Secuencia '3D shapes' - · PDF filex Identificación de figuras geométricas 3D...

TABLA DE INDENTIFICACIÓN DE LA TAREA

TÍTULO3D Shapes

IDIOMA Inglés

ÁREA/ MATERIA Matemáticas

NÚCLEO TEMÁTICO Geometría

GUÍON TEMÁTICOIdentificación de figuras geométricas 3DReconocimiento de las propiedades de las figuras tridimensionalesCálculo de áreas y volúmenes de figuras 3DAdquisición de vocabulario específico en inglés

CORRESPONDENCIA CURRICULAR (etapa,curso)

2º de E.S.O

AUTORÍA José Manuel Muñoz Sánchez

TEMPORALIZACIÓN APROXIMADA 6 sesiones

COMPETENCIAS BÁSICAS

Competencia en comunicación lingüística:

Conocer, adquirir, ampliar y aplicar el vocabulario del temaEjercitar una lectura comprensiva de textos relacionados con el núcleo temático

Competencia Matemática:

Identificar poliedros y sus partes.Identificar la esfera, cilindro y cono con superficies de revoluciónUtilizar las fórmulas para calcular sus superficies y volúmenesResolver problemas matemáticos sobre volúmenes y superficies

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 tresdimensiones

Autonomía e iniciativa personal:

Ser autónomos para realizar las actividades individuales

OBSERVACIONES

Distinguimos tres núcleos:

Pretareas: destinadas a introducir vocabulario específico y conceptos.

Tareas: núcleo central. Actividades de comprensión del tema.

Postareas: destinadas a la revisión.

2º de ESO: 3D shapes 2

TABLA DE PROGRAMACIÓN DE LA TAREA

TEMA O SUBTEMA OBJETIVOS CONTENIDOS DEL

ÁREA CONTENIDOS

LINGÜÍSTICOS TAREAS

CRITERIOS DE EVALUACIÓN

Geometría : cuerpos geométricos, área y volumen.

‐ Incorporar la terminología matemática al lenguaje habitual con el fin de mejorar el rigor y la precisión en la comunicación.

‐ Identificar las formas y figuras planas y espaciales, analizando sus propiedades y relaciones geométricas.

‐ Comprender y expresarse en una o más lenguas extranjeras de manera apropiada

‐Poliedros regulares: elementos y sus partes.

‐ Propiedades de los poliedros: Fórmula de Euler.

‐ Prismas y pirámides. Áreas y volúmenes.

‐ Cuerpos redondos o de revolución. Áreas y volúmenes.

FUNCIONES: ‐ Comprender información general y específica de textos escritos ‐ Escuchar y comprender información general de mensajes orales. ‐ Argumentar respuestas ‐ Redactar conclusiones

ESTRUCTURAS: Work out the volume /surface area.. I think, …. We get… turning a …. around.. Firstly,… so … then … Finally .. In conclusion … What do you think …. ? I agreed with … I don’t think so. LÉXICO: Area, surface, area, volume, height, base, edge, vertex, face, sphere, cone, cylinder, prism, cube, pyramid, solid, shape, length, width, net tetrahedron, dodecahedron, icoshedron, , octahedron, , turn polyhedron,..

‐ Relacionar figures con sus nombre.

‐ Contar caras, vértices y aristas y deducir la relación entre ellas.

‐ Definir algunas figuras de revolución a través de giros de figuras planas.

‐ Completar un texto con vocabulario específico del tema.

‐ Calcular el área y volumen de un poliedro o superficie de revolución.

‐ Leer un texto y realizar las preguntas adecuadas a una respuestas dadas.

‐ Hacer corresponder los sólidos platónicos con sus desarrollos planos.

‐ Calcular áreas y volúmenes de figuras en la vida real (casa, piscina,..

1.- Conocer los elementos característicos de los poliedros y los cuerpos de revolución.

2.‐ Resolver problemas relacionados con el mundo físico que impliquen la estimación y el cálculo de longitudes, superficies y volúmenes.

3.‐ Utilizar estrategias y técnicas de resolución de problemas, tales como el análisis del enunciado, la división del problema en partes, así como la comprobación de la coherencia de la solución obtenida, y expresar, utilizando el lenguaje matemático adecuado a su nivel, el procedimiento que se ha seguido en la resolución.


Pre-tasks: 3D shapes

This task will show you how to:

1. Use the vocabulary correctly. 2. Visualize 3D shapes. 3. Know their names and their parts. 4. Find out properties which link their parts.

Activity 1.- Put each solid with its name. Choose from the vocabulary below.


