Maths in Plasencia Final

7/27/2019 Maths in Plasencia Final

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MATHS IN PLASENCIA

Premio Joaqun Sama a la Innovacin Educativa 2013

J. Csar Brcena SnchezM. Teresa Martn Gmez


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INTRODUCCINLa actividad MATHS IN PLASENCIA, nace del trabajo colaborativo de dos profesores de la

seccin bilinge del IES Sierra de Santa Brbara, que trabajando dentro de unametodologa AICLE, pretendemos por un lado hacer a los alumnos protagonistas de supropio aprendizaje y por otro buscar espacios de trabajo interdisciplinares donde elestudio y desarrollo de una segunda lengua extranjera cobre realmente un sentidoprctico.La idea de MATHS IN PLASENCIA nace dentro del seno del proyecto europeo ITEC, quepretende poner en marcha escenarios de aprendizaje para las aulas del futuro,introduciendo importantes transformaciones metodolgicas de la educacin y el uso denuevas herramientas tecnolgicas.El trabajo ha sido elaborado por los alumnos del 1 de ESO de la seccin bilinge del IESSierra de Santa Brbara junto a los profesores de ingls y matemticas del mismo.

El objetivos de MATHS IN PLASENCIA es la de crear un juego, a modo de gymkanamatemtica, donde se presentan diversos problemas matemticos REALES, que deben serresueltos en su propio entorno.Uno de los atractivos ms importantes de la actividad es que dicho juego ha sidoelaborado al 100% por los alumnos de 1 de ESO del IES Sierra de SantaBrbara, con el objeto de ser puesto en marcha, no por ellos mismos, sino por losalumnos de 6 de primaria del colegio San Miguel Arcngel de Plasencia, con quieneshasta hace unos meses compartan centro de estudios.Al margen de los objetivos y contenidos puramente acadmicos, nos ha permitidoestrechar los lazos y colaboraciones con el colegio, acercando nuestros profesores,instalaciones y medios a quienes seran nuestros futuros alumnos, relajando lo que en

algunos casos supone un traumtico paso de una etapa a otra. Gracias a la interaccin dealumnos de los dos centros hemos conseguido en parte, suavizar los grandes cambios quepara nuestros nuevos alumnos ha supuesto ese cambio.

En las siguientes pginas encontrars las pruebas que se presentan a los grupos, sussoluciones, los recorridos de los diferentes equipos.Tras cada prueba cada equipo recibe una de las letras que forman la palabra CATHEDRAL(palabra secreta y que ser el punto final de nuestro viaje).

Esperamos que lo disfrutis tanto como nosotros lo hemos hecho!


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GRUPO 1


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GEOMETRICAL SHAPES

QUESTIONWe can find geometrical shapes everywhere.

You have to look for and take photos of objects with octogonal, triangular, square, rectangularand circular shapes.

You must show your pictures before you get the last test .


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SIMMETRY

QUESTIONWe can find symmetry in many elements of nature, but also in many objects objects around

us, in our cities.

Look at the car tyres around you. Many of them have pentagonal symmetry (the samegeometrical structure is repeated 5 times closing the circumference)

You have to look for and take photos of at least 3 wheels which have this property.



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THE BINAvda. Del Valle

QUESTIONNow that summer is here, we like to drink fizzy drinks when it's hot. After drinking them, youmust throw the can into the bin!Do you know how many cans of coke or any other soft drink can fin (without squashing them)in the bin you have in front of you?

CLUESVolume of a cylinder V= r2 h Volume of a coke can

ANSWERSa) 171 cans Go to point 15

b) 103 cans Go to point 5

c) 77 cans Go to point 7

d) 52 cans Go to point 6


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CALCULATIONSFirst of all, we calculate the volume of the bin (cylinder). We need to measure the height andthe radius:

radius r = cm height h = cm

The volume is V= r2

h = cm3

Now, we convert the volume in liters, dividing by 1000

Vbin = l

And we also convert the volume of the can to liters

Vcan= l

Finally to find the number of cans that fit in the bin we divide both volumes:

Number of cans = Vbin : Vcan = cans

YOUR ANSWER IS:


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THE RAMPPza. San Nicols

QUESTIONThe maximum inclination of the access ramps must be 12% when the length is less than 3m,10% when the length is less than 10 m and 8 % in the rest of ramps.

Does the access ramp in San Nicols church fulfil these conditions?

How much is the slope?

CLUES

ANSWERSa) slope = 9% and it fulfils the conditions Go to point 3

b) slope = 11% and it doesn't fulfil the conditions Go to point 5

c) slope = 11% and it fulfils the conditions Go to point 2

d) slope = 6% and it fulfils the conditions Go to point 4

slope

rise

run

slope=(rise : run) 100


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CALCULATIONS

YOUR ANSWER IS:


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THE STAIRSAvda Del Valle

QUESTIONFor stairs to be comfortable, measurements must followsome conditions:

60 cm < 2 x tread + riser < 65 cm

Do these stairs follow the rules?

