TÍTULO RATIO AND PROPORTIONS NIVEL LINGÜÍSTICO A2.1IDIOMA InglésMATERIA Matemáticas NÚCLEO TEMÁTICO Aritmética y Álgebra

GUIÓN TEMÁTICO Identificación del concepto de razón y proporción. Equivalencias con números fraccionarios y números decimales. Reconocimiento en el entorno del alumno. Calculo de porcentajes, incrementos y reducciones porcentuales. Descripción y clasificación de todos estos conceptos mediante el vocabulario básico de la unidad.

FORMATO PDFCORRESPONDENCIA CURRICULAR

1º E.S.O.

AUTORÍA Juan Antonio Espinosa Pulido TEMPORALIZACIÓN 6 sesiones COMPETENCIASBÁSICAS

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 razones y proporciones. Calcular porcentajes. Resolver problemas cotidianos y reales en los que aparezcan estos contenidos. Aprender a aprender : Reconocer razones y proporciones en su entorno para poder aplicar los conocimientos de la unidad en la resolución de problemas reales. Autonomía e iniciativa personal : Conocer y poner en práctica las fases de desarrollo de un proyecto. Planificar, identificar objetivos y gestionar el tiempo con eficacia. Social y ciudadana : Ser capaz de trabajar en grupo Tratamiento de la información y competencia digital :Buscar y seleccionar información con distintas técnicas según la fuente o el soporte, valorando su fiabilidad.

OBSERVACIONES

La unidad puede utilizarse para trabajar contenidos similares en cursos posteriores. Así mismo, puede ir acompañada de más actividades de aplicación de lo aprendido.

IDENTIFICACIÓN DEL MATERIAL AICLE

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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. Asumir responsablemente sus deberes, conocer y ejercer sus derechos en el respeto a los demás, practicar la tolerancia, la cooperación y la solidaridad entre las personas y grupos. 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. Comprender y expresarse en una o más lenguas extranjeras de manera apropiada. Apreciar la creación artística y comprender el lenguaje de las distintas manifestaciones artísticas, utilizando distintos medios de expresión y representación.

CONTENIDOS DE CURSO/CICLO

Razones y Proporciones

TEMA O SUBTEMAS Razón ProporciónMagnitudes directamente e inversamente proporcionales PorcentajesFracciones, decimales y porcentajes Presencia de las razones y proporciones en el entorno del alumno.

MODELOSDISCURSIVOS

Clasificar y describir las razones y proporciones. Estudiar los porcentajes y ver su relación con fracciones y decimales. Explicar la presencia de razones y proporciones en el entorno del alumno. Dialogar para la resolución de actividades que requieren la colaboración y el trabajo en grupo del alumnado.

TAREASActividades con proporciones y porcentajes para adquirir el vocabulario específico. Lluvia de ideas relacionada con razones y proporciones en el entorno del alumno. Audición y lectura comprensiva de textos. Realización de sopa de letras para el conocimiento y la consolidación de vocabulario. Bingo de porcentajes.

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Realización de mapas conceptuales para relacionar los contenidos de la secuencia. Búsqueda de información acerca de los contenidos del tema.Proyecto final de identificación de razones y proporciones en el entorno del alumno. Exposición oral de la información obtenida. Autoevaluación.

CONTENIDOSLINGÜÍSTICOS

FUNCIONES:

Comprender información general y específica de textos escritos.Explicar qué es una proporción y para que se usan. Escuchar y comprender información de mensajes orales. Argumentar el uso de las razones en la vida cotidiana. Explicar y dialogar con el resto de compañeros de clase, desde el respeto de las diferentes opiniones. Sintetizar y seleccionar datos de las diferentes fuentes de información y transmitirlas de manera coherente al resto.

ESTRUCTURAS:

It’s a place where...It’s a thing which... I agree/ disagree with you because… I think… / In my opinion… I can use…to … It’s difficult/easy to say if /that… Do you find …? What direction is … in? Can you show me where … is? It’s in column…and row… To begin with...On the other hand....Some days later... The biggest difference between…and…is… Can you help me with the word…? Do you know what the first letter of …is? What do you think …is? How do you spell…? Where would you put …?Please tell us what is connected with… Can you show me …..? This is called…. To calculate ………… you have to…… Do you have any doubts?Do you understand me? Can you repeat? I haven’t understood… From my very point of view, I think that + statementAs you probably know,I understand what you say but....

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LÉXICO:

Ratio, proportions, equivalent fractions, quantities, rate, measures, amounts, quantiles, direct proportionality, inverse proportionality, fractions, decimals , percentages, decrease, increase, reduce, find out, …

CRITERIOS DE EVALUACIÓN

Distingue razones y proporciones y sus elementos. Relaciona porcentajes con decimales y fracciones. Resuelve problemas con porcentajes. Reconoce magnitudes directamente e inversamente proporcionales.Reconoce y valora la presencia de la proporcionalidad en su entorno.

