05 from flatland to spaceland

From Flatland to SpacelandSpaceland

MATHEMATICS. 2nd ESOby Rafael Cabezuelo Vivo

May 2011

IDENTIFICACIÓN DEL MATERIAL AICLE

TÍTULO FROM FLATLAND TO SPACELAND

NIVEL LINGÜÍSTICO SEGÚN MCER A2.1

IDIOMA INGLÉS

ÁREA/ MATERIA MATEMÁTICAS

NÚCLEO TEMÁTICO GEOMETRÍA

GUÍON TEMÁTICO (no más de 100 palabras)

La unidad pretende pasar de las figuras planas a los cuerpos tridimensionales, haciendo un recorrido por las principales características de éstos. Se utiliza lo aprendido para describir objetos de uso cotidiano. Se incluye una autoevaluación.

FORMATO PDF

CORRESPONDENCIA CURRICULAR 2º ESO

AUTORÍA RAFAEL CABEZUELO VIVO

TEMPORALIZACIÓN APROXIMADA

6 SESIONES más una tarea final y una autoevaluación de contenidos y destrezas.

COMPETENCIAS BÁSICAS

Lingüística: Mediante la lectura comprensiva de textos, la resolución de problemas y el uso de descripciones.Matemática: Con la interpretación y descripción de la realidad a través del pensamiento matemático, aplicando los conocimientos a objetos y realidades cercanas.Interacción con el mundo : A través de las estructuras geométricas, desarrollando la visión espacial y relacionando las formas estudiadas con objetos cotidianos.Aprender a aprender: Por medio de la perseverancia, la sistematización, la autonomía y la habilidad para comunicar con eficacia los resultados del propio trabajo.

OBSERVACIONES

Los contenidos de las sesiones pueden exceder de una hora de clase real, especialmente cuando se llevan a cabo algún ‘role play’, trabajo grupal y/o manual. Las dificultades matemáticas pueden también suponer una necesidad de adaptación de la duración de cada actividad.Las actividades de postarea, al final de cada sesión o grupo de sesiones podían utilizarse todas como actividades finales, junto a la ficha de autoevaluación. Además, cada sesión puede utilizarse de forma independiente.

Secuencia AICLE 2o ESO 2 From Flatland to SpacelandSpaceland

TABLA DE PROGRAMACIÓN AICLE

OBJETIVOS DE ETAPA

• Identificar las formas y relaciones espaciales que se presentan en la vida cotidiana, analizar las propiedades y relaciones geométricas implicadas y ser sensible a la belleza que generan al tiempo que estimulan la creatividad y la imaginación.

• Integrar los conocimientos matemáticos en el conjunto de saberes que se van adquiriendo desde las distintas áreas de modo que puedan emplearse de forma creativa, analítica y crítica.

CONTENIDOS DE CURSO

• Poliedros y cuerpos de revolución. Desarrollos planos y elementos característicos. Clasificación atendiendo a distintos criterios. Utilización de propiedades, regularidades y relaciones para resolver problemas del mundo físico.

• Volúmenes de cuerpos geométricos. Estimación y cálculo de longitudes, superficies y volúmenes.

• Utilización de procedimientos para analizar los poliedros u obtener otros.

TEMA O SUBTEMA

• Geometría• Figuras planas• Cuerpos geométricos• Poliedros

• Cuerpos de revolución• Áreas• Volúmenes• Historia de la Matemática

MODELOS DISCURSIVOS

• Comparar objetos reales con las figuras estudiadas• Analizar y describir objetos de uso cotidiano• Explicar procesos de cálculo

TAREAS

• Análisis de las figuras planas como tarea previa de comprensión de los cuerpos sólidos.

• Construcción y análisis de los cuerpos platónicos.• Cálculo de superficie y volumen de los principales poliedros y cuerpos de

revolución (prismas, pirámides, cilindros y conos).• Descripción y análisis geométrico de un objeto cotidiano.

CONTENIDOS LINGÜÍSTICOS

FUNCIONES:Hacer descripciones, explicar cálculos.