Activity 2.- For each object , name the solid in the activity 1, that closely matches its

shape:

1. Cornflake packet ________________ 2. Can of beans ________________ 3. Dice ________________ 4. Ice cream ________________ 5. Tent ________________ 6. Billiard balls ________________ 7. Egyptian’s tomb ________________

Activity 3.- Complete the table for the following solids:

Name of solid Nº of faces Nº of vertices Nº of edges


Activity 4.- In pairs, and using the table above, try to find a formula to link:

the number of faces f

the number of edges e

the number of vertices v

You can use the chart of the activity 3.

+ = + 2

EULER’S POLYHEDRON FORMULA

Activity 4.- Three of 3D-shapes, that you have seen in the activities 1 to 3, aren’t

“polyhedrons (closed among polygons)”. Would you be able to recognize its names?

“ I think that they are ________ , _________ and __________”

Activity 5.- In groups of three try to think about how you can get the 3D shapes who

are not polyhedrons:

Clues:

Write down the answers:

______________________________________________

______________________________________________

______________________________________________


Tasks: 3D shapes.


1. Identify polyhedrons. 2. Visualize 3D shapes. 3. Know their names and their parts. 4. Develop their nets. 5. Calculate surface areas and volumes of 3D shapes.

Activity 1.- Listen to your teacher and complete the text below.

• A _______ is a flat surface of a solid

• An ________ is where two faces meet

• _________ is another word for a corner. The plural is ________

• A ________ is a polyhedron consisting of two equal and parallel polygons (named _______ ) and parallelograms ( named ______ )

• A ___________ is a polyhedron consisting of a __________ (named _______) and lateral triangular __________ with a common vertex.

• Turning a rectangle around one of its ________, we get a __________.

• Turning a right __________ around one of its legs, we get a ___________ .

• A _________ is generated by a half circle turning around its diameter.

Clues:

Activity 2.- The net of a 3D shape is the 2D (flat) shape, which is folded to make the

3D Shape.

Examples:


The net of the hexagonal prism allow us to see the surface area clearly:

Lateral surface area = Perimeter of the base · Height = · ℎ

Total surface area = Lateral surface area + 2· Base surface area = + 2 ·

Use the picture above to solve the following exercise:

Mary wants to paint over the pyramid completely (even the bottom of the object). She knows that 1 gallon of paint covers 350 square feet. To buy the right amount of paint, she has to calculate the surface area of the shape. Solve with a decimal, then round to the nearest tenth foot.

Solution:

Firstly, the net of the square based pyramid is:


So the lateral surface area is:

Then the total surface area is:

Finally, we are going to calculate the amount of paint:

In conclusion:

Mary has to buy _______ gallons of paint.

Activity 3.- Now you can solve the amount of paint that Peter and Caroline have to

buy:

You can use:

Firstly, …

So …

Then ….

Finally, …

In conclusion , …


Solutions:

Peter:

Caroline:


Activity 4.- To calculate the volume of a 3D Shape we will use the following rules:

Prism and cylinder volume:

All of them have two bases, so the volume is calculated by the formula:

= ·

Pyramid and cone volume:

All of them have a base and a vertex, so the volume is calculated by the formula:

= 13 ·

Now you can calculate the volumes of the shapes that Peter, Mary and Caroline have painted:


Activity 5.- In groups of three you have to fill the following table.

I think the name is ..., and surface area formula is ..., because …

What do you think ….?

I agreed with you, because ….

I don’t think so ….

Name Shape Net Surface area Volume


Activity 8.- Read the text below, then write on the question for each answer done.

The Platonic Solids

The Platonic Solids belong to the group of geometric figures called polyhedral. A polyhedron is a solid bounded by plane polygons called faces; they intersect in edges, the points where three or more edges intersect are called vertices.

A regular polyhedron is one whose faces are identical regular polygons. Only five regular solids are possible:

Tetrahedron: Four triangular faces, four vertices and six edges.

Cube: Six square faces, eight vertices and twelve edges.

Octahedron: Eight triangular faces, six vertices and twelve edges.

Dodecahedron: Twelve pentagonal faces, twenty vertices and thirty edges.

Icosahedron: Twelve triangular faces, twelve vertices and thirty edges.

These have come to be known as “The Platonic Solids”.

Plato associated four of The Platonic Solids with four elements. He wrote:

“We must proceed to distribute the figures (solids) we just have describe between fire, earth, water and air… “

“Let us assign the cube to earth, for it is the most immobile of the four bodies and most retentive of shape.”

“The least mobile of the remaining figures, icosahedron, to water.”

“The most mobile, tetrahedron, to fire.”

“The intermediate, octahedron, to air.”

1) ______________________________________________________ ? The four elements are earth, fire, water and air.

2) ______________________________________________________ ? They are cube, tetrahedron, icosahedron and octahedron.