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RATIO AND PROPORTIONS

Brainstorm

Think about this topic: in daily life and in business operations it is necessary to compare things. Try to use the words on the right in your answers:

How could you compare amounts of something?

A label says: “1 measure screen wash to 10 measures water”.

How many measures of water do you need if you have 1 measure of screenn

wash?

How do you know? What do you use to express these measures?

When two quantiles are direct proportionality? And inverse proportionality?

What’s the meaning of 25% of an amount? How do you calculate it?

What’s the relation between fractions, decimals and percentages?

MOTION

In my opinion, to compare ........

As far as I know, to express measures ......

You must use ...... measures of ................... to ...... measures ..............

I would use ....

From what I remenber, two quantiles are direct/inverse proportionality .....

In my opinion to work out a percentage of something, you have to .....

Any percentage/fraction/decimal is just .....

1º de ESO: Ratio and proportions 6

Look at this box with different expressions associated with Ratio and Proportions:

Try to explain to the rest of your classmates using the following phrases. Do

you recognize the equivalence between some of these expressions? Do you

know how to pronounce these expressions?

VOCABULARY PRACTICE

0, 4 Decrease 30€ by 25%

2 x=5 100

40% Increase 120 by 10%

6 40=100x Find 10% of 35

25

40100 Reduce 20€ by 20%

...................... is equivalent to ......................

The way to read the expression ...................... is ......................

The result of increase/decrease is ......................

...................... represents ......................

The result of reduce/find is ......................

The way to find out the missing “x” in this expression is......................

...................... is pronounced how ......................

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Find the words in the list on the right.

With the help of your teacher/assistant try to describe the position of

each word. Use this expressions:

TANGLED

Did you find ……?

What direction is ………… in? (forward/blackwards/down/up/ diagonal)

Can you show me where ......... is?

It’s in column ............ and row ...........

What is the meaning of ............?

I don’t understand the exact meaning of ……………..Could you it explain me?

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Famous Mathematician: HYPATIAListen this text read by your teacher/assistant twice. The first time

you have to fill in the gaps with some dates or words given in the

previous page.

LISTENING

Hypatia of Alexandria was the first ________ recognized as a mathematician

and scientist since the recording of history. She was a great teacher, scholar,

_________ , philosopher, scientist, and compiler and preserver of important

scientific writings.

Hypatia was _______ in 370 AD in the center of

learning that was _________ , Egypt. Her

________ was Theon, a famous mathematician-

philosopher. Undoubtedly, her learned father

trained and taught her, and together, they later

collaborated in writing certain commentaries to

prominent __________ works, such as Ptolemy’s

comprehensive astronomical writings. On her

own, Hypatia herself authored similar

commentaries on important writings, making

them more accessible and understandable to

many __________. Examples of these were her

commentaries on Apollonius’s Conics and

Diophantus’s Arithmetica.

Hypatia ______ in March 415 under gruesome circumstances. Some accounts

say that she was murdered by fanatical _________ monks. Others say that

she was attacked by an angry religious mob. Apparently, Hypatia was accused

of being a ________ or a proponent of pagan beliefs. At that time, women

who demonstrated great learning and scientific knowhow were apt to be

singled out as witches, because their progressive ideas were a threat to the

prevailing religious and superstitious way of __________.

Hypatia led a life full of ________ intellectual accomplishments. For many

people, she epitomizes the fearless and progressive attitude of a true

________ . She has inspired many modern ________ to compose stories,

novels and even movies about her.

1º de ESO: Ratio and proportions 9

After listening the second time, answer the following questions:

Would you like to know more things about Hypatia? Make more questions

using the previous text:

Who was Hypatia?

Where was Hypatia born?

What did Hypatia discover?

Where did Hypatia live?

How did Hypatia die?

What is Hypatia remarkable for?

Who killed Hypatia of Alexandria? Why?

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PROPORTIONAL LOTTERY!

Also draw a line through the question that has its answer below

234 2 40 9168 104 35 30

10 144 116 32

GAME

With these 30 questions you have to find some of the answers on the Bingo

card at the bottom of the page. When you find the answer to one of the

questions, draw a line through it.

When you have completed a line of answers, call LINE and when you have

found all the answer call BINGO.

We’ll all start together. Are you ready?

