Set of Science Tasks Teaching Through Robotics

8/15/2019 Set of Science Tasks Teaching Through Robotics

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PHYSICS, MATHEMATICS AND INFORMATION TECHNOLOGY TASKSconcerning using Lego robots

in building industry and environment protection

PHYSICS

Task 1

Fill in:

1. ____________ of movement we call lines which describes a body performing themovement.

2. We call a rectilinear motion which ____________ is______________ line.

3. A motion which trajectory is a curve track is called ________________.

4. The length of the trajectory between two points is called _____________ travelledby the object.

5. Examples of the distance is measured by __________ and __________________.

Solution:

1. ___Trajectory_________ of movement we call lines which describes a bodyperforming the movement.

2. We call a rectilinear motion which _____trajectory_____ is _____straight________line.

3. A motion which trajectory is a curve track is called _______curvilinear_________.

4. The length of the trajectory between two points is called the_____distance_____travelled by the object.

5. Examples of the distance is measured by ___meter____ and ____kilometer_____.


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Task 2

The figure below shows the Wanderer's way from home to school.

1. Mark the vector on the figure showing the movement of the Wanderer from hometo school.

2. The beginning of displacement vector is at the point ___________.

3. The end of displacement vector is at the point ___________.

4. Calculate the approximate length of the vector displacement. Assume that 1 cm is100 m.

5. Calculate the distance travelled by the Wanderer from home to school. Assumethat 1 cm equals 100 m.

6. Calculate the difference between the way Wanderer travels from home to schooland the length of the displacement vector.

7. Describe the displacement vector features.

Solution:

1. Mark the vector on the firgure showing the movement of the Pilgrim from home toschool.

2. The beginning of displacement vector is at the point ____A_______.

3. The end of displacement vector is at the point ______E_____.

4. Calculate the approximate length of the vector displacement. Assume that 1 cm is100 m.

800m.

A

B

C

SZKOŁA

,,,,,,,,,,E

D


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5. Calculate the distance travelled by the Pilgrim from home to school. Assume that 1cm equals 100 m.

0.7 + 2.4 + 4.1 + 4.1 + 0.3 = 11,6cm

11.6 * 100 = 1160m

6. Calculate the difference between the way Pilgrim travels from home to school andthe length of the displacement vector.

1160m-800m = 360m

7. Describe the displacement vector features.

Direction: southeast, length 8cm, turn: southeast, point of application: point A.

Task 3

Name trajectories of the Wanderer's movement along a geometrically defined route(square, triangle),following the dark line and along the wall.

Solution:

Rectilinear and curvilinear trajectories.

Task 4

The Wanderer moves uniformly straight and pulls a colorful block. Name all theforces the robot must struggle with. What can you say about the values of theseforces? Plot these forces on the graph.


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Solution:

Fg - force of gravity of the robot,

Fn - lift,

Fc – thrust of the engines,

Fo – drag

These forces are balanced.

Task 5

Build a running track measuring 2,60 meters for the Pilgrim. Using the circumferenceformula calculate the radius of the wheel which will be used to draw a circle.

Solution:

We use the circumference formula 2 r.

260cm=2*3,14*r

260=6,28*r

r=260/6,28

r=41,4cm

Answer: The radius is 41,4cm.


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1. Measure the time it took the Pilgrim to travel one lap, and calculate the robot'svelocity and impetus.

Solution:Use the formulae for velocity and impetus:

V=s/tp=m*v

2. Fill in the table using the data of relationship between the impetus of thePilgrim and duration.

p(m∙kg/s)

0,4

0,2t(s)

1 5

Solution:

m is a mass of the robot.

3. A voice travels 340 m/s. How long will it take you to hear your friend who iscalling you from the end of the room (the room is 7 meters long)?

Solution:

Data: Searched:V=340m/s t= ?

t(s) p(m∙kg/s) V(m/s)

0

1

25

8

12

t(s) p(m∙kg/s) V(m/s)

0 0 0

1 0,4 0,4/m

2 0,6 0,6/m

5 0,6 0,6/m8 0,6 0,6/m

12 1,4 1,4/m


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s=7mV=s/tt=s/vt=7/340=0,2s Answer: It will take you 0,2s. to hear the voice of your friend from the end of

the room.

Task 6

Build an obstacle course for the Pilgrim. Program it so it travels the course as fast asit can. Measure the distance and time, then calculate the robot's velocity andimpetus.

Solution:Use the formulae for velocity and impetus:

V=s/tp=m*v

Task 7

Having in mind that the Pilgrim moves with constant speed of 0,3 m/s, fill in the gaps:

t(s) 0 5 10 15

s(m) 0 9 12

Using the data from the table plot the graph of relationship between the distance andtime.

