Surface area and volume

CONSEJERÍA DE EDUCACIÓN
Dirección General de Participación e Innovación Educativa
Identificación del material AICLE
TÍTULO
Surface Area and Volume
NIVEL LINGÜÍSTICO
SEGÚN MCER
A2.2
IDIOMA
Inglés
ÁREA / MATERIA
Matemáticas
NÚCLEO TEMÁTICO
Geometría
GUIÓN TEMÁTICO
- Identificación de volúmenes. Cálculo de sus superficies y volúmenes
- Adquisición del vocabulario básico de la unidad
FORMATO
Material didáctico en formato PDF
CORRESPONDENCIA
CURRICULAR
3º de Educación Secundaria
AUTORÍA
Patricia Sánchez España
TEMPORALIZACIÓN
APROXIMADA
6 sesiones
COMPETENCIAS
BÁSICAS
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:
- Identificar poliedros y sus partes. La esfera
- Utilizar las fórmulas para calcular sus superficies y volúmenes
- Resolver problemas matemáticos sobre volúmenes
Competencia en tratamiento de la información y competencia digital:
- Realizar las actividades propuestas haciendo uso del ordenador
Aprender a aprender:
- Interpretar la información sobre las diferentes formas geométricas en tres dimensiones
Autonomía e iniciativa personal:
- Ser autónomos para realizar las actividades individuales
OBSERVACIONES
Las fichas de vocabulario de trabajo en parejas, se pueden usar como
introducción a la unidad.
La unidad se puede explicar por completo en la segunda lengua.
Atención a la diversidad
Ampliación: Writing Word Problems
Refuerzo: Sugar Cubes
Material AICLE. 3º de ESO:
Surface Area and Volume
3
Tabla de programación AICLE
OBJETIVOS
- Concebir el conocimiento científico como un saber integrado, que se estructura en
distintas disciplinas, así como conocer y aplicar los métodos para identificar los problemas en los diversos campos del conocimiento y de la experiencia
- Comprender y expresarse en una o más lenguas extranjeras de manera apropiada
CONTENIDOS
DE
CURSO / CICLO
1. Contenidos comunes referentes a la resolución de problemas y la utilización de
herramientas tecnológicas.
4. Geometría.
TEMA
- Elementos de los poliedros
- Poliedros regulares
- Prismas y pirámides. Áreas
- Cuerpos redondos o de revolución. Áreas
- Volúmenes del ortoedro, cubo, prisma, pirámide, cilindro, cono y esfera
MODELOS
DISCURSIVOS
- Distinguir las partes de un cuerpo en tres dimensiones
- Clasificar los distintos tipos de volúmenes
- Identificar las fórmulas para el cálculo de superficies y volúmenes
TAREAS
- Figuras geométricas
- Grabaciones audio-visuales en DVD
CONTENIDOS
LINGÜÍSTICOS
CRITERIOS DE
EVALUACIÓN
4
FUNCIONES:
- Comprender información
general y específica de
textos escritos
- Escuchar y comprender
información general de
mensajes orales.
- Argumentar respuestas
- Redactar conclusiones
ESTRUCTURAS:
Find the volume
How many sides does a
rectangular prism have?
No, the sphere does not
go in this box.
I think this is a pyramid. I
agree. I don’t think so.
What’s the name for …?
How do you read this?
Can this be a...?
LÉXICO:
Area, surface area, volume,
height, radius, base, right
prism, pyramid, right cylinder,
right cones, spheres, to
measure, solid, metric units
(length: m, surface: m2,
volume: m3)...
- Distinguir los tipos de poliedros y sus elementos
- Identificar prismas y pirámides, así como sus elementos característicos
- Reconocer los cuerpos de revolución y sus elementos
- Resolver problemas que impliquen el cálculo de áreas de prismas, pirámides y
cuerpos de revolución
- Calcular el volumen del ortoedro, cubo, prisma, pirámide, cilindro, cono y esfera
- Resolver problemas que impliquen el cálculo de volúmenes de cuerpos geométricos
Material AICLE. 3º de ESO:
Surface Area and Volume
SURFACE AREA AND VOLUME
How many figures do you know?
What is the blue figure called?
Can you see figures with
similar properties?
How many vertexes ...?
Do you know their volumes?
Do you know other figures?
Key vocabulary
Material AICLE. 3º de ESO:
Surface Area and Volume
5
VOCABULARY PRACTICE
Can you give me the
formula for the volume?
Yes, it is ...
I don’t think so.
I agree
Can this be the pyramid?
Surface Area and Volume PPT
a. Listen to teacher’s directions before continuing, raise your hand and ask questions if
necessary. Pay attention to the formulas given by your teacher and how they read them.
b. Get your worksheet ready to record the information.
c. Go to the next exercise only if you have finished the one you are working on.
d. Do not rush; you have enough time to finish.
e. Work in pairs.
3-D Objects
…
…
…
…
…
6
Material AICLE. 3º de ESO:
Surface Area and Volume
1. NAME THE FOLLOWING THREE-DIMENSIONAL OBJECTS AND
TRY TO DRAW A FLAT PATTERN FOR EACH OF THESE SOLIDS.
