Lifelong Learning ProgrammeComenius Multilateral

Schoolpartnership:

“To play or not to play with water”

Mathematical workshop:“Water in numbers”

Gimnazija Matije Antuna Reljkovića, Vinkovci, Croatia

Task 1.

1) Study each country's monthly water bill of an average family.

2) Set a function which will help you to calculate a monthly cost of x m3 of used water.

3) Represent the function graphically.4) Calculate how much it has to be paid for

10m3, 20m3, 30m3.5) How much water was used if the family

paid 30€, 50€, 100€? 6) How many ice-cream balls can you buy

with the money used to pay 10m3 of water?

Task 2.1) Tap in your kitchen is damaged,

therefore water is dripping out of it. In 5 minutes 100 ml of water go out of the damaged tap. How much water ( litres) drips out of the tap per month?

2) Calculate the percentage of  rising water amount, if  previous month amount was 193.51 kn (26.2 €).

3) How many ice-cream balls can you buy for that money?

Task 3

1) Cistern in your bathroom is not good and water leaks. For 1 minute 50 ml of water leaks. Calculate how much has leaked ( litres) for a month?

2) How much it will increase the account in percentage, if the bill for the previous month was 193.51 kunas or 26.2 €?

3) How many ice-cream balls "have leaked"?

Task 4.1) In our school there are 25 classes. Every

class cleans school board approximately 50 times a week. If 2 litres of water is spent for one cleaning of a school board, how many cubic meters do we spend in one month?

2) How much do we pay for spent water in one month?

3) If smart board approximately costs 1000€, how many months should we stop cleaning school board, to raise enough money to buy one?

Task 5.How can bathers prevent wasting water?• Every pair of shorts absorb about 100 ml of

water more than Speedo swimming pants.• Calculate:• How much more water will be drained from a

pool where 200 men swim every day and then go out of the pool to dry out three times a day?

• Calculate the amount of water for:• a week• a month • a season (3 months).• Convey the results in liters and cubic meters !

Task 6.

• 150 students completed a questionnaire about water. One question was: „ What do you drink at home? WATER JUICES SOFT DRINKS „

• The results of questionnaire have shown that water is being drunk by 100 of students

• juices - 85 students• soft drinks - 65 students• water and juices - 55 students• water and soft drinks - 40 students• juices and soft drinks - 30 students• How many students drink water together with

juices and soft drinks?

Results:

Task 1.Bulgaria Croatia France Germany Italy Lithuania

2) C(x)=x C(x)=1.31x

C(x)=2.85x C(x)=5.04x C(x)=0.86x C(x)=1.77x

4) C(10) =10€C(20) =20€C(30 )=30€

C(10) =13,1€C(20) =26,2€C(30 )=39,3€

C(10) =28.5€C(20) =57€C(30 )=85.5€

C(10) =50.4€C(20) =100.8€C(30 )=151.2€

C(10) =8.6€C(20) =17.2€C(30 )=25.8€

C(10) =17.7€C(20) =35.4€C(30 )=53.1€

5) 30€ -30 000 l50€ -50 000 l100€ -100 000 l

30€ -22 900 l50€ -38 168 l100€ -76 336 l

30€ -10 500 l50€ -17 540 l100€ -35 080 l

30€ -5 990 l50€ -9 920 l100€ -19 840 l

30€ -34 700 l50€ -57 900 l100€ -115 800 l

30€ -16 940 l50€ -28 480 l100€ -56 500 l

6) 10 19 14 67.2 8 20.58

Task 1. 3) Represent the function graphically

• grafovi

100

90

80

70

60

50

40

30

20

10

-10

-20

€

-50 -40 -30 -20 -10 10 20 30 40 50m3

m3Italy x = 0,86xLithuania x = 1,77xGermany x = 5,04xFrance x = 2,85xCroatia x = 1,31xBulgaria x = x

6) How many ice-cream balls can you buy with the money used to pay 10m3 of water?

10

1914

67

8

20

0

10

20

30

40

50

60

70

Bulgaria Croatia France Germany Italy Lithuania

ice-cream balls

Bulgaria

Croatia

France

Germany

Italy

Lithuania

Task 2. 100 ml …….5 min.

x ml ……….30 days = 43 200 min x = 0.864 m3 Bulgaria Croatia France Germany Italy Lithuani

a

1) C(0.864)=0.864 €

C(0.864) = 1.13 €

C(0.864)=2.46 €

C(0.864)=4.36 €

C(0.864)=0.5 €

C(0.864)=1.53 €

2) 3.27% 4,3% 9.4% 16.64% 2% 5.8%

3) 0.864 ice-cream balls

1.7 ice-cream balls

1.23 ice-cream ball

6 ice-cream balls

0.5 ice-cream balls

2 ice-cream balls

Task 2. 3)

0,864

1,71,23

6

0,5

2

0

1

2

3

4

5

6

Bulgaria Croatia France Germany Italy Lithuania

ice-cream balls

Bulgaria

Croatia

France

Germany

Italy

Lithuania

Task 3 50 ml …….1 min.

x ml …… 30 days = 43 200 min. x = 2.16 m3 Bulgaria Croatia France Germany Italy Lithuani

a

1) C(2.16) =

2.16 € C(2.16) =

2.83 €

Home work

C(2.16) =

10.89 €

Home

work

Home work

2) 8.24% 10,8% 41.55%

3) 2.16 ice-cream

balls

4,16 ice-cream

balls 14.3 ice-

cream

balls

Task 4. 1) One class cleans the bord 4x50 = 200 times a month, 25 classes 25x 200 = 5 000 times a month. 5 000 x 2l = 10 000 l = 10 m3

Bulgaria Croatia France Germany Italy Lithuania

2) Home work

C(10) = 26.1€

Home work

Home work

Home work

Home work

3) 3 years

2 months and 9

days

Task 5.

• 100 ml = 0.1 l • 200 men three times a day = 60l• a week 420 l a month 1680 l • a season (3 months) 5400 l = 5,4

m3

Task 6.

25

1504030557065858595100

x

xxxxxxx

water - 100 students juices - 85 students

soft drinks - 65 students water and juices - 55 students

water and soft drinks - 40 students juices and soft drinks - 30 students

water, juices and soft drinks - x

65 - ( 70 - x)

85 - (85 - x )

100 - (95 - x)

30 - x

40 - x

Soft drinks

JuicesWater

55 - x

x

Prepared by:Students: Tanja Šarčević, Luka Budak,

Jan Dolanski, Domagoj Jelić, Marin Maršić, Borna Rapčan, Marin Tandara

Teacher: Snježana Lukač