Solution:

t(s) 0 5 10 30 40 15

s(m) 0 1,5 3 9 12 50


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Task 8

Three teams have to perform a clean-up work. The first team would accomplish thistask within 12 days, a second team within 15 days, and the third team in 8 days.

What time would all the teams need to accomplish this task if we assume that they

will work together?

Solution:

x- number of days needed for all three teams to carry the task

The efficiency of the first team 1/12 x

The efficiency of the second team 1/15 x

The efficiency of the third team 1/8 x

The equation will be as follows:

1/12 x+1/15 x+1/8 x = 1

10/120 x+8/120 x+15/120 x = 1

33/120 x = 1

x = 1/120

33 =1 *

33

120

x = 311

7

Answer : 311

7

days.


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Task 9

Calculate an average velocity of the Pilgrim clearing up the plot.

Solution:

Data:

s – a distance travelled by the Pilgrim during the clean-up

t – time needed by the Pilgrim to do the clean-up

To find:

V avg. =?

Solution:

V avg. = s:t

To get the average velocity divide distance by.

Task 10

Calculate the average velocity of the Pilgrim cleaning up the mock-up.

Solution:

Data:

s – a distance the Pilgrim travelled

t – time

To find:

V avg =?

Solution:

V avg = s:t

Divide the distance by time to get the average velocity.


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Task 11

Explain why different objects have different colors?

Solution:

The white light is a mixture of lights of different colors. An object is seen as white if itreflects all of the components of white light, and the object is seen as red when itreflects the red light and absorbs other colors.

Task 12

Use the Pilgrim and a prism to refract the white light into other several colors. List

colors you see passing continuously one into the other in the spectrum of white light.

Which color of light is dispersed quicker and which is the slowest?

Solution:

White light is a mixture of these colors: red, orange, yellow, green, blue and violet.The red light is dispersed quickly, whereas the violet light is dispersed slowly.

Task 13

Observe the colored blocks through a red light filter. What have you noticed?

Solution:

Only red light is dispersed by a light filter and all the other colors are absorbed. Thecolored blocks which are of different color than red will be seen as black when welook at them through the red light filter.

Task 14

Perform needed calculations and fill in the gaps in the table.

No. Force F(N) Distance s(m) Work W(J) Time (s) Power P(W)

1 20 400 50

2 90 2700 60

3 150 10500 120

4 240 60 20

5 15 7500 50


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Solution:

Use these formulae:

W= F*s;

P=t

W

No. Force F(N)Distance s

(m)Work W(J) Time (s) Power P(W)

1 20 400 8000 50 160

2 30 90 2700 45 60

3 150 70 10500 120 87,5

4 240 5 1200 60 20

5 500 15 7500 150 50

Task 15

Using a kitchen scale calculate the influence of gravity force over the Strongman.

Assume the gravitational acceleration is 10 m / s2.

Solution:

Data:

g=10m/s2

the Strongman’s mass given in kilograms

To find:

Fc=?

Use given formula

Fc= m*g and the result is given in Newtons.


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Task 16

What kind of work will the Strongman perform by lifting the can of GREEN-UP drink?Measure the quantities needed with proper instruments.

Solution:

Data:

m=0,276kg

h=14 cm=0,14m

g=10m/s2

To find:

W=?

W=Ep=m*g*h

W= 0,276*0,14*10(kg*m*m/s2)=0,3864J

Answer: Work equals 0,3864 J.

Task 17

The Strongman moved the can of GREEN-UP drink for 50 cm moving on the flattable. Calculate work the Strongman did.

Solution:

Work equals 0J because the force of the direction perpendicular to the direction ofmovement of the body does not perform any work.

Task 18

The Strongman’s engine Power is 0,4 W. It marched for 5 minutes. What work wasperformed by the Strongman’s engine?

Solution:

Data:

P=0,4W, t=5min=300s

To find:

W=?


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W=P*t=0,4*300(W*S)=120J

Answer: Work equals 120J.

Task 19

The Strongman dropped the can of GREEN-UP drink from the edge of the table.What velocity will the can have when it is near the ground? Measure the height of thetable with a measuring tape.

Solution:

Data:

h=0,75m; g=10m/s2

To find:

V=?

According with rule of conservation of energy there is an equality Ep=Ek, so

m*g*h=1/2*m*v2

when simplified:

V2=2*g*h

V= gh2 = 75,0*10*2 =3,872983346m/s

Answer: The can’s velocity is circa 3,9 m/s.

Task 20

Calculate the kinetic energy of the Strongman travelling a distance of 100 cm. Useproper instruments to measure specified quantities.

Solution:

Data:

s=100cm= 1m

m=1,25kg

t=4,2s

To find:


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Ek=?

V=1:4,2(m/s)=0,238m/s

Ek=1/2*m*v2=1/2*1,25*0,2382(kg*m/s)=0,0354J.

