Ebook by Ivita Saldava

Mathematical tasks on cultural and historical objects of the Czech Republic and Latvia

Group name: Pythagore Lions Students Name

Country

Petr

Czech Republic

Adam

Czech Republic

Diana

Latvia

Kristine

Latvia

Picture and description of building, monument, etc.

Task through math

Solution, answer

https://www.google.com/maps/ @49.2025854,16.5799919,19. 42z

What is the area of our school? (“základní škola”)

The school can be divided into three rectangles, which areas are 38*10, 27*13 and 12*27. Then we have to count the resulting numbers380+351+324=1055m2 The answer: The area of yours school is about 1055m2

https://www.google.com/maps/ How long are sites of pool with place/Herkulova+font%C3%A1 Herkule´s fountain in Prague? na/@50.0907658,14.4081874, 19.29z/data=!4m5!3m4!1s0x47 0b94e0e1ecc1ad:0x6d34d36d 59afa355!8m2!3d50.0907381!4 d14.4085399

Picture taken from: http://www.praga-praha.ru/wpcontent/uploads/2015/10/Herkulovafont%C3%A1na-4.jpg

3. Here is a link. Choose the shortest distance!

Jelgava palace (picture taken fromhttps://en.wikipedia.org/wiki/Jelgava_Palac e)

1.) A tourist group and a guide went from Riga, when they visited Riga Cathedral and St. Peter's church, to Jelgava, when they has to visit Jelgava palace. The tourist group went by bus, but gide was driving by car. The average speed of the bus was 50 km/h. However the average speed of the car was 80 km/h. 2.) Solve- How long the guide has to wait for the tourist group,if he reached Jelgava?

45,1:80=0,563=*100=56 min 45,1:50=0,902*100=90 min 90-56=34 The guide needs to wait 34min. For the tourist group.

Group name:

Crazy numbers

Students Name

Country

Adam

Czechia

Mirek

Czechia

Amanda

Latvia

Linda

Latvia

Picture and description of building, monument, etc.

1 Picture taken from: http://frypat.blog.cz/1503/mout nice-kostel-sv-jilji

Task through math

Solution, answer

a) Mirek goes to bus stop to go to a) Answer: 2,4 min school. He goes around a football pitch. solution: His speed is 4km/h and the distance to 1) 175*0,001=0,175km the pitch is 175m. How long does Mirek 2) 0,175/4=0,04h go to the pitch? 3) 0,04h=2,4min b)From the pitch he goes 7min at speed 4km/h to the bus stop. What is b) Answer:480m the distance from the pitch to the bus solution: stop? 1) 7/60=0,12h 2) 0,12*4=0,48km 3) 0,48km=480m Calculate the diagonal line of football pitch in Moutnice which measures 90x45m.

Soccer field diagonal is 100,62m 1)45*45+90*90=10125m

Freedom Monument is a memorial located in Riga, Latvia wich we measured. How long is Freedom Monument if you stand 40 meters from it and with the help of laser, measure from your location up to Freedom Monuments top is 58 meters?

Height of the monument is 42m.

Picture taken from: https://en.wikipedia.org/wiki/Fre edom_Monument#/media/File: Monumento_a_la_Libertad,_Ri ga,_Letonia,_2012-0807,_DD_10.JPG 4.

Picture taken from: http://sapnumedniece.lv/magis ka-liela-kemeru-tirela-laipa/

We went on a tour if Big Kemeri Moud. We calculated it with triple. It is Its one of the largest moss parks in 3,4km. Latvia since 2000. This place is very important nesting site for rare bird species. The speed we went on this trail was 66,7m/min. We finished the trail in 51min. If you want to know the length of this trail you have to: 1)convert given numbers to km/h. 2)To get accurate trails length you have to round those mesures you got from converting to one decimal number. 3) Use formula to help you get length of the trail using given values.

Group name: Math Gang Students Name

Country

Brian

Czech Republic

Aram

Czech Republic

Elza

Latvia

Amanda

Latvia

Picture and description of building, monument, etc.

Picture taken from: https://cs.wikipedia.org/wiki/Zeln%C3%BD _trh_(Brno)#/media/File:Brno_Zeln%C3%B D_trh_a_Ditrich%C5%A1tejn_ve%C4%8D er_5.jpg

Task through math

Solution, answer

Zelny trh in shape of rectangle has 4 sides.The lenght of first side is 200m.The lenght of second side is 150 meters.What is the area of Zelny trh?

