IDENTIFICACIÓN DEL MATERIAL AICLE NIVEL LINGÜÍSTICO A2.1

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2 IDENTIFICACIÓN DEL MATERIAL AICLE TÍTULO 3D- shapes NIVEL LINGÜÍSTICO A2.1 IDIOMA Inglés MATERIA Matemáticas NÚCLEO TEMÁTICO Geometría GUIÓN TEMÁTICO Identificación de cuerpos geométricos. Descripción de los mismos utilizando el vocabulario básico de la unidad. Cálculo de superficies y volúmenes y su aplicación a problemas reales. FORMATO PDF CORRESPONDENCIA 2º de E.S.O. CURRICULAR AUTORÍA Irene Mª Dávila Gámez TEMPORALIZACIÓN 8 sesiones COMPETENCIAS BÁSICAS Competencia en comunicación lingüística: Conocer, adquirir, ampliar y aplicar el vocabulario básico del tema. Ejercitar una lectura comprensiva de textos relacionados con el núcleo temático Dialogar y discutir con los compañeros sobre las actividades propuestas Competencia matemática Conocer e identificar los diferentes cuerpos geométricos Calcular sus áreas y volúmenes Resolver problemas cotidianos y reales en los que aparezcan dichos cuerpos Aprender a aprender Ser capaces de aprender a calcular áreas y volúmenes a partir de la información y actividades on-line Autonomía e iniciativa personal Ser autónomos para realizar las actividades individuales Iniciativa para elaborar un listado de vocabulario desconocido que va apareciendo en la unidad Social y ciudadana Organizarse para trabajar y colaborar en el grupo Tratamiento de la información y competencia digital Realizar las actividades on-line propuestas en la unidad OBSERVACIONES Aunque la unidad está pensada para 2º de ESO también puede trabajarse en 3º de ESO. La unidad puede ir acompañada de más problemas de aplicación de lo aprendido a la vida real. Las funciones comunicativas de las actividades indican el propósito de las mismas. 2º de ESO: 3D shapes 2

3 TABLA DE PROGRAMACIÓN AICLE OBJETIVOS DE ETAPA Desarrollar y consolidar hábitos de disciplina, estudio y trabajo individual y en equipo Desarrollar destrezas básicas en la utilización de las fuentes de información para, con sentido crítico, adquirir nuevos conocimientos. Adquirir una preparación básica en el campo de las tecnologías, especialmente las de la información y la comunicación Concebir el conocimiento científico como un saber integrado, así como conocer y aplicar los métodos para identificar los problemas en los diversos campos del conocimiento y de la experiencia Desarrollar el espíritu emprendedor y la confianza en sí mismo, la participación, el sentido crítico, la iniciativa personal y la capacidad para aprender a aprender, planificar, tomar decisiones y asumir responsabilidades. CONTENIDOS DE CURSO/CICLO TEMA O SUBTEMAS Comprender y expresarse en una o más lenguas extranjeras de manera apropiada Poliedros. Áreas y volúmenes de los poliedros. Cuerpos de revolución. Áreas y volúmenes de cuerpos de revolución. Elementos de los poliedros. Prismas. Ortoedro y cubo. Pirámides. Poliedros regulares Cuerpos de revolución (cilindro, cono y esfera) MODELOS DISCURSIVOS Áreas y volúmenes Clasificar los distintos cuerpos geométricos y describirlos utilizando sus elementos. Definir los poliedros regulares. Explicar el proceso para calcular áreas y volúmenes de los cuerpos geométricos, obteniendo las fórmulas para dicho cálculo. Analizar la información encontrada en un problema para debatir con los compañeros/as la resolución del mismo. Dialogar para la resolución de problemas que requieren la colaboración y el trabajo en grupo. Ejemplificar la presencia de los cuerpos geométricos en nuestro entorno. 2º de ESO: 3D shapes 3

4 TAREAS CONTENIDOS LINGÜÍSTICOS Lluvia de ideas acerca de la identificación de cuerpos tridimensionales en monumentos y lugares importantes. Audición y lectura comprensiva de textos. Construcción de cuerpos geométricos en cartulina Búsqueda de información acerca del cálculo de áreas y volúmenes Exposición oral de la información obtenida Proyecto final de identificación de cuerpos geométricos en nuestro entorno FUNCIONES: Describir cuerpos geométricos utilizando el vocabulario básico de la geometría referido a las diferentes formas geométricas planas y a los elementos de los cuerpos en el espacio. Explicar el procedimiento del cálculo de áreas y volúmenes describiendo las operaciones necesarias paso a paso. Explicar y dialogar con el resto de compañeros de clase, desde el respeto de las diferentes opiniones. Formular preguntas y dudas que puedan ir surgiendo durante una exposición de contenidos. Elaborar cuestiones sencillas sobre el cálculo de áreas y volúmenes para planteárselas al resto de la clase. ESTRUCTURAS: I think / In my opinion I visited/ I haven t visited Did you find.? What direction. is? Can you show me..? How many faces..? What is the base like? This is called. It has./ Its base is.. The height is.. cm 2º de ESO: 3D shapes 4