Answer: Kinetic energy of the Strongman equals 0,0354J.

Task 21

Using a kitchen scale calculate the influence of gravity force over Amoeba. Assumethe gravitational acceleration is 10 m / s2.

Solution:

Data:

g = 10m / s2

Amoeba’s weight in kilograms

To find:

Fc =?

Use the formula:

Fc = m * g, and the result is given in Newtons.

Task 22

Calculate the pressure Ameoba exerts on the ground. Estimate the area of the Amoeba’s parts that touch the ground with the use of graph paper.

Solution:

Data:

m= 1,35kg , g=10m/s2

s- the area of the Amoeba parts that touch the Grodnu is Niven in square meters

To find:

p=?

F=1,35kg*10m/s2= 13,5 N


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Use the formula:

p= F : s and result is given in Pascals.

Task 23

What work will be performed by Amoeba when it will be moving for 2 minutes? Amoeba engine’s power is 0,4W.

Solution:

Data:

P=0,4W, t=2min=120s

To find:

W=?

W=P*t=0,4*120(W*S)=48J

Answer: Work is 48J.

Task 24

What is the result of collision of Amoeba with an obstacle? What kind of influence isit?

Solution:

Mutual influence of the bodies is direct, but the results of the influences will be:

Static – a body deformation,

Dynamic – change in body’s velocity.

Task 25

Draw vectors of forces balancing the forces influencing Amoeba. Name those forcesand state their sources.


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Solution:

Fc

Fg – a robot’s gravity force,

Fn – the lift force,

Fc – the thrust force of the engines,

Fo – drag

These forces are in balance.


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Task 26

A. Make your prediction for the black and white lines on the graph using data

logging. Label each line clearly. Why and how did you decide?

___________________________________________________________________

___________________________________________________________________

B. Based on the black and white sensor values, what kinds of colors do you think will

produce high color sensor readings in general? Lighter or darker ?

Task 27

A. Add lines to the graph below, showing what you think the lines for the colors red,

blue, green and grey will look like. How did you decide? why?

___________________________________________________________________

___________________________________________________________________

0

20

40

60

80

100

0 0,5 1 1,5 2 2,5 3

PREDICTION OF THE COLOR

SENSOR’S READINGS


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B. Now, measure the actual readings of the color sensor and state it in the table.

Color Reading

Red

Blue

Green

Grey

Black

White

Task 28

A. What’s the difference between color and hue / shade ?

___________________________________________________________________

___________________________________________________________________

0

20

40

60

80

100

0 0,5 1 1,5 2 2,5 3


SENSOR’S READINGS


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B. Why is it important to choose shades of the same color for this comparison?

Because in order to make a “fair comparison”, you needed to eliminate as many other

possible factors as possible. This is directly related to the “fair test” concept, where

external factors which bias the comparison need to be eliminated or controlled as

much as possible. If you did not do so, the real reason for the difference would be

unclear – is it the thing you’re examining, or the other unintended difference?

___________________________________________________________________

___________________________________________________________________

Task 29

Suppose the robot runs through a 10m stretch of tube/ cylinder and gives thefollowing data..

What does each arrow represent? ( the leftmost arrow, rightmost and middle arrow):

___________________________________________________________________

___________________________________________________________________

Why the middle arrow has a lower sensor reading?

___________________________________________________________________ ___________________________________________________________________


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SOLUTIONS TO TASKS 26 – 29

Task 26

A. Make your prediction for the black and white lines on the graph using data

logging. Label each line clearly. Why and how did you decide?

___________________________________________________________________

___________________________________________________________________

B. Based on the black and white sensor values, what kinds of colors do you think will

produce high color sensor readings in general? Lighter or darker ?

Task 27

A. Add lines to the graph below, showing what you think the lines for the colors red,

blue, green and grey will look like. How did you decide? why?

___________________________________________________________________

___________________________________________________________________

0

20

40

60

80

100

0 0,5 1 1,5 2 2,5 3


SENSOR’S READINGS


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B. Now, measure the actual readings of the color sensor and state it in the table.

Color Reading

Red 60

Blue 40

Green 50

Grey 65

Black 5-10

White 90

0

20

40

60

80

100

0 0,5 1 1,5 2 2,5 3


SENSOR’S READINGS


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Task 28

A. What’s the difference between color and hue / shade ?

___________________________________________________________________

___________________________________________________________________

B. Why is it important to choose shades of the same color for this comparison?

Because in order to make a “fair comparison”, you needed to eliminate as many other

possible factors as possible. This is directly related to the “fair test” concept, where

external factors which bias the comparison need to be eliminated or controlled as

much as possible. If you did not do so, the real reason for the difference would be

unclear – is it the thing you’re examining, or the other unintended difference?

