CONSEJERÍA DE EDUCACIÓN Dirección General de Participación e Innovación Educativa Identificación del material AICLE TÍTULO The beginning: numbers NIVEL LINGÜÍSTICO A2+ SEGÚN MCER IDIOMA Inglés ÁREA / MATERIA Matemáticas NÚCLEO TEMÁTICO Números - Tipos de números, operaciones GUIÓN TEMÁTICO - Aproximaciones. Radicales FORMATO Material didáctico en formato PDF CORRESPONDENCIA 3º de Educación Secundaria CURRICULAR AUTORÍA Cristina López Lupiáñez TEMPORALIZACIÓN Unas 10 sesiones (más las necesarias para las post-task) APROXIMADA Competencia en comunicación lingüística - Conocer, adquirir, ampliar y aplicar el vocabulario del tema - Ejercitar una lectura comprensiva de textos relacionados con el núcleo temático Competencia Matemática - Conocer las nociones básicas sobre números - Distinguir los tipos de números y la relación entre ellos, realizar operaciones (radicales incluidos), aproximar y estimar errores de aproximación COMPETENCIAS - Resolver situaciones utilizando las nociones matemáticas aprendidas BÁSICAS Aprender a aprender - Aprender a relacionar los conceptos tratados - Organizar las nociones, ideas y argumentos de forma ordenada y constructiva Autonomía e iniciativa personal - Ser autónomos para realizar las actividades individuales - Tener capacidad de juicio crítico ante opiniones - Expresar ideas propias de forma argumentada La unidad puede dividirse en dos. Es muy importante el tratamiento del vocabulario básico inicial (ver primera actividad) por ser la primera unidad del OBSERVACIONES curso. Si se detecta carencia en el vocabulario básico (ver siguiente etiqueta) se debe incidir aún más en él. Puede ser útil completar las actividades propuestas con ejercicios para mayor práctica. Los alumnos/as necesitarán cintas métricas. 3 Material AICLE. 3º de ESO: The beginning: numbers Tabla de programación AICLE - Reconocer y plantear situaciones susceptibles de ser formuladas en términos matemáti- cos, elaborar y utilizar diferentes estrategias para abordarlas y analizar los resultados - Actuar ante los problemas que se plantean en la vida cotidiana de acuerdo con modos propios de la actividad matemática, tales como la exploración sistemática de alternativas, la precisión en el lenguaje, la flexibilidad para modificar el punto de vista o la perseverancia en OBJETIVOS la búsqueda de soluciones - Elaborar estrategias personales para el análisis de situaciones concretas y la identifi- cación y resolución de problemas, utilizando distintos recursos e instrumentos y valorando la conveniencia de las estrategias utilizadas en función del análisis de los resultados y de su carácter exacto o aproximado - Números decimales y fracciones. Transformación de fracciones en decimales y viceversa. Números decimales exactos y periódicos. Fracción generatriz CONTENIDOS DE - Operaciones con fracciones. Cálculo aproximado y redondeo. Error absoluto y relativo. CURSO / CICLO Utilización de aproximaciones y redondeos en la resolución de problemas de la vida cotidiana - Potencias de exponente entero. Significado y uso - Comparación de números racionales - Tipos de números: fracciones, decimales, números reales - Operaciones con fracciones. Potencias TEMA - Aproximación de números reales (truncamiento, redondeo). Errores - Radicales: significado y operaciones - Redactar argumentos y conclusiones - Argumentar respuestas MODELOS - Exponer ejemplos, nociones e ideas DISCURSIVOS - Expresar acuerdo o desacuerdo con las ideas de otros - Preguntar el por qué de ciertas afirmaciones - Actividades para adquirir el vocabulario específico - Actividades para la comprensión significativa y relacional de los conceptos tratados TAREAS - Ejercicios para practicar los procedimien-tos tratados - Proyectos: History of numbers. Number Π. FUNCIONES: ESTRUCTURAS: LÉXICO: - Reconocer la necesidad I think it has to be / it BASIC INITIAL VOCABULARY: the de los números y can be … students should remember (see first activity) conocer la evolución de I obtained the same words related to: Numbers, ordinals, los mismos number because … order, magnitudes of the figures (decimal - Diferenciar los distintos I think you are wrong numbers), mathematical operations tipos de números y because … (addition, subtraction, multiplication, distinguir la problemática Don’t you think there division), equality of mathematical que resuelve cada uno are more options? I do expressions… Vocabulary (this unit): CONTENIDOS - Realizar cálculos (con because … Whole number, integer, rational-irrational- LINGÜÍSTICOS fracciones, números This way we won’t real number, opposite, proper/improper irraciones, radicales…) get anything useful fraction, equivalent