1. Reduce 230€ by 10% _____

2. 1/2 = _____ %

3. 1/4 = _____%

4. 2/5 = _____%

5. 30€ + 20% = _____ €

6. Increase 80 by 30% _____

7. 10% of 320 = _____

8. Find 40% of 160 _____

9. 20% of 40 = _____

10. 180€ + 30% = _____ €

11. Reduce 125€ by 40% _____ €

12. 0,03 = _____ %

13. 6/8 = 0,_____

14. Find 20% of 50 = _____

15. 380€ + 8% IVA = _____ €

16. 25% of 200 = _____

17. 0,35 = _____ %

18. Find 75% of 12€ _____

19. 100€ + 16% IVA = _____ €

20. 0,3 = _____ %

21. 4/5 = _____ %

22. Increase 120 by 40% _____

23. 400€ + 16% IVA = _____ €

24. 0,55 = _____ %

25. 1/50 = _____ %

26. Reduce 10€ by 75% _____ €

27. 2/10 = _____ %

28. 20,50€ + 8% IVA = _____ €

29. Decrease 240€ by 40% = _____ €

30. 20% of 150 = _____

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In this movie you will find some brief explanatory notes about those

elements which have a highly mathematical nature, including the

works of that great Dutch artist, Escher, that appears throughout the

film.

Now try to do this exercise:

MATHEMATICAL MOVIE

Match the words and the pictures:

Galton Box

Newton's cradle

Fermat's Last Theorem

Chess

The seven bridges of Königsberg

Spirals

Euler's Formula

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Now try to do this exercise:

Match the words, the images and the explanations:

1. Pentominoes puzzle

A. Escher was in the habit of tying his scissors by a string subject to a nail under the table, so that their children could not take and lose it.

2. Tangram B. It is an ancient Chinese game

that is to form figures with seven pieces.

3. Reptiles

C. Is a simple game created with 12 pieces, which when arranged in a certain way they fit perfectly into their box.

4. Reuleaux Triangle

D. It's considered the oldest calculating device, adapted and used by many cultures around the World.

5. Leonardo Bridge

E. This is an ingenious construction designed by Leonardo da Vinci, in which stability is achieved throughout the structure without using nails or ropes.

6. Scissors unleashed

F. I was very surprised to find out that it was possible to build rollers with a quasi-triangular section in a way that a platform could roll over them, like with cylinders.

7. Abacus G. This is the main protagonist of

the animation. One of the best known works by Escher.

8. Hourglass H. This is a simple instrument for

measuring a certain lapse of time.

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After this, try to explain to the rest of your classmate some of the

mathematical elements which appear in the previous video. Use these

expressions:

In in the animation we see a ................

This is one of the most famous ................

It is considered as one of the most “beautiful” ................

................are made with ................

................can be constructed from ................

This is a device developed by ................

This is a 3D representation of ................

This is another model that represents ................

This is an ingenious construction designed by ................

This is a simple instrument for ................

Is another simple game created with ................

Another detail taken from this video is ................

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Listen to the following song that a math teacher wrote to teach you how

to do proportions and try to fill in the gaps:

MATHEMATICAL SONGS

LYIRICS

When you have a _______ you don’t have very far to go to get

a _______.

Set it _______ to another one then you say bring on the fun

you gotta proportion.

So many things proportions bring to _______.

You’ll be ecstatic when you know _______ measurement.

Find what x represents.

(Chorus)

Its so fun its so neat before now your life was _______,

but now you _______ about proportions.

You’re so smart now you know the _______.

Cross _______ is the right tool

get the one step _______.

_______ the variable you got the gist

remember before you would have _______,

but now you know about proportions.

(Chorus)

Its so fun its so neat _______ now your life was incomplete,

but now you know about proportions.

1º de ESO: Ratio and proportions 15

This is another videoclip about ratio and proportions. Try to guess the

chorus and the main ideas about ratio and proportions presented in the

video. Enjoy it!

CHORUS:

MAIN IDEAS:

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PROJECT 1.-

Write the key words using the vocabulary given in these units. Make

a “WORD MAT” with these words:

PROJECT 2.-

Work in groups of four.

a) Look for information on the net about ratio and proportions.

b) Take photos by yourself of things which represents ratios or proportions

that appear around you.

c) Make a presentation with the best photos.

d) Finally, explain to your classmates the main ideas of your presentation

and the relationship with this unit.

FINAL PROJECT

Key vocabulary

WORD MAT:

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Know the elements of a ratio. YES NO NOT YET

Know the elements of a proportion. YES NO NOT YET

Understand the difference between ratio and proportions. YES NO NOT YET

Calculate increase and decrease percentages. YES NO NOT YET

Solve real situations exercises by using percentages. YES NO NOT YET

Know the relation between percentages, fractions and decimals.

YES NO NOT YET

Know the difference between direct and inverse proportions.

YES NO NOT YET

Be able to work in a group. YES NO NOT YET

Be able to seek information from various sources. YES NO NOT YET

Explain well reasoned the kind of proportion used. YES NO NOT YET

Know how to reduce a percentage. YES NO NOT YET

Recognize the presence of the proportionality around me. YES NO NOT YET

Describe a proportion through its elements. YES NO NOT YET

Explain the components of a proportion. YES NO NOT YET

Make a short presentation. YES NO NOT YET

Describes some examples of magnitudes directly proportional.

YES NO NOT YET

I

CAN

Describes some examples of magnitudes indirectly proportional.

YES NO NOT YET

SELF-ASSESSMENT

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