___________________________________________________________________

___________________________________________________________________

Task 29

Suppose the robot runs through a 10m stretch of tube/ cylinder and gives the

following data..

What does each arrow represent? ( the leftmost arrow, rightmost and middle arrow):

Hole μεγαλύτερη απόσταση, μηδενική μέτρηση

___________________________________________________________________

________________________________________________________________

Why the middle arrow has a lower sensor reading?

Hole μεγαλύτερη απόσταση, μηδενική μέτρηση


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MATHEMATICS

Task 1

Draw a square, an equilateral triangle and hexagon with a side of 65 cm. Calculatethe area and circumference of these figures.

Solution:

a=65cm

Use these formulae:

Triangle:

P=a2 3 /4

Circumference=3a

P=65*65 3 /4=4225 3 /4=1056,25 3 cm2

Circumference=3*65=195cm.

Square:

P=a2

Circumference =4a

P=65*65=4225cm2

Circumference =4*65=260cm.

Hexagon:

P=6a2 3 /4

Circumference =6a

P=6* 65*65 3 /4=6*1056,25 3 = 6337,5 3 cm2

Circumference = 6*65=390cm.


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The area of the square equals 4225cm2, triangle = 1056,25 3 cm2, and hexagon's

area is 6337,5 3 cm2 . The circumference of square equals 260cm, triangle =

195cm, and hexagon's circumference is 390cm.

Task 2

The graph shows the relationship between the velocity and time of the Pilgrim during12 minutes of its working.

V(cm/min) 300

50

1 2 t(min)

1. The Pilgrim moved with a speed of ____________________ for 2 minutes.

2. With a ration of 200 cm / min the Pilgrim moved between ______ min to _______min.

3. During the whole operating time the Pilgrim stopped ___________ time(s).

4. The total operating time was _________min.

5. The distance the Pilgrim travelled with the speed of 100 cm / min

is _________cm.

6. The distance traveled by the Pilgrim during 12 minutes is ______________.

7. The Pilgrim, moving with the speed of 300 cm / min, travelled ______ timesgreater distance than when it was moving with a speed of 150 cm / min.

8. The average velocity of the Pilgrim during the whole operating time is _____ cm /min.

Do necessary calculations.


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Solution:

1. The Pilgrim moved with a speed of ______300 cm/min_________ for 2 minutes.

2. With a ration of 200 cm / min the Pilgrim moved between______2min_________ to

_______4min______.

3. During the whole operating time the Pilgrim stopped _____1______ time(s).

4. The total operating time was _____1min____________.

5. The distance the Pilgrim travelled with the speed of 100 cm / min

is ______200cm_________.

6. The distance traveled by the Pilgrim during 12 minutes is ______________.

600cm + 400cm + 200cm + 500cm + 300cm = 2000cm

7. The Pilgrim, moving with the speed of 300 cm / min, travelled ___2___ timesgreater____ distance than when it was moving with a speed of 150 cm / min.

8. The average velocity of the Pilgrim during the whole operating time is ___ 167cm /min _____.

2000cm / 12min = 166, (6) cm / min.

Task 3

Use a running track measuring 2,60 meters to count:

1. How many laps will a sprinter run for:

a) 100m,Solution:

100/2,6=38,46

Answer: He must run 38,5 laps.

b) 200m,Solution:

200/2,6=76,92

Answer: He must run 77 laps.

c) 400m,Solution:

400/2,6=153,85



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d) 800m,Solution:

800/2,6=307,69


e) 5 km,Solution:

5000/2,6=1923,08


f) 10kmSolution:

10 000/2,6=3846,15


2. Calculate the area of a given athletics stadium and an area of a given runningtrack.

Solution:Use the formula for area of circle r 2.

P =3,14*41,4*41,4=5381,8344cm2 (stadium)

The width of the running track 20,5cm.

41,4 – 20,5=20,9cm

P (inner circle) = 3,14*20,9*20,9=1371,5834 cm2

P (outer circle)=5381,8344cm2 - 1371,5834 cm2 = 4010,251 cm2.

Answer: The area of the stadium and the running track is 5381,8344cm2

and 4010,251 cm2 respectively.

3. Calculate the circumference of the stadium.

Solution:Measure the radius of the stadium and calculate the circumference with the

2 r formula.

4. What percentage of the whole stadium is a running track?

Solution:

4010,251 cm2 / 5381,8344cm2 =0,745

0,745*100%= 74,5%

Answer: 74,5%

5. How many acres is the athletics stadium area?


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Solution:

The area of a stadium =5381,8344cm2= 0,53818344m2= 0,0053818344 acres. Answer: 0,0053818344 acres

6. How many minutes did it take the Pilgrim to run 6.5 kilometers on the 2.60meter long stadium if it travelled one lap in 12 seconds?