ESTRUCTURAS:I think that…, The object/building is like a..., From my point of view…On one hand… on the other hand..., I (don't) agree with you, etc.a times/plus/minus/divided by b, one third (fractions), is equal to, etc.

LÉXICO:apex, apothem, cone, cross section, cube, cubic, cylinder, dimension, dodecahedron, dodecahedron, edge, face, figure, flat, flatland, height, hexagon, icosahedron, irregular, n-sided, oblique, octahedron, pentagon, perimeter, pi (π), plane, platonic solids, polygon, polyhedron, prism, pyramid, radius, rectangle, regular, right, shape, side, slant length, solid, space, square, square root, squared, straight, surface-area, tetrahedron, triangle, vertex, volume, etc.

CRITERIOS DE EVALUACIÓN

• Relacionar a Escher con la geometría.• Conocer y distinguir los cuerpos platónicos.• Conocer y distinguir los principales poliedros y cuerpos de revolución.• Calcular la fórmula de Euler• Calcular el área y el volumen de prismas, pirámides, conos y cilindros.


Image 1 Image 2

What can you tell me about these images?


Session 1Pretask

1. Word cloud. Look at the words and the images above. First, listen and repeat the words. Then, fill in the gaps in the texts below. Gaps with the same letter must be filled with the same word.

Image 1 shows a a)_____________ that can be drawn on a b)_____________ surface called a c)_____________ (it is like on an endless piece of paper). Our world has three d)_____________, but there are only two d)_____________ on a plane that are length and height, or x and y.

A e)_____________ is a 2-dimensional shape made of f)_____________lines. Image 1 shows a e)_____________ named g)_____________, do you know more of them? h)_____________, i)_____________ and _____________.

Image 2 shows a j)_____________, which is a three-dimensional k)_____________. k)_____________ Geometry is the geometry of three-dimensional l)_____________, the kind of k)_____________ we live in. It is called three-dimensional, or 3-D because there are three dimensions: width, depth and height or x, y and z.

A m)_____________ is a j)_____________that has 12 n)_____________ (from Greek -dodeca- meaning 12). Each face has 5 o)_____________, and is actually a pentagon. When we say m)_____________ we often mean regular m)_____________ (in other words all n)_____________ are the same size and shape), but it doesn't have to be. If you have more than one m)_____________ they are called p)_____________. It is one of the five platonic k)_____________. More k)_____________ are q)_____________, r)_____________, etc.


Task: Living in Flatland2. Listening.

You are going to listen a text from the book "Flatland: A Romance of Many Dimensions". It is an 1884 science fiction novel by the English schoolmaster Edwin Abbott Abbott. Listen carefully and underline the words that you hear:

flatland space figures triangles heptagons

sheep surface readers squares paper

sinking world rising countrymen lower

pentagons curved lines edges my universe border

3. Now answer these questions about the text and Flatland:

What kind of figures can you find in Flatland?

Name as many of these figures as you can remember. It doesn't matter if they don't appear in the text:

These are the characteristics of certain plane figures. Which figures are we talking about?

They are 2-dimensional shapes.They are made of straight lines.The shape is "closed" (all the lines connect up)

4. Make questions using the information you can find in this website:

http://www.mathsisfun.com/geometry/polygons.html


http://www.mathsisfun.com/geometry/polygons.html

Statements QuestionsPolygon comes from Greek. Poly- means "many" and -gon means "angle".

Where does the word polygon come from? or What is the origin of the word polygon?

It is an Icosagon.

All sides has the same lenght and all angles are also equal.

It is a polygon with, at least, one internal angle greater than 180º.

Another name is Tetragon.

5. From the same book now read this text:

"Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view ; and at last when you have placed your eye exactly on the edge of the table

(so that you are, as it were, actually a Flatland citizen) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line."

What is the writer describing?

The editor of the book tells you to make three drawings as an illustration to make the text clear. Use the empty boxes provided next to the text.


What I Learned6. True or False.