5 To calculate you have to The.. is found by multiplying Do you have any doubt? Do you understand me? / Can you repeat? I haven t understood What is the surface are/volume of..? Calculate the.. of.. whose What figure appears in.? Can you remind me..? What do we have to calculate? Where would you put.? It depends on.. LÉXICO: Polyhedron, geometric solid, prism, pyramid, cuboid, cube, cylinder, cone, sphere, base, height, radius, diameter, apothem, stant length, edge, vertex, diagonal, face, surface area, volume, regular, triangular, quadrilateral, square, rectangular, hexagonal, tetrahedron, hexahedron, octahedron, dodecahedron, icosahedrons, oblique, right, flat pattern, formula, formulae. CRITERIOS DE EVALUACIÓN Distingue los tipos de poliedros y sus elementos. Identifica prismas y pirámides, así como sus elementos y características. Reconoce el ortoedro y el cubo como un caso particular de prisma. Conoce los cuerpos de revolución y sus elementos. Calcula el área y el volumen de prismas, ortoedros, cubos, pirámides, poliedros regulares, cilindros, conos y esferas. Resuelve problemas que impliquen el cálculo de áreas y volúmenes de los cuerpos geométricos estudiados. 2º de ESO: 3D shapes 5

6 3-D SHAPES 1. Brainstorm Look at the pictures and answer the questions. Do you know these places? Have you visited any of them? What shape is picture number? Do you know any another site with a similar shape? I think the first picture is called I visited it I haven t visited it but I can recognize a in image number 2º de ESO: 3D shapes 6

7 2. Word search: Find the words in the list on the right: Did you find? What direction is in? (forward/backwards/up/down/diagonal) Can you show me where is? It s in the column and in the row 3. Work in pairs: Look at the geometric solid that your teacher has given to you and try to describe them to your partner answering his/her questions. Use the vocabulary you have learnt. How many faces this polyhedron has? What is the base like? Can you show me the radius/ apothem/height/ of this solid? 2º de ESO: 3D shapes 7

8 4. Regular polyhedra. Now, listen to your teacher speaking about regular polyhedra and complete the text. The words you have to use are given below. A regular polyhedron is a in which: Every is a polygon. On each, the same number of concur. The dihedral between any two faces is always the. These are also known as Platonic, since Plato described them in his work. There are only regular polyhedra. The five solids are: Tetrahedron: is a polyhedron composed of four faces, three of which meet at each vertex. It has edges and four. The tetrahedron is the only convex polyhedron that has four faces. Cube: it has six faces, three of which meet at each vertex. The cube can also be called a regular hexahedron. It is a special kind of square. Octahedron is a solid composed of eight triangles, four of which at each vertex. Dodecahedron: it is composed of regular faces, three of which meet at each vertex. It 20 vertices and 30 edges. Icosahedron: is a polyhedron with 20 equilateral triangular, 30 edges and 12 vertices. It has five triangular faces meeting at vertex. prism, vertex, same, edges, twelve, polyhedron, regular, equilateral, each, five, face, triangular, six, square, Platonic, Polyhedron, solids, meet, identical, pentagonal, has, angle, regular, vertices, faces. Take down all the words you don t understand: 2º de ESO: 3D shapes 8

9 5. Using the information given in the text above, match the image of each regular polyhedron with its name. TETRAHEDRON HEXAHEDRON (CUBE) ICOSAHEDRON DODECAHEDRON OCTAHEDRON 2º de ESO: 3D shapes 9

10 6. Area and volume. - Divide the class into five groups. - Each group will work with a different type of polyhedron (prism, cuboid-cube, pyramid, cylinder and cone). This is what you have to do: - Make the flat pattern of the figure using a cardboard. - Look for information about its surface area and volume. Here you have some web sites that may help you Calculate the surface area and volume of the polyhedron you have made. 7. Show your work and explain it to your partners. The rest of the class can make questions to the group that is explaining. Take notes into your notebook to complete the chart in exercise 8. This 3d-shape is called. It has / This is Its base is/bases are The height/base radius/base side is cm. To calculate the base area/lateral surface area/volume you have to The surface area/volume is found by multiplying Do you have any doubt? /Is that clear? / Do you understand me? For asking questions: Can you repeat this? I haven t understood this, can you explain it again? 2º de ESO: 3D shapes 10

