IDENTIFICACIÓN DEL MATERIAL AICLE
TÍTULO
NIVEL LINGÜÍSTICO
IDIOMA
MATERIA
NÚCLEO TEMÁTICO
GUIÓN TEMÁTICO
FORMATO
CORRESPONDENCIA
CURRICULAR
AUTORÍA
TEMPORALIZACIÓN
COMPETENCIAS BÁSICAS
OBSERVACIONES
2º de ESO: 3D shapes
3D- shapes
A2.1
Inglés
Matemáticas
Geometría
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.
PDF
2º de E.S.O.
Irene Mª Dávila Gámez
8 sesiones
• 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
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.
2
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
TAREAS
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
CONTENIDOS
LINGÜÍSTICOS
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.
E Explicar y dialogar con el resto de compañeros de clase,
desde el respeto de las diferentes opiniones.
SS Formular preguntas y dudas que puedan ir surgiendo
durante una exposición de contenidos.
E 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
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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
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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?
3
4
2
1
5
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
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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
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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:
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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
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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.
http://www.learner.org/interactives/geometry/area_volume.html
http://www.mathsisfun.com/geometry/
http://math.about.com/od/formulas/ss/surfaceareavol.htm
- 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
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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
BASE AREA
It depends on the
shape
Height
Lateral
faces
REGULAR
PRISM
Example: In a
triangular prism
b × hB
AB =
2
LATERAL
AREA
AL = P·h
TOTAL AREA
AT = AL + 2· AB
VOLUME
V = AB ·h
P= perimeter
of the base
h= height of
the prism
b= base
hB= vertical height
of the triangle
CUBOID
CUBE
REGULAR
PYRAMID
CYLINDER
CONE
SPHERE
2º de ESO: 3D shapes
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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.
2
The surface area of a sphere of radius r is given by: A = 4π r
A=
The volume of a sphere of radius r is determinated by:
4π r 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
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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 cm2 , 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 €/m2.
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?
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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/cm3.
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
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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
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14. Self-assessment
I
CAN
NOT
YET
Know different kinds of 3d-shapes.
YES
NO
Recognize the elements of each geometric solid (base, height,
faces, vertex, ….).
YES
NO
NOT
YET
Describe a geometric solid through its elements.
YES
NO
NOT
YET
Recognize cuboids and cubes as particular types of prims.
YES
NO
NOT
YET
Know the characteristics of a regular polyhedron.
YES
NO
NOT
YET
Know the name of the five regular polyhedra and describe
them.
YES
NO
NOT
YET
Draw the flat pattern of the 3d-shapes and use it to make a
cardboard figure.
YES
NO
NOT
YET
Know the difference between surface area and volume.
YES
NO
NOT
YET
Distinguish between lateral area and base area.
YES
NO
NOT
YET
Calculate the surface area of a geometric solid.
YES
NO
NOT
YET
Calculate the volume of a geometric solid.
YES
NO
NOT
YET
Solve real situations exercises by using areas and volumes.
YES
NO
NOT
YET
Recognize the presence of 3d-shapes in my environment.
YES
NO
NOT
YET
2º de ESO: 3D shapes
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