• The plural of polyhedron is polyhedrons. T / F• Flatland is a two-dimensioned country. T / F• There are lots of dodecahedra living in Flatland. T / F• Figures in Flatland can rise above or sink below the surface. T / F• A polygon is a closed plane figure made of stright lines. T / F

7. Classify these plane figures in the category they straight best (it can be more than one). Use X to select the category:

Figure Name Not a Polygon

PolygonsRegular Irregular Concave Convex

Triangle

8. Colour the regular polygons


Session 2Pretask

1. Vocabulary activation. Listen and repeat. Then match pictures and words:

1 23

4 5 6


2. Answer these questions in groups of four:

• What does the building in the second picture look like?

• How many sides do you think the dice has?• What is the main difference between the third

and the sixth picture?• Do you think that solid geometry is important

in our lifes? Why?

Task: Moving to Spaceland3. Video

You are going to see a video about how solids can be seen in a place like Flatland. The narrator is Maurits Cornelis Escher (1898-1972), most commonly known as M. C. Escher. He was a fascinating artist whose compositions are worldwide famous. Escher became fascinated by the mosaics and symmetries in Alhambra, when he visited it in 1922.

Watch the video in this link: http://www.dimensions-math.org/Dim_E.htm(you may need to download the video before watching)

Now read these questions about the video before watching it again. It is the time to resolve any doubt you can have, so ask your teacher anything you don't understand.

• Complete the following table with the names, number of faces, vertices and edges for each polyhedron.

Icosahedron Hexahedron

Octahedron Dodecahedron

Tetrahedron Cube


I think that…The object/building is like a...

From my point of view…On one hand… on the other hand...

I agree with you / I don’t with youBecause...

http://www.dimensions-math.org/Dim_E.htm

Picture Name Faces Vertices Edges

• Can you identify the polyhedron by its plane section? Write them here in order of appearance (from 5'10" to 6'20").


• In the video there is a second and colorful method to explain polyhedra to our flat friends, the lizards. Underline the correct answer.

Stereographic projection Solid inflation Face colouring

• Can you identify the polyhedron by it's plane proyection? Write them here in order of appearance (from 10'20" to 12'20").

• The Greek philosophers attributed a magical importance to these 5 solids, associating one of the fundamental elements from which the world is formed to each of them. What is the name for these figures? Underline the correct answer.

Fantastic Solids Platonic Solids Plutonic Solids

4. Do it yourself

Now it's your time. The best way to understand _________ solids is to build them. For this you have to follow the instructions given in this website (use models with tabs):

http://www.mathsisfun.com/geometry/model-construction-tips.html

Some games (role-playing games) use these solids as dice. To make them you have to write a number on each face, but you have to follow this simple rule:

Opposite faces must always add up to the same value!!(use a regular cubic dice to check it)

5. Counting Faces, Vertices and Edges.

If you count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron, you can discover an interesting thing:

The number of faces plus the number of vertices minus the number of edges equals 2 . This can be

written neatly as a little equation:

Euler's Formula F + V - E = 2


← Fill in from the last question



It is known as the "Euler's Formula", and is very useful to make sure you have counted correctly! Now it is your turn! Check Euler's Formula for the platonic solids, and now you can use your models to count everything!!

Name Image Faces Vertices Edges F + V - E

Dodecahedron

Tetrahedron

Icosahedron

Hexahedron

Octahedron

What I Learned6. Fill in the blanks. Use the words given to complete this summary.

In this lesson on three-dimensional solids, you've seen a lot of _____________. But there are five special _____________, known collectively as the _____________, that are different from all the others.

What makes the _____________ special? Well, two things, actually.

1. They are the only polyhedra whose _____________ are all exactly the same. Every _____________ is identical to every other _____________. For instance, a cube is a Platonic solid because all six of its _____________ are congruent _____________.


2. The same number of _____________ meet at each _____________. Every _____________ has the same number of adjacent _____________ as every other _____________. For example, three equilateral triangles meet at each _____________ of a _____________.