fraction, amplify/ - Estimar valores because… simplify a fraction, irreducible fraction, aproximados a uno dado. We have to consider parenthesis, power, base, exponent, even- Estimar el error cometido How do you calculate/ odd number, radical, similar radicals, root, - Discernir la estimate/ define... this? index, radicand, decimal number, exact- conveniencia de la Why do you think that? recurring decimal number, period, prime, realización de una (to) approximate, absolute/relative error, (to) aproximación round, (to) truncate. - Conocer los diferentes tipos de números - Conocer y aplicar la relación entre fracciones y decimales CRITERIOS DE - Realizar adecuadamente cálculos de diversa índole con números y fracciones EVALUACIÓN (operaciones básicas, potencias, radicales…) - Realizar convenientemente aproximaciones numéricas (por truncamiento y redondeo) y estimar el error cometido al aproximar 4 Material AICLE. 3º de ESO: The beginning: numbers NUMBERS… FROM THE BEGINNING Very ancient numbers With the activities of this section you will realize two things: numbers are very (very!) ancient and numbers are everywhere. But before you will check how well you remember vocabulary you learnt in other courses. Work in pairs! 1) What about your memory? Let’s play; you and your partner will be a team: Prepare twelve pieces of paper. Write six expressions about numbers and operations with numbers in English. Fold the papers. The game goes like this: On your turn, you will choose three papers from the other teams. For every paper you will give an example of the expression or calculate if it is an operation. You will get one point for every paper you do correctly. 2) Time ago... When do you think numbers appeared? Read and you’ll know. After reading the following text you and your partner will do a role play. One of you will be the teacher testing how well the other understood the text. After that, change your roles. 5 Material AICLE. 3º de ESO: The beginning: numbers Text: The origin of numbers is very, very ancient. The phenomenon of numbers appeared (probably) in different places around the   world. We could say they appeared because human beings needed to count things. But it is not a simple phenomenon, and until recently people of some tribes still counted using only “one”, “two” and “many”! At the beginning people counted using stones or notches on wood or bones. One interesting example is the bone with 29 notches that was found in Lebombo (South Africa). It is a baboon bone and it is 37,000 years old. A wolf bone was discovered in Czechoslovakia, with 57 notches on it (divided into 5 groups of 11 and two more). This bone is 30,000 years old. These ancient bones are two of the most ancient counting objects ever found. Some people think they are related to the study of moon phases. The origin of ordinals is supposed to be related to religious rites. But… how did humans create signs to symbolize numbers? The origin of written numbers is, like writing itself, associated with advanced societies. There were social structures where it was important to write down things about accountancy, taxes, properties… Most ancient signs to represent numbers originated in ancient Mesopotamia: people used special signs that were written on little clay boards, used to count goods. Some of them are dated 8,000 B.C. Writing numbers was related not only to economy or trade, but also to agriculture (measuring fields). And numbers were used in astronomy too, to describe planets movements. So you can see that the origin of civilization was possible because of the origin of numbers and… the origin of mathematics!! Teacher: Student A Teacher: Student B Questions: Questions: Is there any evidence about the origin of When did numbers appear? numbers? Why did prehistoric people need How did prehistoric people represent numbers? numbers? What kind of numbers did prehistoric Are there other types of numbers that people use? were used later? Evaluation: my partner… Evaluation: my partner… Understood the text perfectly. Understood the text perfectly. Understood the main ideas in the text. Understood the main ideas in the text. Didn’t understand the text very well. Didn’t understand the text very well. 6 Material AICLE. 3º de ESO: The beginning: numbers 3) Think carefully. Select the right options (in pairs).     For the wrong sentences give an example to show they are not right (write the examples in the box below). a) When you add two whole numbers you ALWAYS obtain a whole number. b) When you divide two whole numbers you ALWAYS obtain a whole number. c) When you subtract two whole numbers you ALWAYS obtain a whole number. d) When you multiply two whole numbers you ALWAYS obtain a whole number. Examples: Now do not forget to take notes in your vocabulary notebook: WHOLE NUMBER(S)   4) Old friends.   