Solution:

6500m/2,6m= 2500 laps2500*12min=30000s=500min=8,5 h Answer: About 8,5 h

Task 4

Change hours to minutes. Find the answers in the box and fill the gaps in the tablewith the corresponding letters. Read password.

45 min O 50 min I 75 min D

25 min Ł 20 min U 33 min E

10 min H 30 min R 66 min W

40 min C 15 min T 6 min Z

Solution:

Task 5

Build a plot with the completed house within its boundaries basing on the given

architectural plan. Do the necessary calculations related to the scale of the map.

Hours 1/2h

1/3h

2/3h

1/6h

0,25h

0,75h

0,1h

1,25h

0,5h

3/4h

1,1h

5/6h

0,55h

Minutes

Letter

Hours 1/2h 1/3h 2/3h 1/6h 0,25h 0,75h 0,1h 1,25h 0,5h 3/4h 1,1h 5/6h 0,55h

Minutes 30 20 40 10 15 45 6 75 30 45 66 50 33

Letter r u c h t o z d r o w i e


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Solution:Calculate the actual dimensions of the plot, outbuildings and skips:Plot:Width: 20cm*10=200cmLength:10cm*10=100 cmHouse:Width : 6cm * 10= 60 cmLenght: 3,6 cm * 10=36 cmOutbuildings:

1. Width : 1cm * 10= 10 cmLength: 0,4 cm * 10=4 cm


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2. Width : 0,9cm * 10= 9 cmLength: 0,6 cm * 10=6 cm

Skip:Width : 0,5cm * 10= 5 cmLenght 0,4 cm * 10 = 4 cm

Build the construction site.

Task 6

Calculate the area of the built plot and other buildings on this plot. What part of the

area of the whole plot is an area occupied by buildings on this plot?

Solution:

Use the formula of the area of the rectangle.

P= a*b

The area of the plot:

200cm*100cm=20 000cm2

The area of the outbuildings:

60cm*36 cm=2160 cm2

10cm*4cm=40cm2

9cm*6cm=54cm2

The area of the skip:

5cm*4cm=20cm2

6*20=120cm2

What part of the area of the whole plot is an area occupied by the outbuildings?

2160+40+54=2254

2254/20 000=0,1127.

Task 7

Calculate the cubature of the house on a plot and the outbuildings. The house is 50

cm high. How many cm3 are there per a single person, if there are three people living

there?

Solution:

The house’s cubature:

2160*50=108 000cm3

The cubature of the outbuildings:


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40*50=200cm3

54*50=2700cm3

108 000:3=36 000 cm3.

Answer: There are 36000 cm3 of the building per each person.

Task 8

How many centimeters of the fence is needed to acquire in order to enclose the

entire plot? The main gate is 4cm wide, and two wickets are 1 cm wide each.

Solution:

4cm+2*1cm= 4cm+2cm=6cm

Calculate the area of the plot:

2*200cm+2*100cm=600cm

600cm-6cm=594cm.

Answer: In order to enclose the entire plot 594 cm of the fence are needed.

Task 9

Delineate a line of the sidewalk and the main entrance to the plot on the mock-up

which are meant to be tiled with square tiles of 1.5 cm each. How many tiles should

you use?

Solution:

The sidewalk and the entrance are 6cm wide, and 4 cm long.

The area of the sidewalk and the entrance is:

6cm*4cm=24cm2

The tile’s area is:

1,5cm*1,5cm=2,25cm2

How many tiles are necessary to be used:

24:2,25=10,(6).

Answer: 11 tiles will be used.


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Task 10

How many apple trees can be planted on part of the plot with dimensions of 25cm x

12cm, if one fully-grown apple tree should cover an area of 25cm2 to fruit?

Solution:

Calculate the area of the part of the plot on which the fruit trees will be planted:

25cm*12cm=300cm2

How many trees can be planted?

300:25=12

Answer: 12 trees can be planted.

Task 11

1 liter of paint is enough to paint 8m2 of a flat surface. How many liters of paint will be

used to paint a cubic container of 8m3 volume? The container will be painted inside

and outside.

Solution:

Calculate the edge of the container:

a3

= 8

a = 3 8

a = 2 m

The area of the container:

P = 6a2

P=6*22=6*4=24m2

24*2=48m2

How many litres of paint are needed?

48:8=6

Answer: 6 litres of paint is needed to paint the container.

Task 12

There is the same amount of air in the given room like in the cube which edge is 4 m

long. Is it possible for 7 people to stay in that room if it is known that one personneeds 6m3 of air to breathe?


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Solution:

Calculate the volume of the room:

V= 43

=64m3

The number of people who can stay inside the room:

64:6=10,(6)

Answer: There can be 7 people in the room.

Task 13

Brimful skips and garbage containers pose increasing problems with their disposal.Each of us produces approximately 300 kg of garbage per year. How many 8 ton

cars do we have to use to dispose of annual collection of garbage from our town?