No other _____________ satisfy both of these conditions. Consider a pentagonal prism. It satisfies the second condition because three _____________ meet at each _____________, but it violates the first condition because the _____________ are not identical; some are _____________and some are _____________.


Session 3Pretask

In the following sessions (3 to 6) you are going to work with 3D solids.

1. Vocabulary activation. Listen and repeat. Then write the appropiate words under each picture (one word can be written under more than one picture):


2. Video: You are going to see a video about some properties of solids.

http://www.brightstorm.com/math/geometry/volume/3-d-solid-properties

Now you have to say if the following statements are true or false. You can review the video at home if you need it.

• A vertex is a line where three or more faces intersect. T / F• Where two faces intersect you create an edge. T / F• Bases are polyhedra. T / F• The bases are lateral faces. T / F• Right and Oblique prisms have the same volume and surface area. T / F

(With the same bases and height)

Task: Square goes upward Flatland3. Reading: Adapted from Flatland (p73-74.)

In section sixteen a stranger named Sphere tries to reveal to the main character, Square, the mysteries of Spaceland.

Sphere. Tell me, Mr. Mathematician ; if a Point moves Northward, and leaves a luminous tail, what name would you give to the tail? Square. A straight Line with two extremities.Sphere. Now the line moves parallel to itself, East and West, so that every point in it leaves behind it the tail of a Straight Line. What name will you give to this Figure?Square. A Square, with four sides and four angles.Sphere. Now open your imagination a little, and imagine a Square in Flatland, moving parallel to itself upward.Square. What? Northward? Sphere. No, not Northward ; upward ; out of Flatland altogether. I mean that every Point in you (because you are a Square), in your inside, passes upwards through Space. Each Point describes a Straight Line of its own.I was now impatient and under a strong temptation to launch my visitor into Space, or out of Flatland, anywhere, so that I could get rid of him. Instead I replied:Square. And what is the nature of this Figure? I hope you can describe it in the language of Flatland.Sphere. Oh, certainly. It is all plain and simple, but you must not speak of the result as being a Figure, but as a Solid. But I will describe it to you.- We began with a single Point, which of course being itself a Point has only one terminal Point.

- One Point produces a Line with two terminal Points. - One Line produces a Square with four terminal Points. Now you can answer to your own question: I, 2, 4, are evidently in Geometrical Progression. What is the next number?Square. Eight. Sphere. Exactly. The Square produces something which we call a Cube with eight terminal Points. Now are you convinced?Square. And has this Creature sides, as well as angles or what you call "terminal Points"?Sphere. Of course; and we call them faces.Square. And how many faces or sides will I generate by the motion of my inside in an "upward" direction, and whom you call a Cube?Sphere. How can you ask? And you are a mathematician! The side of anything is always, if I may so say, one Dimension behind the thing. Consequently, as there is no Dimension behind a Point, a Point has 0 sides ; a Line, has 2 sides (for the Points of a Line may be called by courtesy, its sides) ; a Square has 4 sides ; 0, 2, 4 ; what kind of Progression do you call that? What is the next number?Square. Arithmetical. Six.Sphere. Exactly. Then you see you have answered your own question. The Cube which you will generate will be bounded by six sides. You see it all now, eh?


http://www.brightstorm.com/math/geometry/volume/3-d-solid-properties

4. Text attack!

Write the following questions in chronological order, then match them with the correct answers. Find the odd answer:

• Where does the square need to move to create a cube?

• Why is Square impatient?• Sphere sum up the whole process again, write it

in the correct order:• How is the square obtained?• How can Square know the number of faces in a

cube?• How can Square know the number of vertices in a

cube?• What does Square understand when Sphere tells

him that a square shoud move upwards to construct a cube? Why?

• What does Square want to do with Sphere?• What would be the name of the cube faces in

Flatland?

• Here is how the figures are formed:Point → Line → Square → Cube.

• Square understand northward instead of upward, beacuse he lives in Flatland and it is difficult for him to undertstan the three-dimensional space.