CLUES

ANSWERSa) 2 x tread + riser = 222 cm and the stairs follow the rule Go to point 5

b) 2 x tread + riser = 182 cm and the stairs follow the rule Go to point 4

c) 2 x tread + riser = 182 cm and the stairs don't follow the rule Go to point 9

d) 2 x tread + riser = 222 cm and the stairs don't follow the rule Go to point 7


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CALCULATIONS

YOUR ANSWER IS:


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THEFLOWERPOTC/ Arcediano

QUESTIONHow much money would it cost to refill with soil one of the the flowerpots in Calle Arcediano ifa sack of 15 litres costs 5.50?

CLUES

ANSWERSa) 29.5 Go to point 6

b) 88 Go to point 3

c) 95.8 Go to point 2

d) 53 Go to point 1


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CALCULATIONSFirst of all, we calcullate the volume of the flowerpot (cuboid). We need to measure the height,width and length:

width w = cm height h = cm

length l = cm

The volume is V=w l h = cm3


Vflowerpot = l

We calculate the number of sacks we need dividing the volume of the flowerpot by the volume

of the sacks:

Number of sacks = So, we need sacks

Finally we calculate the total price multiplying the number of sacks by the price of each sack

Total price = Number of sacks x Price=

YOUR ANSWER IS:


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THE FOUNTAINPza. San Nicols

QUESTIONHow long would it take to fill this fountain if it wasempty?

Use the empty bottle that we give you.

CLUES

Vprism=Abase x height

Aregular.octagon=Perimeter x apothem

2

Consider the base of the fountain as a regular octagon

ANSWERSa) 4860 seconds

b) 9720 seconds

c) 1110 seconds

d) 2 minutes


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CALCULATIONSFirst of all, we measure the side, apothem and height of the fountain:

side s = cm height h = cm

apothem a = cm

The area of the base is Abase=Perimeter x a

2= cm2

The volume is Vfountain=Abase x height = cm3

The volume in liters is =

Now, we are going to calculate how many liters of water we get form each water supply:

Measure the time we need to fill the botle (1 liter)

t1 liter = s So we need the same time to get 4 liters (4 water supplies)

Finally, find out how long would it take to fill the fountain:

t = (Vfountain x t4 liters ) : 4 = seconds

YOUR ANSWER IS:


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THE ELEVATORLa Isla

QUESTIONHow long could a person of 70 Kg survive trapped in anelevator?Supposing there is not any hole to let the air come in.

CLUESOne person of 70 kg needs 0,245 liters of oxygen in 1

minute.

Air: 21% of oxygen and 79% of nytrogen.

ANSWERSa) 45 hours Go to point 9

b) 88 hours Go to point 7

c) 10 hours Go to point 6

d) 53 hours Go to point 7


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CALCULATIONSFirst of all, we calcullate the volume of the elevator (cuboid). We need to measure the height,width and length:


length l = cm



Velevator = l

Only the 21% of this volume is oxygen:

Voxygen=Velevator x21

100= l

A person of 70 Kg needs 0.245 liters / minute

Dividing both volumes, we get how long could a person survive

tsurvive=Voxygen :Vneeded = min = hours

YOUR ANSWER IS:


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THEBOLLARDSAvda de la Salle

QUESTIONWe want to paint the bollards that are in the Puerta del Sol and they have a spherical shape.We have chosen some cans of paint that cost 10 . Each can contains 5 kg of paint. We knowthat we can paint 5m2 with 1 kg of paint.

How much will it cost to paint all the balls that are on the pavement?

CLUES

ANSWERSa) 40 Go to point 15

b) 30 Go to point 6

c) 20 Go to point 4

d) 10 Go to point 9


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CALCULATIONSFirst of all, we calcullate the surface area of the sphere. We need to measure the radius:

radius r = cm

The area is V=4 r 2

= cm2

Now, we convert the area to cm2 dividing by 10000

A = m2

Now we count the number of bollards we have to paint: bollards

So the total area to paint is m2

We need cans, therefore we will spend euros

YOUR ANSWER IS:


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THE GARDENQUESTION

You have reached the final point of our game. Nowwe want you to calculate the area of one of thegardens placed in front of the CATHEDRAL.

Consider it as a rectangle minus a quarter of a circle

CLUES

ANSWERSa) 171 m2

b) 103 m2

c) 77 m2

d) 52 m2


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CALCULATIONSWe measure both sides of the rectangle (b and h) and the radius of the quarter of circle.

base b = m height h = m

radius r = m

We start calculating the area of the rectangle:

Arectangle=b x h = m2

Now, the area of the quarter of circle

Aq.circle= x r

2

4= m2

The final area is the difference of both areas.

Agarden=ArectangleAq.circle = m2

YOUR ANSWER IS:


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GRUPO 2


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GEOMETRICAL SHAPES





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SIMMETRY


us, in our cities.