a) What is the main difference between “5-3” and “3-5”? Discuss with your partner and write a brief text about the need for new numbers. The difference is…   We need other numbers because we cannot… 7 Material AICLE. 3º de ESO: The beginning: numbers b) Now listen to your teacher and complete the text. After that take note of the new vocabulary:     At the _________ people used _________________ to _________ their goods and identify things, and they were able to ________ and _________ those numbers (obtaining ________ whole numbers). They could subtract when the minuend was __________ than the subtrahend. But people created other _________ of ________ to express debts and other ________ with other kinds of ___________: if the ________ is ________ than the __________ the ________ is NOT a ____________! These new numbers are called integers. The set of the integers ________ the whole numbers, the ______ and the opposite of every whole number (expressed by the _________ “-” before it, like -6). So the result of a sum/ multiplication/subtraction of two _________ is another integer, that can be zero (0), a __________ number (2, 6, 152…) or a ______ number (-24, -85, -652…). Words to complete the text: other, minuend, whole number/s, zero, situations, add, negative, subtraction, higher, less, kinds, numbers, beginning, subtrahend, result, multiply, contains, sign, count, integers, positive. c) Now prepare a brief exposition for the rest of your classmates, about the following questions: Do we need other kind of numbers besides integers? Why? What numbers do we need? Now ‘listen to your teacher and take note of the new vocabulary: RATIONAL NUMBER(S).   5) Rational numbers. a) Match the two halves of the sentences.   First half of the sentence Second half of the sentence With a rational number you can express by a fraction You can represent a rational number a numerator and a denominator that represents an integer is 1 A fraction has two parts: The denominator of the fraction the division of two integers 8 Material AICLE. 3º de ESO: The beginning: numbers b) Fractions in English. You surely remember how to read and write fractions in English......   (1) Listen to your teacher and complete the text, the words you (and your partner) have to use are given below.   it   indicates   the     number   of   ______   we   _________.   This   cNausme  etrhaet  orfr:action   means   ________   fourths.   A fraction has ____ parts:      it  ______  the  number   of  _______  parts  in  which  we  _______   Dtheen  womhoilnea.  tTohri:s  case  we  divide  the   whole   into   4   parts.   Every   part   is   ONE   _______,   we   use   ordinal   numbers.     If the denominator is equal to _____, the parts are not “seconds”, every part is a _____. So ½ is one half, 5/2 means five ________, etc. Another __________, especially if the numbers are _____, is to read the _______ using this formula: “numerator” _______ “numerator”, without using ________. So we can read _ 5 _ 0 _ this way: ______ over thirty. 30 Words to complete the text: equal, possibility, half, over, three, big, two, ordinals, divide, consider, fifty, parts, indicates, halves, two, fourth, fraction. Word to take note: whole, numerator, denominator, fraction. (2) Now practice: • Everyone in class will read aloud the following fractions: _5__ ; _9_1_ ; _7__ ; _2_7_ ; _8__ ;_6__5_ ; _1_2_ 2 230 3 6 10 6301 8 • Listen to your teacher dictate some fractions. Write them in words and as fractions. 9 Material AICLE. 3º de ESO: The beginning: numbers 6) Equivalent fractions.   We are going to eat a pizza. Consider the pizza is the whole. Be careful, don’t eat too much!! a) Talk to your partner and select the pairs of fractions that represent the same amount of pizza to eat. You can do pictures if you need.   for you to take notes and do pictures:           b) Read carefully: take note of the new vocabulary.     Two   fractions   are   equivalent   fractions   if   they   represent   the   same   amount,   the   same   number.   We   can   check   if   two   fractions   are   equivalent  by  doing  the  corresponding  pictures  to  represent  them.   But  the  best  way  to  check  it  is  to  multiply  “doing  a  cross”,  like  this:     are   equivalent   fractions   because   5x8   is   equal   to   . 4x10:           are   NOT   equivalent   fractions   because   5x3   is   not   . equal  to  4x10:             10 Material AICLE. 3º de ESO: The beginning: numbers