Solution:

Number of citizens living in Zawiercie: 51 860300 * 51860= 15558000kg the number of kilograms of garbage collected in town15558000:8=1944750 Answer: We need 1944750 cars to remove the garbage from the town.

Task 14

Composting the wastes produced in a single household reduces the overall amount

of rubbish. Approximately 1/4 of waste generated in the household and the garden is

compostable. How many kg of waste is composted in the household with a family of

five? What percentage of all wastes from Zawiercie constitute the garbage of this

family? Present the result as exponential notation.

Solution:

The amount of garbage collected in the household of five

300*5=1500kg

1500:4=375kg- the amount of wastes able to be composted

1500-375=1125kg

Calculate what percentage of all wastes from Zawiercie constitute the garbage of the

given family.

(1125: 15558000)*100%=0,007231%=7,231*10-3 %.


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Task 15

In a town, solid waste removal costs 10 zloty per person in case of segregated

wastes, otherwise the amount for removal is 15 zloty per person. There has been a

15% increase of charge for that service in June. How much money will a family of five

pay for removal of waste in both cases? How much money will they save if theysegregate wastes?

Solution:

The bill for segregating wastes will amount:

0,15*10=1,5

1,5*5=7,5

10*5=50

50+7,5=57,50zł

The bill for non-segregated wastes

0,15*15=2,25

2,25*5=11,25

15*5=75

75+11,25=86,25zł

86,25-57,50=28,75zł

Answer: The family will save 28,75 zloty per month.

Task 16

A garbage bin volume is 2 litres. Calculate how many bins of that type full to the brim

are needed to fill in 75% the tank with a volume of 3m3.

Solution:

2l= 2dm3=0,002m3

0,75*3=2,25m3

2,25:0,002=1125

Answer: We need 1125 two-litre bins.


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Task 17

In Poland, 530 000 tons of paper waste are used annually. A paper recovery rate is

35%. How many tons of paper are recovered in Poland?

Solution:

0,35*530 000=185500t

Answer: 185500 tons of paper are annually recovered in Poland.

Task 18

In Poland, 12% glass (42 500 tons) is annually recovered from the whole waste glass

amount. How many tons of waste glass are produced in Poland annually?

Solution:42 500 : 12%= 42 500 : 0,12= 354166,7 t

Answer: 354166,7 tons of waste glass are produced in Poland annually.

Task 19

Three piles of garbage weight a total of 26kg. The ratio of their weight is 1: 5: 7. How

much weigh the heaviest?

Solution:

1+5+7=13- number of all piles

26:13=2- a part of one pile

7*2=14kg

Answer: The heaviest garbage pile weighs 14kg.

Task 20

The waste removal company hires 6 men more than women, and for every 4 women

there are 5 more men. How many employees does the company employ?

Solution:

x - number of women

x+6- number of men

Use an equation

4(x+6)=5x

4x+24=5x


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5x-4x=24

x=24

24+24+6=54

Answer: The company hires 54 employees.

Task 21

The Pilgrim's task is to sow 1.5 hectare of land in the shape of a rectangle with an

ecologic type of grain. How long will it take it to sow this area? Using a mock-up of

1,5m x 2m make the appropriate measurements and answer the question.

Solution:

It takes the Pilgrim 180 seconds to sow the whole area with seed - those are themeasured results.

The mock-up's area is

1,5*2=3m2

1,5 ha=15000m2

15000m2: 3 m2=5000

240*5000=900000 seconds = 15000 minutes = 250 hours

Answer: The Pilgrim will sow the area in 250 hours.

Task 22

The Strongman consumes 248 kcal when marching for 60 minutes. How many cans

of GREEN-UP drink would it have to drink to travel a distance of 100 cm? Show the

relationship between joules and calories. Find the required data on the can.

Solution:

By reading the information from the can we know that 114kcal=477kJ.

114cal=477J

We derive the relationship between calories and Joules dividing by 114 and we get

1cal= 477:114J

1cal=4,184J.

We know that


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60min - 248kcal

1min - 248:60kcal=4,13kcal

1 s - 0,0688(3)kcal

4,2 s- 0,2891 kcal

From the previous task we know that the Strongman travels 100 cm in 4,2 secondsso it Leeds 0,2891 kcal to accomplish this task.

How much drink will the Strongman need to drink?

0,2891kcal:114kcal=0,0254.

Answer: The Strongan will drink 0,0254 of the can’s volume.

Task 23

Build a slalom for Amoeba. State the starting and stopping point. Measure the time Amoeba needs to finish the slalom, measure the course’s length and measure itsvelocity.

Solution:

Data:

s – distance travelled by Amoeba,

t – time Amoeba needs to travel the course [s]

To find:

V avg =?