11 8. Complete the chart with the formulae of the surface area and volume of the 3dshapes you have studied. Draw pictures that can help you. 3D-SHAPE NAME PARTS BASE AREA LATERAL AREA TOTAL AREA VOLUME REGULAR PRISM Base Height Lateral faces It depends on the shape Example: In a triangular prism A B b h = 2 B AL = P h P= perimeter of the base h= height of the prism A = A + 2 A V = A h T L B B b= base hb= vertical height of the triangle CUBOID CUBE REGULAR PYRAMID CYLINDER CONE SPHERE 2º de ESO: 3D shapes 11

12 9. Now, listen to your teacher reading the definition of a sphere. The word sphere comes from the Greek word sphaira meaning globe or ball. The sphere is a 3-dimensional object shaped like a ball. It has no edges or vertices. It is not a polyhedron. Every point on the surface is the same distance from the center. Like a circle, a sphere has a radius and a diameter. A tennis ball is a sphere with a radius of about 2.5 inches. The Earth Planet, our home, is nearly a sphere, except that it is squashed a little at the poles, it has a radius of about 4000 miles. The surface area of a sphere of radius r is given by: A = 4π r 2 The volume of a sphere of radius r is determinated by: 4π r A = 3 3 This formula was discovered over two thousand years ago by the Greek philosopher Archimedes. He also realized that the volume of a sphere is exactly two thirds the volume of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere. For a given surface area, the sphere is the one solid that has the greatest volume. This is the reason why it appears in nature so much, such as water drops and bubbles. Take down all the words you don t understand: 2º de ESO: 3D shapes 12

13 Answer the questions: The sphere appears in nature whenever a surface wants to be as small as possible. Examples include bubbles and water drops, can you think of other examples? What is the surface area of a sphere of diameter 42 cm? What is the volume of a sphere of radius 6 inches? The surface area of a sphere is 200 cm 2, what is the lenght of its radius? 10. Areas and volumes game! Make groups of four people. Every team will prepare three questions about areas and volumes of the 3-d shapes. On your turn, ask one of the questions to the rest of the class. The first team to answer the question will get one point. The team that has obtained the highest punctuation at the end of the game will be the winner. The questions can be similar to these: What is the surface area of whose is and is? If the volume of a cube is, what is the length of its side? Calculate the surface area/volume of this solid (...) 11. Solve these problems in pairs. a) A swimming pool has a length of 8 m, a breadth of 6 m and a heigth of 1.5 m. The cost of painting is 6 /m 2. How much is painting the swimming pool? How many litres of water will you need to fill it? b) Calculate the quantity of tinplate necessary to make 10 cylindrical cans with 10 cm of diameter and 20 cm of heigth. c) Peter has made 10 caps with the shape of a cone for a party. How much cardboard has he used if the radius of the base is 15 cm and the heigth is 20 cm? 2º de ESO: 3D shapes 13

14 d) A marble obelisk is made of a cuadrangular prism of 2 m of side and 6.5 m of heigth and a pyramid with the same base and 8 m of heigth. Find the mass of the obelisk if its density is 2.2 g/cm 3. Talk and discuss with your partner: What figure appears in the problem? What do we have to calculate? Can you remind me the formula of? Is it right? The formula is The solution is 12. Complete the following map with the given words and then make suggestions to the rest of the class: 2º de ESO: 3D shapes 14

15 square faces Regular polyhedra volume vertex cone cuboid hexahedron regular radius circular Class discussion: Where would you put? I wrote next to I think that this concept might be placed next to In my opinion the concepts that are connected with are 13. Project. Look for a geometric solid in your environment Work in groups of four. a. Look for a real object with the same shape as one of the solid you have studied in this unit. b. You will have to describe it, measure it and calculate its surface area and volume. To show it to the class you can record it on a video or take photos while you are doing the work and make a presentation. c. After your presentation, you have to prove that your calculations about the volume are right. Introduce your object in a graded container with water. Check if the quantity of water taken out is equal to the calculated volume. Don t forget that the result may not be as precise as you expect due to the possible errors made when measuring the object and because of the differences in its shape. 2º de ESO: 3D shapes 15

16 14. Self-assessment Know different kinds of 3d-shapes. YES NO Recognize the elements of each geometric solid (base, height, faces, vertex,.). YES NO Describe a geometric solid through its elements. YES NO Recognize cuboids and cubes as particular types of prims. YES NO Know the characteristics of a regular polyhedron. YES NO Know the name of the five regular polyhedra and describe them. YES NO I CAN Draw the flat pattern of the 3d-shapes and use it to make a cardboard figure. YES NO Know the difference between surface area and volume. YES NO Distinguish between lateral area and base area. YES NO Calculate the surface area of a geometric solid. YES NO Calculate the volume of a geometric solid. YES NO Solve real situations exercises by using areas and volumes. YES NO Recognize the presence of 3d-shapes in my environment. YES NO 2º de ESO: 3D shapes 16

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