NAME
PATTERN
X
z
Material AICLE. 3º de ESO:
Surface Area and Volume
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2. WRITE A DEFINITION OF ‘SURFACE AREA’
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
3. WRITE A DEFINITION OF ‘VOLUME’
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
8
Material AICLE. 3º de ESO:
Surface Area and Volume
PRISM
4. WRITE A DEFINITION OF ‘PRISM’
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
5. GIVE SOME EXAMPLES OF OBJECTS SHAPED LIKE A PRISM.
WHY DO THEY HAVE THIS SHAPE?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Material AICLE. 3º de ESO:
Surface Area and Volume
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PRISM
LATERAL AREA
base
P = perimeter
Surface Area
B = area
SA = 2B + Ph
Volume
height
V=Bh
h
6. FIND THE SURFACE AREA AND THE VOLUME OF THE
FOLLOWING PRISMS. WORK WITH YOUR PARTNER.
10
PRISM
BASE
HEIGHT
rectangular
b=4 w=2
10
cube
s=3
3
Material AICLE. 3º de ESO:
Surface Area and Volume
SA
V
PYRAMID
7. WRITE A DEFINITION OF ‘PYRAMID’
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
8. GIVE SOME EXAMPLES OF OBJECTS SHAPED LIKE A PYRAMID.
WHY DO THEY HAVE THIS SHAPE?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Material AICLE. 3º de ESO:
Surface Area and Volume
11
PYRAMID
LATERAL AREA
lateral
height
l
Surface Area SA = B + 1/2 Pl
Volume
base
V = 1/3 B h
P = perimeter
B = area
9. FIND THE SURFACE AREA AND THE VOLUME OF THE FOLLOWING
PYRAMIDS. WORK WITH YOUR PARTNER.
12
PYRAMID
BASE
LATERAL
HEIGHT
square
s=5
10
rectangular
b=3 w=4
12
Material AICLE. 3º de ESO:
Surface Area and Volume
SA
V
CYLINDER
10. WRITE A DEFINITION OF ‘CYLINDER’
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
11. GIVE SOME EXAMPLES OF OBJECTS SHAPED LIKE A
CYLINDER. WHY DO THEY HAVE THIS SHAPE?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Material AICLE. 3º de ESO:
Surface Area and Volume
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CYLINDER
LATERAL AREA
radius
r
Surface Area SA = 2πr2+2πrh
height
h
Volume
V = π r2 h
12. FIND THE SURFACE AREA AND THE VOLUME OF THE
FOLLOWING CYLINDERS. WORK WITH YOUR PARTNER.
14
RADIUS
HEIGHT
5
12
6
9
Material AICLE. 3º de ESO:
SA
Surface Area and Volume
V
CONE
13. WRITE A DEFINITION OF ‘CONE’
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
14. GIVE SOME EXAMPLES OF OBJECTS SHAPED
LIKE A CONE. WHY DO THEY HAVE THIS SHAPE?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Material AICLE. 3º de ESO:
Surface Area and Volume
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CONE
LATERAL AREA
lateral
height
l
Surface Area SA = πr2 + πrl
radius
r
Volume
15. FIND THE SURFACE AREA AND THE VOLUME OF THE
FOLLOWING CONES. WORK WITH YOUR PARTNER.
16
RADIUS
HEIGHT
5
10
3
4
Material AICLE. 3º de ESO:
SA
Surface Area and Volume
V = 1/3 πr2 h
V
SPHERE
16. WRITE A DEFINITION OF ‘SPHERE’
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
17. GIVE SOME EXAMPLES OF OBJECTS SHAPED LIKE
A SPHERE. WHY DO THEY HAVE THIS SHAPE?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Material AICLE. 3º de ESO:
Surface Area and Volume
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SPHERE
radius
r
Surface Area
Volume
18. FIND THE SURFACE AREA AND THE VOLUME OF THE
FOLLOWING SPHERES. WORK WITH YOUR PARTNER.
RADIUS
SA
4
25
18
Material AICLE. 3º de ESO:
Surface Area and Volume
SA = 4 π r2
V = 4 /3 π r3
V
19. COMPLETE THE TABLE, TAKE A FEW MINUTES TO GO OVER ALL
FORMULAS AND WORK INDIVIDUALLY ON YOUR PRACTICE WORKSHEETS.
FORMULAS
Surface Area
Volume
Prism
Pyramid
Cylinder
Cone
Sphere
Material AICLE. 3º de ESO:
Surface Area and Volume
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SURFACE AREA AND VOLUME PRACTICE
20. Listen to your teacher and complete the text below. Make a note of new
vocabulary in the box below.
SURFACE AREA AND VOLUME
Surface area is the amount of space covering the ________________
of a three-dimensional (3D) object. The surface area of a polyhedron
is found by finding the sum of the area of all of the ____________.
The surface area is found between many three-dimensional shapes
using formulas.