Solution:

V avg = s:t

Divide distance by time to find out what the average velocity is.


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Task 24

(A) In groups of three to four students, create and label a straight line (made from

strip) that is divided in 5 points as follows:

‘ Start, Checkpoint 1, 2, 3, Finish’.

(B) Program the robot (ROBOMATH ) to reach to the Finish line. As the robot moves

along the straight line, from Start point to Finish point, time the progress of the robot

at each checkpoint i.e. Checkpoint 1, 2, 3 and at the Finish line and record the time

the robot crosses each mark.

(C) Repeat the activity for each robot.

(D) Identify the equation that can be used to calculate times for longer courses.

(E) Repeat the activity with different types of robots and compare the slopes of all the

robots’ times.

Figure 1, Straight Line course

Table 1

Robot name _________

Checkpoint 1 Checkpoint 2 Checkpoint 3 Finish

START FINISH1 2 3

FINISH31

2

START


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Task 25

Summary:Students will work in groups of three to four. Each team will time various robots’

progression at four points on a straight-lined course (see figure 1) and will use thetime data to create X/Y tables with equations and a coordinate graph to show andcompare slopes.

Outline:

Organize the times each robot passed the checkpoints and the finish line in adata table for each robot tested.

Write and use an equation to calculate the times when the robots would crosscheckpoints on a longer course.

Use the data table to construct a coordinate graph showing the slopes foreach robot timed.

Activity A: A. Organize the time information from each of the robots’ drag race in a data table(see Sample Chart and Data Worksheet). Each group will develop an equation thatwill be used to calculate times at other checkpoints along the same course as well asalong the length of a longer course.Student groups will use a piece of graph paper to create a coordinate graph to plotthe slopes for each robot drag race.Students will plot the ordered pairs for each race by using a different color for eachrobot.

Robot name: the “RoboMath ”

Chart:

X (checkpoints) Equation Y (time in secs) Ordered pair

0 (start)

1

2

3

4 (finish)

Compare the results w ith the other teams . Did you com e up with the sameequat ion? If not, what factor do y ou b el ieve was the main on e for th is result ?

Activity B:Complete the two different following charts. Use the information given to figure outthe missing gaps:(Create and use an algebraic equation to make probable predictions).

Robot name: the “Baymax”

Chart:


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X checkpoints Equation _________

Y (seconds) Ordered pair

1 3.5 (1, 3.5)

2 (2, ___)

3 10.5 (3, 10.5)4 (finish) (__ , __)

Robot name: the “Robix” Chart:



1 (___, __ )

2 8 (2, 8)

3 (3, ___ )

4 (finish) (__ , __ )

Which robot won the race? ___________ How much faster did he run the course? ___________ If the course was twice as long, what would be the finishing times for:

the “Baymax” __________ , the “Robix” _______________ Create a coordinate graph on a piece of graph paper to show slopes for the

“Baymax” and , the “Robix”. Use different colors for the 2 slopes.


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SOLUTIONS TO TASKS 24, 25

For this activity we used a tape of length 40cm which we divided into four parts. Afterwards, we measured the times of five different robots at the checkpoints and

noted the results in the table below.

Robot name Checkpoint 1 Checkpoint 2 Checkpoint 3 Finish

RoboMath1 0.528 s 1.012s 1.564s 2.237s

RoboMath2 0.626s 1.172s 1.568s 2.195s

RoboMath3 0.544s 0.990s 1.452s 1.902s

RoboMath4 0.493s 0.903s 1.406s 1.840s

We plo t ted the po in ts on coord inate

axes for each robo t .

START FINISH1 2 3


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Then, we used regression to find the line of best fit.

The formula for the regression line is = + , where =

, = ̅.

The lines of best fit for each robot were calculated by Geogebra :

Robot Name Equation Slope

RoboMath1 = 0.569 0.0845 0.564

RoboMath2 = 0.51 + 0.11 0.51 RoboMath3 = 0.45 + 0.09 0.45 RoboMath4 = 0.45 + 0.02 0.45


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Activity:

Complete the two different following charts. Use the information given to figure out

the missing gaps:(Create and use an algebraic equation to make probable predictions).

Robot name: Baymax



1 3.5 (1, 3.5)

2 7 (2, 7)

3 10.5 (3, 10.5)

4 (finish) 14 (4 , 14)

Gradient =−

−=

.−.

