ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO Curso de...

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A PRIMER ON CARNOT GROUPS: HOMOGENOUS GROUPS, CC SPACES, AND REGULARITY OF THEIR ISOMETRIES ENRICO LE DONNE Abstract. Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks. We consider them as special cases of graded groups and as homogeneous metric spaces. We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups. Contents 0. Prototypical examples 4 1. Stratifications 6 1.1. Definitions 6 1.2. Uniqueness of stratifications 10 2. Metric groups 11 2.1. Abelian groups 12 2.2. Heisenberg group 12 2.3. Carnot groups 12 2.4. Carnot-Carathéodory spaces 12 2.5. Continuity of homogeneous distances 13 3. Limits of Riemannian manifolds 13 3.1. Tangents to CC-spaces: Mitchell Theorem 14 3.2. Asymptotic cones of nilmanifolds 14 4. Isometrically homogeneous geodesic manifolds 15 4.1. Homogeneous metric spaces 15 4.2. Berestovskii’s characterization 15 5. A metric characterization of Carnot groups 16 5.1. Characterizations of Lie groups 16 Date : May 6, 2016. 2010 Mathematics Subject Classification. 53C17, 43A80, 22E25, 22F30, 14M17. This essay is a survey written for a summer school on metric spaces. 1

Transcript of ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO Curso de...

Page 1: ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO Curso de …esjcp.aeghd.pt/Arvore_2012_13/Arvore_PAA/PLANIFICACOES... · 2014-01-27 · ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO Writing sentences

ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

Module 1 – My Personal and Daily World

Conteúdos Competências Estratégias/Actividades Avaliação Aulas

Lexicais

Gramaticais

- Asking for and giving personal information; - Introducing oneself and others; - Greeting; - Describing family relationships; - Describing one’s family; - Describing habits; - Describing houses / rooms; - Describing school life; - Telling the time.

Listening Listening to:

vocabulary related to the topic area;

grammar structures; texts; dialogues; CDs; songs.

Speaking

Asking and answering

questions; Asking and answering

about the topic area; Talking about the topic

area.

Reading

Reading words,

- Diagnostic test;

- Direct observation

of students’

involvement in class

activities;

- Worksheets;

- Table on attitudes

and behaviour in

class;

- Individual and pair

work;

- Written test;

- Self-evaluation.

1st and 2nd

Terms

- Personal information: name, age, address, telephone number, nationality, …; - Cardinal and Ordinal numbers;

- Family members; - Colours; - House chores;

- Subject and object personal pronouns; - Present Simple – to be; - Present Simple – have got; - Possessive determiners; - Present Simple – affirmative form; - Frequency adverbs / time expressions; - Prepositions of place; - Prepositions of time;

Curso de Educação e Formação de Empregado de Mesa Planificação a longo prazo

Disciplina: INGLÊS Ano Letivo: Biénio 2012/2014 Professora: Sara Coelho

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ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

- House and garden; - Rooms /furniture in a house; - School subjects; - School objects; - The time; - Days of the week; - Parts of the day; - Classroom language.

- Articles: a/an and the

sentences, texts, a dialogue, an interview.

Writing

Writing words and sentences about the topic area;

Writing sentences using the given structures;

Filling in an ID; Completing/ building a

dialogue; Writing a paragraph/

biography. - Watching a documentary on Cameron Duncan, a teenager / film director from New Zealand.

-Watching videos or scenes from films on Youtube

showing waiters serving at tables.

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ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

Module 2 – Activities and Routines

Conteúdos Competências Estratégias/Actividades Avaliação Aulas

Lexicais

Gramaticais

- Describing the weather; - Describing daily routines; - Expressing likes and dislikes; - Asking for preferences; - Expressing preferences.

Listening Listening to:

vocabulary related to the topic area;

grammar structures; texts dialogues; CDs; songs.

Speaking

Asking and answering questions;

Asking and answering about the topic area;

Talking about the topic area.

Reading

Reading words, sentences, texts, a dialogue, an interview.

Writing Writing words and

sentences about the topic area;

- Direct observation

of students’

involvement in

class activities;

- Worksheets;

- Table on attitudes

and behaviour in

class;

- Individual and pair

work;

- Written test;

- Self-evaluation.

2nd and

3rd Terms

- Months and seasons; - Weather; - Daily Routine; - Food; - Animals; - Places; - Music; - Films; - TV programmes; - Free time activities; - Sports; - Sports equipment.