The surface area is useful because it tells you how much material is
required in order to cover the object. For example, how much paint
is needed to paint a table. Surface area is the ___________ of the
faces, or surfaces, of a three dimensional shape.
The volume of an object describes how much physical space it takes
up using the three ______________ of width, depth, and height.
The word volume can be used to describe real things like boxes, lakes,
and buildings. All of these things have width, depth, and height. The
formula for measuring _______________ is width×depth×height.
20
Material AICLE. 3º de ESO:
Surface Area and Volume
21. Find the surface area of each solid to the nearest tenth (use π = 3.14)
Draw the correct 3D object for each exercise, and label it with its
measurements. Explain your reasoning.
a) Rectangular prism with l=3cm, w=2cm, and h=10cm
b) Square pyramid with side of the base 5in and lateral height 7in
c) Cylinder with radius 3m and height 5m.
d) Cone with r= 8in and l= 6in.
Material AICLE. 3º de ESO:
Surface Area and Volume
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e) Sphere with a radius 20 mm.
22. Find the volume of each solid to the nearest tenth (use π = 3.14) Draw
the correct 3D object for each exercise, and label it with its measurements.
Explain your reasoning.
a) Rectangular prism with l=30cm, w=20cm, and h=10cm
b) Square pyramid with side of the base 5in and height 6in
22
Material AICLE. 3º de ESO:
Surface Area and Volume
c) Cylinder with radius 3m and height 5m.
d) Cone with r= 8in and h= 5in.
e) Sphere with a diameter 30mm.
Material AICLE. 3º de ESO:
Surface Area and Volume
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23. Solve the following word problems. Work in pairs, do
your operations and write your conclusions.
a) Miriam added liquid soap to the cylindrical fill cup of her parents’ laundry
machine. If the cup was 5 centimeters deep with a radius of 4 centimeters,
how many cubic centimeters of soap did she need to fill half of it?
The object is ____________________________ because ______________
_________________________________________________.
The formula is ___________________ and the solution is:
b) A water tank has been purchased for the farm. It will be used to water cattle.
It is an oval shaped metal container that is 2.7 feet tall. The area of the bottom
of the tank is 12.8 square feet. If the farm animals drink two hundred seventeen
cubic feet of water a day, how many times per day will the tank have to be filled?
The object is ___________________________________.
The formula is ___________________ and the solution is:
c) An underground chamber has been discovered in an old mansion. The
chamber is thought to have been used for storing ammunition. The dimensions
of the chamber are 12 feet by 7 feet by 7 feet. An old ammunition crate was also
found in the chamber and it had dimensions of 1 foot by 1 foot by 2 feet. What is
the maximum number of ammunition boxes of that size that could be put in the
underground chamber?
The object is __________________________________
and the formula is ___________________ and the solution is:
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Material AICLE. 3º de ESO:
Surface Area and Volume
WRITING WORD PROBLEMS
We should start by…
We have considered that…
How long is the radius?
How long is this side?
If we analyze …
The volume is ...
and its surface area is ...
To summarise,
we can say that…
24. Write 2 different word problems where the solution is finding the surface
area or the volume of a 3D object. Solve them and present them to your class.
The shape of a _____________________ is a
________________ that measures _________________
___________________. Find the __________________.
The ______________________________________
___________________________________. Find the
__________________.
Material AICLE. 3º de ESO:
Surface Area and Volume
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SUGAR CUBES
How many cubes
are there?
How long is this side?
The volume is ...
and its surface area is ...
25. Use sugar cubes and glue to build the following objects. Each sugar cube
has dimension 1x1x1. Work in pairs.
1x2x3
Now, without pictures, build:
a. 3x3x3
b. 2x2x1
c. 3x2x4
Volume will be the number of cubes you have used. Record the volume of all your solids.
Use the colors to paint all faces of those solids.
Surface Area will be the number of faces of the cubes you have painted. Record the
surface area of all your solids.
Solid
Volume
2x2x2
1x3x2
1x3x3
3x3x3
2x2x1
3x2x4
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Material AICLE. 3º de ESO:
Surface Area and Volume
Surface Area
FINAL PROJECT
I chose a tree because ...
The tree has this shape
in order to be more ...
The radius is...
and its height is ...
To summarise, we can
say that…
26. Grab your camera and take a picture of an object with
your favorite 3D shape, give it a title and describe its
properties. Prepare a short presentation of your piece of art.
Pinsapo, Sierra de las Nieves,
Málaga
Material AICLE. 3º de ESO:
Surface Area and Volume
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SELF ASSESSMENT
ALWAYS
SOMETIMES
LISTENING
I understand when someone talks
about 3D objects
READING
I can read texts about 3D objects
and understand the most important
information
SPEAKING
I can explain the characteristics
of 3D objects
WRITING
I can write about 3D objects
VOCABULARY
I recognise words and expressions
related to 3D objects, areas
and volumes
Pictures taken from:
http://bancoimagenes.isftic.mepsyd.es/
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Material AICLE. 3º de ESO:
Surface Area and Volume
NEVER