− = 3.5

Equation: 3.5 = 3.5( 1)

= 3.5

Robot name: Robix



1 4 (1, 4 )

2 8 (2, 8)

3 12 (3, 12)

4 (finish) 16 (4 , 16 )

Gradient =−

−=

−

− = 4

Equation: 4 = 4( 1)

= 4

Which robot won the race? Baymax

How much faster did he run the course? 2 seconds

If the course was twice as long, what would be the finishing times for:Baymax : 28 seconds, Robix : 32 seconds

Create a coordinate graph on a piece of graph paper to show slopes forBaymax and Robix . Use different colors for the 2 slopes


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BaymaxRobix


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INFORMATION TECHNOLOGY

Task 1

Find Polish equivalents of words: algorithm, instruction, flowchart, list of steps, verbal

description, rectangle


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Task 2

Write the algorithm in the form of a list of steps and a flowchart for the Pilgrim movingforward in a straight line forward for 2 seconds.Use the Word to do the task and save it on your desktop as "thePilgrim".doc

List of steps

1. Start the Pilgrim.

2. Immediately start the left and right engines for 2 seconds.

3. Stop the Pilgrim.

A flowchart

Programming language LEGO

Start block

Move Steering block is responsible for moving forward the two engines. You mustselect one of three modes:• Depending on the time (On for Seconds)• Depending on the number of degrees (On for Degrees)• Depending on the number of rotations (On for Rotations),direction of the robot's movement, the power of the engines.

Move forward for 2 s.

START

STOP


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Task 3

Podaj przykłady zastosowania Wędrowca z wykorzystaniem: Give the examples ofusing the Pilgrim for:

a) linear algorithm - moving forward, backwards, moving from school to home

b) conditional algorithm - waste segregation c) iteration:

a fixed number of iterations – move along a square, triangle, hexagon

with When the instruction is repeated until the condition is met - cleaning thebuilding site,

When the condition is checked first, and only its performance allowsexecution of instructions.

Task 4

Write the algorithm in the form of a list of steps showing the movement of the Pilgrimalong the sides of a square (a side being 65 cm).Calculate the distance in meters for 1, 2,.... 10 laps using the spreadsheet. Name thespreadsheet "distance".Save the file on your desktop as "wedrowiec.xls"

lap side a[cm]

side a[m]

distancetravelled [m]

1

2

3

4

5

6

7

8

9

10

List of steps:

1. Start2. Forward for 0,65m3. Turn right4. Forward for 0,65m5. Turn right6. Forward for 0,65m7. Turn right8. Forward for 0,65m

9. Turn right10. Stop


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lapside a[cm]

side a[m]

distancetravelled [m]

1 65 0,65 2,6

2 65 0,65 5,2

3 65 0,65 7,8

4 65 0,65 10,4

5 65 0,65 13

6 65 0,65 15,6

7 65 0,65 18,2

8 65 0,65 20,8

9 65 0,65 23,4

10 65 0,65 26

Task 5

Write the algorithm in the form of a list of steps for the way the Pilgrim must travelfrom home to school according to the following figure (the scale being 1cm: 100m).Calculate the way from home to school in meters including the condition that theinput data is different from zero. Name your spreadsheet "home".

List of steps:

1. Start2. Forward for 70 m3. Turn left4. Forward for 240 m5. Turn right6. Forward for 410 m7. Turn left8. Forward for 410 m9. Turn left10. Forward for 30 m

11. Stop


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Task 6

Draw a table using a spreadsheet. Use the data from the Physics lesson. Enter theappropriate formula for calculating velocity checking the condition of "Do not divideby 0". Save the spreadsheet as "velocity".

DISTANCE[cm]

TIME [s] VELOCITY[cm/s]

TIME [s] VELOCITY[cm/s[

Notes

Draw the line graph of the relationship between the distance and time of the Pilgrim.

Task 7

Program the Pilgrim to move forward in a straight line for 20 seconds

.

Task 8Program the Pilgrim so it moves from one line to another and turns in the spot.

In order to make the Pilgrim turn in the spot we should"

• set the direction of the left engine movement backwards,

• set the direction of the right engine movement forward,

• set the same speed for both engines.


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Move forward

Turn

Move forward

START

STOP

Algorithm (flowchart)

List of steps

1. Start.

2. Instantaneous start the bothengines for specified time/number of

rotations.

3. Turning in the spot.

4. Instantaneous start the both

engines for specified time/number of

rotations.

5. Stop.

1. 2. 3. 4. 5.

Task 9

Program the Pilgrim so it moves along the sides of a square (one side being 65 cm).


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Task 10

Program the Pilgrim to move along a regular octagon.

Task 11

Write Polish words.

1. sorted by:

2. blocks3. a machine

4. the way of doing something

5. a task

6. sorting

7. sorted by:

8. the blocks used during IT class

9. f.e. touch

10. a plan


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1 W S T A W I A N I E

2 L E G O

3 R O B O T

4 A L G O R Y T M

5 O B O W I Ą Z E K

6 P O R Z Ą D K O W A N I E

7 S C A L A N I E

8 M I N D S T O R M S

9 C Z U J N I K

10 P R O J E K T

By Polish and Cypriot teachers

Documents

Set of Science Tasks Teaching Through Robotics