S=200*150=30000m2 The area of Zelny trh is 30000 m2 Correct

About The Pulveower: The Pulvertower, formerly called Sand Tower, is located in Riga, Latvia. This is an architectural monument of national significance, in the actual possession and use of the Latvian War Museum. Task: Given cylinder and roof in cone shape . Cylinder height is 20 meters, diameter 14 meters, wall thickness 3 meters and cone volume 245 m3. Calculate the cylinder base and volume. Then calculate the entire volume of the building with the roof.

d=14m r=7m-3m=4m base=π.r2=3,14.1 6=50,24m2 V=1004,8m3 1004,8+245=1249, 8m3

2. Picture taken from: https://www.google.lv/search?q=pulvertorni s&client=tablet-androidsamsung&prmd=imvn&source=lnms&tbm= isch&sa=X&ved=0ahUKEwjE89rjj6HaAhU DDJoKHeRNAf4Q_AUIESgB&biw=1280&b ih=800#imgdii=HxpCVBC6f8zGM:&imgrc=tZPK7OsEFmGDGM:&isa= y

3. Picture taken from: https://www.google.lv/search?q=p%C4%93 terbazn%C4%ABca&rlz=1C1GGRV_enLV 761LV761&source=lnms&tbm=isch&sa=X &ved=0ahUKEwiIhLuJ7aLaAhUiCpoKHdG FCPsQ_AUICigB&biw=1280&bih=918#img rc=ffeN6hL4_7wcWM:

Riga St. Peter's Church is the highest church in Riga.800 000 (0,30 s)

X2=1392- 632 x2=193213969=15352 x=123,9m

Task: How long is Riga St.Peter’s Church if you stand 63 meters from it? From the place you stand, up to Riga St. Peter’s Church’s top is hypotenuse=139 meters.

4. https://www.google.com/maps/ @49.1970109,16.5769245,3a, 75y,154.85h,89.43t/data=!3m6! 1e1!3m4!1sw7Nx0iQJiGmIPA4 ZXYt5pQ!2e0!7i13312!8i6656

Preslova street is 160 m long.To go along the whole street you need 3 minutes but yesterday workers started street work and now you have to walk 252 m. How much time does it take?

1)160:3=53,3 2)252:53,3=4,7 minutes To walk 252m, you need 4,7 minutes. Correct

Group name: Number heads Students Name

Country

Martin

Czechia

Roman

Czechia

Ruta

Latvia

Davids

Latvia

Picture and description of building, monument, etc.

Task through math

Solution, answer

https://mapy.cz/zakladni?x=14.426 3457&y=50.0816587&z=17&sourc e=pubt&id=15306059

Calculate the area of Václavské náměstí (Vaclav`s Square in Prague

We found the sizes the length is 692m and the width is 60m and then we calculated the area of the square and it was 40920m2 We also found on the internet a different size which was 45000m2 so which one is the right one? We think that the calculated one is the right one so u have done it well

Picture taken from: http://img.magazin.libimseti.cz/img/img/25e061b 6e3d2.jpg

https://www.prague.eu/cs/objekt/mi sta/1878/socha-sv-vaclava

Picture taken from: https://media.novinky.cz/064/320644-top_foto19qp5x.jpg?1357300020

Can you find out the differences of height of the Vaclav`s statue with and without the spear?

Vaclav`s statue is 7,2 m high with the spear and 5,5 m high without the spear.

1. Figure out where does the equation (y=2*x-18) crosses the x axis, will give you the last number of an important year [120_]. Why is this year so important? 2. Find a pattern and figure out how much equals 9, if:

Reference: Picture taken from https://upload.wikimedia.org/wikipedia/commons /9/97/St._Peter%27s_Church.JPG

Hint: http://bit.do/Gold-bar

Place the number you found in this http://bit.do/bird** links (URL) empty spots to get information for the last task.

Reference: Picture taken from http://www.infotop.lv/article/lv/aptauja-parvisainaviskako-vietu-latvija-tiek-atzits-gaujasnacionalais-parks

2. 9 equals 72

3.We figured out that the area of rooster is 6 square meters,but we don`t know exactly how thick the rooster is gold plated

3. Approximately how many roosters of St. Peter's Church in Riga can you gold plate with one gold bar? Gauja National Park is the largest and oldest national park in Latvia. To calculate the year the Gauja National Park has been created, it is necessary to visualize the trapezium area.

1.By the calculations we figured out that it's 1209 year and it's important because in this year was the first mention about St. Peter`s Church.

1. Given values : Shortest edge - 96,8 cm The longest edge - 100,5 cm Height - 20 cm

After some time we found out that the trapezium area is [(100.5+96.8)*20] /2 = 1973 the year when the Gauja National Park has been created

Group name: Team Quick Maths Students Name

Country

Antonie

Czechia

Nikola

Czechia

Reinis

Latvia

Ričards

Latvia

Picture and description of building, monument, etc.