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The volume is V= r2

h = cm3


Vbin = l


Vcan= l



YOUR ANSWER IS:


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CLUES





slope

rise

run



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CALCULATIONS

YOUR ANSWER IS:


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CLUES






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CALCULATIONS

YOUR ANSWER IS:


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CLUES


b) 88 Go to point 3


d) 53 Go to point 5


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length l = cm



Vflowerpot = l


of the sacks:




YOUR ANSWER IS:


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CLUES



2


ANSWERSa) 4860 seconds Go to point 1

b) 9720 seconds Go to point 2

c) 1110 seconds Go to point 3

d) 2 minutes Go to point 3


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apothem a = cm


2= cm2








YOUR ANSWER IS:


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THE ELEVATORLa Isla



minute.







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length l = cm



Velevator = l



100= l




YOUR ANSWER IS:


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CLUES

ANSWERSa) 40

b) 30

c) 20

d) 10


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radius r = cm

The area is V=4 r 2

= cm2


A = m2




YOUR ANSWER IS:


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THE GARDENQUESTION



CLUES

ANSWERSa) 171 m2

b) 103 m2

c) 77 m2

d) 52 m2


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radius r = m




Aq.circle= x r

2

4= m2



YOUR ANSWER IS:


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GRUPO 3


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GEOMETRICAL SHAPES





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SIMMETRY


us, in our cities.





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The volume is V= r2

h = cm3


Vbin = l


Vcan= l



YOUR ANSWER IS:


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CLUES





slope

rise

run



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CALCULATIONS

YOUR ANSWER IS:


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CLUES






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CALCULATIONS

YOUR ANSWER IS:


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CLUES


b) 88 Go to point 3


d) 53 Go to point 1


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length l = cm



Vflowerpot = l


of the sacks:




YOUR ANSWER IS:


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CLUES



2


ANSWERSa) 4860 seconds

b) 9720 seconds

c) 1110 seconds

d) 2 minutes


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apothem a = cm


2= cm2








YOUR ANSWER IS:


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THE ELEVATORLa Isla



minute.







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length l = cm



Velevator = l



100= l




YOUR ANSWER IS:


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CLUES

ANSWERSa) 40 Go to point 15

b) 30 Go to point 6

c) 20 Go to point 1

d) 10 Go to point 4


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radius r = cm

The area is V=4 r 2

= cm2


A = m2




YOUR ANSWER IS:


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THE GARDENQUESTION



CLUES

ANSWERSa) 171 m2

b) 103 m2

c) 77 m2

d) 52 m2


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radius r = m




Aq.circle= x r

2

4= m2



YOUR ANSWER IS:


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GRUPO 4


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GEOMETRICAL SHAPES





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SIMMETRY


us, in our cities.





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The volume is V= r2

h = cm3


Vbin = l


Vcan= l



YOUR ANSWER IS:


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CLUES





slope

rise

run



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CALCULATIONS

YOUR ANSWER IS:


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CLUES






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CALCULATIONS

YOUR ANSWER IS:


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CLUES


b) 88 Go to point 3


d) 53 Go to point 7


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length l = cm



Vflowerpot = l


of the sacks:




YOUR ANSWER IS:


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CLUES



2


ANSWERSa) 4860 seconds Go to point 4

b) 9720 seconds Go to point 2

c) 1110 seconds Go to point 3

d) 2 minutes Go to point 2


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apothem a = cm


2= cm2








YOUR ANSWER IS:


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THE ELEVATORLa Isla



minute.







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length l = cm



Velevator = l



100= l




YOUR ANSWER IS:


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CLUES

ANSWERSa) 40

b) 30

c) 20

d) 10


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radius r = cm

The area is V=4 r 2

= cm2


A = m2




YOUR ANSWER IS:


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THE GARDENQUESTION



CLUES

ANSWERSa) 171 m2

b) 103 m2

c) 77 m2

d) 52 m2


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radius r = m




Aq.circle= x r

2

4= m2



YOUR ANSWER IS:


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RECORRIDOSGRUPOS


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GRUPO 1 Pza. S. Nicols (Ramp) 1

Parking Isla (Elevator) 5

Avda. Del Valle (Bin) 9

Avda del Valle (Stairs) 15

P. del Sol (Bollards) 7

C/Arcediano (Flowerpot) 4

Pza. S. Nicols (Fountain) 1

GRUPO 2 Pza. S. Nicols (Fountain) 1 Pza. S. Nicols (Ramp) 1


Parking Isla (Elevator) 5


Avda. Del Valle (Stairs) 15


GRUPO 3 Parking Isla (Elevator) 5


Avda. Del Valle (Stairs) 15


Pza. S. Nicols (Ramp) 1


Pza. S. Nicols (Fountain) 1

GRUPO 4

Maths in Plasencia Final

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