• The square needs to move upwards to create a cube.

• Becouse he can't understand the three-dimensional space very well.

• He wants to launch Sphere into space or out of Flatland.

• Square launches Sphere into space, out of Flatland.• Because they are in arithmetical progression, each

number is two more than the previous one. So 0 for a point, 2 for a line, 4 for a square, ... and 6 for a cube.

• The name would be sides.• Because they are in geometrical progression, each

number is double of the previous one. So 1 for a point, 2 for a line, 4 for a square, ... and 8 for a cube.

• The line has to move parallel to itself, East and West.


1. How is the square obtained? The line has to move parallel to itself, East and West.

2.

3.

4.

5.

6.

7.

8.

9.

This is the odd answer:

Can you write a title for this chapter of the story?


What solid do you obtain if the square moves upward a length greater than (or less than) the size of the square?

5. Your turn!

Now you have to make your own story. You are going to work in groups of four. The teacher will dictate the beginning of a text, in which you will have to describe how a pentagon from Flatland can be transformed into a pyramid. Then, when the teacher claps one member of the group will continue the text by writing another short paragraph about the transformation. Each time the teacher claps, you will pass the paper to a new group member who will write the next section of text. Continue like this until the circle is complete. The member of the group who wrote the first paragraph will also write the last one. When you finish, choose a spokesperson to read your text out loud to the restof the class.

Teacher’s dictationSphere. Imagine, my friend, that you are now a pentagon in Flatland...

Student's 1 text:

Student's 2 text:

Student's 3 text:

Student's 4 text:

Student's 1 text -last paragraph-:


Session 4Task: Prisms Surface-Area & Volume

1. Reading: Adapted from www.mathsisfun.com

These are the three dimensions that a solid has: width, depth and height

A cross section is the shape you get when cutting straight across an object.

If you make the cross section of a cube you will get a square, and the cross section of this building is a triangle ...

A solid that has the exact same polygon as its cross section all along its length is called a

PrismThe bases of the prism will be also the same polygon. According to the cross section or the base of a prism it can be named...

Triangular prismSquare prism

Rectangular prismPentagonal prism

and so on...

A square prim that has edges of equal length can be called a cube (or hexahedron) and each face will be a square. Do you remember the platonic solids? So a cube is just a special type of square prism, and a square prism is just a special type of rectangular prism, and They are all cuboids!

If the cross section of a prism is a regular polygon (Equilateral Triangle, square, regular pentagon, regular hexagon, etc), then you have a Regular Prism.


width

depth

height

2. Complete the following table with actual prismatic objects:

Figure Base PoligonCross section Name Regular

3. Calculate. Surface-area of a prism.

The surface area of a prism is the sum of the area of all its faces. As the bases are polygons you will need to remember how to calculate their area. It is measured in squared units (f.i. m2, ft2)


You will need to calculate the area of one base (Ab).

s = 5 in (side)a = 3,44 in (apothem)H = 10 in (height)

Ab=p⋅a2

=5⋅s⋅a2

=

p stands for perimeter

=5⋅5⋅3.442

=862

= 43 in²

Then you will have to calculate the area of one face (Af), which will allways be a cuadrilateral.

A f =s⋅H=5⋅10= 50 in²

There are two bases and five lateral faces (in this example), so the total surface area will be:

Atotal=2⋅Ab+5⋅A f =2⋅43+5⋅50=86+250= 336 in²

Now calculate the following prisms' surface areas:

Prism Base area Face area Surface areaRegular prism

Base side: 5 in

Height: 12 in

Base sides:3 x 10 in

Height:17 in

4. Calculate. Volume of a prism.

The Volume of a prism is simply the area of one of its bases times the height of the prism. It doesn't matter if it is a right or an oblique prism. It is measured in cubic units (f.i. cm3, in3). For the previous example we can calculate the volume in this way:


We already know the area of the base. Do you remember it? Ab=p⋅a2

= in²

Can it be that easy? I think you can do it on your own: V =Ab⋅H= ⋅ = in³

Complete the following table:

Prism Base area Height VolumeRegular prism

Base side: 3 in

Apothem: 2 in

Height: 24 in

Regular prism

Base side: 4 in

Apothem: 3,5 in

Height: 11 in

5. Search.

Bullring in Montoro has a prismatic shape. Can you tell me how many sides the base has? What is the name for this n-sided polygon?