- Present Simple: negative and interrogative forms; - Demonstratives; - Nouns: singular and plural; - Irregular plurals; - Present Continuous; - Interrogative pronouns; - The imperative; - Quantifiers.

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ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

Writing sentences using the given structures;

Completing a text; Writing a paragraph; Writing a

questionnaire.

- Watching the film “No

Reservations” by Scott

Hicks.

Module 3 – Lifestyles

Conteúdos Competências Estratégias/Actividades Avaliação Aulas

Lexicais

Gramaticais - Asking / answering about countries and nationalities; - Expressing likes, dislikes and preferences; - Talking about holiday activities; - Describing holidays / festivals; - Asking about and describing clothes; - Expressing possession;

Listening Listening to:

vocabulary related to the topic area;

grammar structures; texts; dialogues; CDs; songs.

Speaking

- Direct observation

of students’

involvement in

class activities;

- Worksheets;

- Table on attitudes

and behaviour in

class;

4th and

5th Terms

- The continents; - Countries and nationalities; - Places to spend holidays; - Holiday activities; - Shops;

- Past Simple: to be; - There to be: Present and Past Simple; -Past Simple (regular and irregular verbs): affirmative form; - The possessive case; - Countable and

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ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

- Clothes; - Patterns/Colours; - ´The human body; - Everyday food; - Vegetables; - Fruits; - Drinks; - Meals; - Types of music; - Musical instruments; - Types of musical performance.

uncountable nouns; - Much, many and a lot of; - Omission of articles; - Comparative and superlative of superiority of adjectives.

- Shopping for clothes / footwear: - Asking about quantity; - Ordering food in a restaurant; - Expressing music preferences;

Asking and answering questions;

Asking and answering about the topic area;

Talking about the topic area.

Reading

Reading words, sentences, texts, dialogues, interviews.

Writing Writing words and

sentences about the topic area;

Writing sentences using the given structures;

Writing a description; Writing a postcard, a

recipe; Writing/ completing

dialogues/ a composition.

- Exploring the website “Languageguide.org”.

- Individual and pair

work;

- Written test;

- Self-evaluation.

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ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

Module 5 – Professional Life

Conteúdos Competências Estratégias/Actividades Avaliação Aulas

Lexicais

Gramaticais

- Describing jobs; - Expressing likes / preferences; - Comparing things; - Asking about skills and qualities; - Applying for a job in writing and by telephone; - Making a phone call; - Asking and answering about qualifications, skills, interests, …; - Giving opinions; - Expressing intentions; - Making predictions.

Listening Listening to:

vocabulary related to the topic area;

grammar structures; texts; dialogues; CDs; songs.

Speaking

Asking and answering questions;

Asking and answering about the topic area;

Talking about the topic area.

Reading

Reading words, sentences, texts, a dialogue, an interview.

Writing Writing words and

sentences about the

- Direct observation

of students’

involvement in

class activities;

- Worksheets;

- Table on attitudes

and behaviour in

class;

- Individual and pair

work;

- Film worksheet;

- Written test;

- Self-evaluation.

5th and

6th Terms

- Jobs; - Work places; - Tools and equipment; - Requirements for a job; - Formal language; - Language for interviews; - Work-related words; - Job activities; - Working conditions.

- Relative pronouns; - Defining relative clauses; - Comparative and superlative of adjectives; - Collective nouns; - Position and order of adverbs; - The Future with will and with going to.

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ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

topic area; Writing sentences

using the given structures;

Asking/ answering questions;

Filling in a CV; Writing a letter of

application; Completing a

telephone conversation;

Roleplay; Writing an interview.

Número de aulas: 1º ano do curso – 144 2º ano do curso – 112

CRITÉRIOS DE AVALIAÇÃO

Competências Específicas e Transversais Parâmetros de avaliação Coeficiente

de ponderação

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ESCOLA E.B. 2,3 GENERAL HUMBERTO DELGADO

Desenvolver capacidades de compreensão, utilização e produção no âmbito da Língua Inglesa através da utilização de estruturas gramaticais, de vocabulário adequado e comparações com a língua materna

CONHECIMENTOS

50%

Competências gerais e específicas: Participação oral Leitura Trabalhos vários Pesquisa utilizando TIC Fichas Testes Outros

ATITUDES E VALORES

50%

Responsabilidade Respeito/ Tolerância Interesse/Empenho Atenção/ Concentração Participação Cooperação e solidariedade Cumprimento de regras Autonomia Pontualidade Material