3) ______________________________________________________ ? It has triangular faces, four vertices and six edges.


4) ______________________________________________________ ?

The cube, because it is the most immobile of the four bodies and most retentive of shape.

Activity 6.- ¿What is the spiral length?

Think !!

Here you have a clue:

Pythagoras’ theorem

Activity 9 .-

If you cut a cylinder or a cone by a perpendicular plane to the axe, you will obtain a circumference. If the plane is not perpendicular you will obtain an ellipse.


We have cut these 3D shapes and we have obtained the following 2D shapes:

In groups of three you have to present to your classmates , how these shapes are obtained from cylinder and cone.

Develop the question:


Post-Tasks: 3D shapes


1. Identify polyhedrons. 2. Visualize 3D shapes. 3. Know their names and their parts. 4. Develop their nets. 5. Calculate surface areas and volumes of 3D shapes.

Activity 1.- Labyrinth

At every number, answer the question and turn left or right according to your answer (the questions are on the next page). If you get the questions right, you will finish at the name of a Platonic Solid. Otherwise, you will end up in another 3D shape.

Geometric journey


ICOSAHEDRON 1) Which is the regular polyhedron with (turn left)

twelve faces?

DODECAHEDRON (turn right)

CONE 2) Which is the 3D shape generated by (turn left)

a right triangle turning around one of its legs? CYLINDER (turn right)

EIGHT

3) How many vertices has an (turn left) octahedron?

SIX

(turn right) TETRAHEDRON

(turn left) 4) Which is the Platonic Solid that

that represented “earth”? CUBE

(turn right)

The 3D shape is _______________


Activity 2.- Find someone who….

You have to find a classmate who knows the answer of one of your questions. For each question he or she must be different. You have to write on the chart the answer and the name of the classmate.

FIND SOMEONE WHO… 1. … knows the volume of a cylinder:

2. … can draw the net of a square based pyramid:

3. … remember the four elements which Plato associated to regular polyhedrons:

4. … how many faces a tetrahedron has:

5. … can explain what a vertex is:

6. … can tell you an exercise to work out a surface area:

7. … knows what a regular polyhedron is:

8. … can write on this worksheet the Euler’s polyhedron formula:

9. … remember the four Platonic Solid and the four elements which represented each one:

10. … is very tired and want to go to home!!!:


Activity 3.- Bingo

Look the words below. Choose nine and write one in each box (each student must have different words). Your teacher will read definitions of the words. Cross out a word when you hear its definition. The first student who completes a line (either horizontal or vertical) shouts BINGO and wins.


Activity 4.- Here are the Platonic Solids and its different nets.

Match the correct solid to each net.

a)

1)

b)

2)

c)

3)

d)

4)

e)

5)

Activity 5.- Now you have to describe the Platonic Solids according to their number of faces, edges and vertices.

Example: The cube is regular polyhendron, which has six square faces, eight vertices and twelve edges.

__________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________


Activity 6.- You can answer the following questions to revise this unit. You have to

describe every part of the exercise using words. Remember:

Firstly, … So … , then …. . Finally, … . In conclusion , …

Don’t forget to draw the 3D shape and write down the data.

1) Work out the volume of a cube whose edge is 5 meters.

2) Work out the volume of a square based pyramid whose base edge is 5 m and whose height is 9 m.


3) A can of tomatoes is a cylinder whose base diameter is 10 cm. If its capacity is 1L, what is its height?

4) Work out the surface area of the following 3D shapes:

Remember:

The net is …., so the lateral surface area is …, then the total surface area is …….


5) Find out how much costs to repair this house if you know that

• Painting its four walls, inside and outside is 2 € 2⁄ .

• Repairing the roof, 4 € 2⁄ .

• Laying the floor, 22 € 2⁄ .


6) Peter’s house has a swimming pool that has the following shape:

• Which is its capacity?

• If we open a tap that pours 1500 L/min, How long will we take to fill the pool,

completely?

• Which is the distance from the water surface to the border?


TABLA DE AUTOEVALUACIÓN

SECUENCIAS DIDÁCTICAS SECUNDARIA

AFTER THIS UNIT….

I CAN…

LISTENING YES NO NOT YET understand when someone talks about 3D objects.

READING read texts about 3D objects and understand the most important information.

SPEAKING explain the characteristics of 3D objects.

WRITING write about 3D objects

VOCABULARY recognise words and expressions related to 3D objects, areas and volumes.

I KNOW…

YES NO NOT YET polyhedrons and other 3D shapes elements.

to solve problems about surface areas and volumes.

to use mathematic language and strategies to solve 3D shapes problems.


Secuencia '3D shapes' - · PDF filex Identificación de figuras geométricas 3D...

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