How can he calculate the surface-area?

- He can calculate the surface-area by adding-up the base and the slant length.

- He can calculate the surface-area by adding-up the base and the faces areas.

- He can calculate the surface-area by adding-up the base and the pentagon areas.

Session 5Task: Pyramids Surface-Area & Volume

1. Video: You are going to see a video about regular pyramids surface-area.

http://www.brightstorm.com/math/geometry/area/surface-area-of-pyramids

Now you have to select the correct answer to the following questions. You can review the video at home if you need it. Then make groups of four to construct the questions and the answers.

2. Calculate: Calculate the surface area of these pyramids.

To calculate the slant length you need to remember the Pythagorean Theorem. If you cut the pyramid by the apothem of the base and the apex (the top point) you can see a right triangle:


What is the slant length?

- The slant length is the length of the side.

- The slant length is the height of the triangular

faces.- The slant length is the length of the height.

What is the first calculations that the man makes?

- The man calculate the surface of the triangle first.

- The man calculate the surface of the length first.

- The man calculate the surface of the pentagon first.

What shapes do the faces of the pyramid have?

- The faces of the pyramid have a triangular shape.

- The faces of the pyramid have a pentagonal shape.

- The faces of the pyramid have a square shape.

http://www.brightstorm.com/math/geometry/area/surface-area-of-pyramids

Imagine a regular square pyramid. Let's calculate its surface area:

Base = 10 inHeight = 12 in

Cutting the pyramid we have an isosceles triangle, that can be divided into two right triangles.

Get focus on ABC, which is a right triangle with a 90º angle at C.

AC = One leg of the right triangle = Heigth of the pyramid = 12 inCB = Other leg of the right triangle = one half of the base of the pyramid = 5 inAB = Hypotenuse of the right triangle = Slant length of the pyramid = Unknown

AB 2=AC 2+CB2 ; AB=√AC 2+CB 2=√122+52=√144+25=√169= 13 in ← Slant length

Area of the base: As it is a square its surface is: Ab=base⋅base=10⋅10= 100 in2

Area of one face: It is the area of a triangle: A f =base⋅height

2=10⋅13

2= 65 in 2

There are one base and four lateral faces, so the total surface-area will be:

Atotal=Ab+4⋅A f =100+4⋅65=100+260= 360 in2

Now calculate the following pyramids' surface areas:

Pyramid Base area Slant length Face area Surface-AreaTetrahedron(regular pyramid)

Base side: 3 in

Regular pyramid

Base side: 3.2 in

Height: 6 in


3. Calculate: Calculate the voume of these pyramids.

The volume of a pyramid is very easy, you just have to calculate one third of the base area times the height of the pyramid. Let's make the previous example:

We already know the area of the base. Do you remember it? Ab=base⋅base= in2

Can it be that easy? V =13⋅Ab⋅H=1

3⋅ ⋅ = in³

Complete the following table:

Pyramid Base area Height VolumeRegular pyramid

Base side: 4.5 in

Apothem: 3.1 in

Height: 12 in

Regular pyramid

Base side: 10 in

Apothem: 8.66 in

Height: 16 in


Session 6Task: Smooth down the Prism and the Pyramid

1. Reading:

When the base of a prism changes from a polygon to a circle then you get a __________. Doing the same with a pyramid what you get is a _____________. The volume can be calculated in a similar way, but the surface-area is slightly different. Here you can see the formulas:

Cylinder Cone

Surface area

2 Bases: Ab=π⋅r2

1 Side: A s=2⋅π⋅r⋅h

TOTAL:Atotal=2⋅Ab+As=2⋅π⋅r⋅(r+h)

Base: Ab=π⋅r2

Side: A s=π⋅r⋅s=π⋅r⋅√h2+r 2

TOTAL:Atotal=Ab+As=π⋅r⋅(r+s)

Volume V =Ab⋅h=π⋅r 2⋅h V =13⋅Ab⋅h=1

3⋅π⋅r 2⋅h

2. It's your turn!

A sheet cylinder:

Look at a sheet of paper, how many cylinders can be made using its dimensions?


