinating the actual needs with providers in different regions and accounting for different personal schedules and start dates is a significant challenge. It is, however, a challenge that must be addressed immediately, as proficiency in English will be a key enabler of success for refugees in this country.
(Adapted from Aaron Ralby http://www.blogs.jbs.cam.ac.uk/ socialinnovation/2015/11/16/)
Read the following article and answer question based on the text.
Faced with the unprecedented stream of migrants fleeing war and trauma in the Middle East and North Africa, Europe needs to take clear-sighted action.
For its part, the UK has agreed to take 20,000 refugees, a significant portion of whom will likely be children and orphans according to report. One key aspect in ensuring their smooth settlement in the UK will be providing these refugees with language training.
Many Syrians are well-educated and many speak fluent English. Others, however, do not speak English well enough to function professionally within the UK. The issue of language is so fundamental to our lives that we often overlook it. Several multi-million pound training contracts have failed to be delivered on account of not addressing the language barrier. All the goodwill, financial backing, and technical expertise to deliver needed medical, economic, military,engineering, or navigational training may be present; but unless there is a shared language in which to impart that knowledge, little will be accomplished.
One of the biggest misconceptions about language is that if you “just go to the country,” you’ll pick it up. Many people believe that immersion will guarantee fluency; yet you may well know several immigrants who have been in this country for years and still only speak broken English. You might also know dozens of expats in various countries across the world who have failed to pick up the local languages of their host countries. Training and effort are both necessary.
Though not a guarantee of fluency, immersion is a wonderful opportunity. The first issue we need to address with respect to refugees is ensuring that those who come will actually be immersed. That is, that they will be welcomed as part of larger communities, and not simply join communities of other refugees. On the other hand, immersion is just an opportunity, and in order to take full advantage of it, training and education are required. In terms of refugees, we need to consider options for the provision of language training, whether by self-study, classroom instruction, private tuition, or some combination of the three.
The array of needs is staggering. In truth, every language learner has a different set of learning objectives, and will require different training to meet those objectives. Coordinating the actual needs with providers in different regions and accounting for different personal schedules and start dates is a significant challenge. It is, however, a challenge that must be addressed immediately, as proficiency in English will be a key enabler of success for refugees in this country.
(Adapted from Aaron Ralby http://www.blogs.jbs.cam.ac.uk/ socialinnovation/2015/11/16/)