Calculate the surface area and the volume of the obtained cylinders, and then compare the values.

The volume of a bucket

Can you tink of the shape of a bucket? What is this shape like?

You will need the diameter or radius of both bases:

D = 2.30 dm d = 1.80 dm height = 4.22 dm

Think the best way to calculate the volume (1 dm3 = 1 l). You could need Thales' theorem to find one missing data.


D

d

What I LearnedFrom session 3 to 6 you have learned a lot of think about polyhedra and non-polyhedra 3d solids. Let's see what you can remember.

3. Word cloud

Match the images with the words:


4. Do it yourself

Most of our buildings have a polyhedra, cylinder or cone shape. Can you analyze one of them. Look at this church. You will have to calculate its surface-area and its volume. Notice that is full of Polyhedra. Use convenient units for all dimensions and calculus.

Cut the different parts of the church and paste them on the next table:


50 ft

50 ft

30 ft

100 ft

40 ft

120 ft

20 ft

17,3 ft

Tower:Type:

Base polygon:

Side:

Apothem:

Height:

Surface-area:

Volume:

Tower roof:Type:

Base polygon:

Side: Apothem: Height:

Surface-area: Volume:

Roof:

Type: Base polygon:

Side: Height:



Building:

Type: Base polygon:

Side: Height:


Now complete the table:

Surface-area Volume

Building

Roof

Tower

Tower Roof

WHOLE CHURCH


HOMEWORK. FINAL SUMMARYFinal Task: Geometry around

1. Description

Find a cool geometrical object at home. You have to create a presentation with the image of the object. You will have to explain later a few things about it to the rest of your classmates.

• What kind of geometrical object does it look like?• Which are its faces, bases, edges, vertices or apex?• Does it check Euler's Formula?• Is it simple (just one shape) or complex (like the church)?• What are its dimensions (you can sketch the object)?• What are its surface-area and volume?• How did you make the calculations?• What is it for?

Use your own pictures and text to make an eye-catching presentation. Remember not to overload the slides, it is better to use single phrases and good pictures to show what you want to say. Think about the student at the end of the class, and use large texts and adecuate colours.

Please, don't forget to bringyour object with you!!


ASSESSMENT WORKSHEET.NAME: DATE:

Your task is reflecting on what you have learned. Read the following statements about skills and knowledge you have learned during the project. Please, circle one of these options: YES NO NOT YET.

Self-assessment chart

I CANOrganize vocabulary into categories YES NO NOT YETTake notes from a listening or a video YES NO NOT YETGet valuable information from different sources YES NO NOT YETDescribe images and pictures YES NO NOT YETSummarize the main ideas from a text YES NO NOT YETParticipate in a role-play YES NO NOT YETUnderstand plane figures YES NO NOT YETCalculate Euler's formula with a polyhedron YES NO NOT YETCalculate surface-area and volume of a solid YES NO NOT YETAnalyse and describe geometrically an object YES NO NOT YET

I KNOWWhat is a platonic solid and their caractheristics YES NO NOT YETEscher was very interested in geometry YES NO NOT YETThe concept of volume and surface-area YES NO NOT YETWhat are the main polyhedra and how to identify them YES NO NOT YET

The difference between the main polyhedra and non-polyhedra YES NO NOT YET

The difference between the main polygons and non-polygons YES NO NOT YET

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CONTENTS

DEVELOPED SKILLS

SUGGESTIONS FOR IMPROVEMENT


05 from flatland to spaceland

Education

Transcript of 05 from flatland to spaceland