Task through math

Solution, answer

-calculate the perimeter of the Špilberk in reality and on a map ( the red one )

P= 94 + 153 + 106 +148 = 501 meters

-count the area of the middle square in Špilberk in reality and on a map ( the green one )

-wha 2.https://www.google.com/maps/plac e/Hrad+%C5%A0pilberk/@49.19458 42,16.598568,217m/data=!3m1!1e3! 4m5!3m4!1s0x4712944e453638ef:0 xb7cc14c2f48283cc!8m2!3d49.1944 928!4d16.599177

S= 38 x 40 = 1520 m²

Reference. Picture taken from: http://www.smartriga.lv/en/useful-tips/need-toknow/interesting-facts-about-riga-and-latvia

The capital of the Republic of Latvia is the city of Riga. The area of Latvia is 64â&#x20AC;&#x2122;589 square kilometers, while the area of Riga is 304 square kilometers. How many Rigaâ&#x20AC;&#x2122;s could you fit into the area of Latvia? (round down the number to get the answer)

4. Latvian National Library

How long will it take to travel from Prague to Latvian Nation Library if you drive with average speed (70km/h) Total distance 1337km

3. Riga

Reference. Picture taken from: https://en.wikipedia.org/wiki/National_Library_of_L atvia

64 589 : 304 = 212,464 and after the rounding 212

Group name: Hidden Math Students Name

Country

Adam

Czech Republic

MarkĂŠta

Czech Republic

Raimonds

Latvia

Matiss

Latvia

Picture and description of building, monument, etc.

Task through math

Solution, answer

1. https://mapy.cz/zakladni?x=16.6 089731&y=49.1942841&z=16&s ource=base&id=1703427

How long will it take to travel from Komenskeho square to the Main station (hl.nadrazi) if I drive at a constant speed 50 km per hour and if they are 1.8km apart?

1.8/50=0.036 It will take 3 mins.

2. https://www.google.com/maps/pl ace/Kalnciema+vidusskola/@56. 8085702,23.6244035,600m/data =!3m1!1e3!4m5!3m4!1s0x46ef20 4e9d21e605:0x3660d8bff2c55fe 7!8m2!3d56.8086613!4d23.6252 886

How long it take to travel from Bratislav to Kalnciema Vidusskola, with average speed of 90km/h? Total road distance 1335 km.

1335:90 is 14.83 rounded to 15. Round will has 15 hours.

Task:Calculate the volume of the tower, take heed of that the roof of the tower is in the form of a regular pyramid and it quadrate with side length 12 m. Height up to pyramid- 37m Height to tower spike- 50m

Reference: Picture taken from http://www.atputasbazes.lv/lv/zinas/2376_mu zeju_nakts_pasakumi_ari_jelgavas_svtrisvien ibas_baznicas_t/

V1=12*12*37 V1=5328m3 V2=12*12*13/3=624m3 V=V1+V2 V=5952m3

Group name: Matrix Students Name

Country

Lucie

Czechia

Nikol

Czechia

Agnese

Latvia

Rainers

Latvia

Picture and description of building, monument, etc.

Task through math

Solution, answer

1. https://mapy.cz/zakladni?x=16.8058452 &y=48.8015260&z=17&base=ophoto&s ource=base&id=1982504

Calculate the perimeter of the greenhouse at castle Lednice which is located in the south of our country.

P=16+88+24+88=21 6m π≈3

Picture taken from: http://tropik.cz/fotky/DSCF2696.JPG

2. https://mapy.cz/zakladni?x=16.8051913 &y=48.8024030&z=17&base=ophoto&s ource=foto&id=625272

Picture taken from: http://www.kvalitazivota.eu/rs/upload/dokumenty_kultur ni/lednice/thumbs/th_lednice1_800x600.jpg

Calculate the area of the square plaza at castle Lednice.

S=96×104=9984 m²

Reference: Picture taken from https://www.lnb.lv/lv/par-biblioteku/lnb-eka

The core functions of the National Library of Latvia are the collection of national literature, its perpetual storage and the long-term provision of access to it.

The area of the first floor is 6131,4m2 and the whole area is 40704,8m2 , so the percentage is 15%

Task:What percentage from all Latvia National Library area takes up first floor? https://lnb.lv/lv/jauna-lnb-eka/lnb-ekastelpu-saraksts-ar-platibam Translation latvian to english: Kopējā platība- total area.

Reference: Picture taken from http://www.atputasbazes.lv/lv/zinas/2376_muzeju_nakt s_pasakumi_ari_jelgavas_svtrisvienibas_baznicas_t/

V1= 12*12*37 V1=5328m3 V2= 12*12*13/3 V2= 624m3 V= V1+V2 V= 5328+624 V= 5952m3

Group name: Big Math Students Name

Country

Alice

Czech Republic

Valentýna

Czech Republic

Toms

Latvia

Edgars

Latvia

Picture and description of building, monument, etc.

Task through math

https://mapy.cz/letecka?x=16.5 Calculate the perimeter of the 978065&y=49.1988799&z=18& park Obilní trh. q=Obiln%C3%AD%20trh%20p ark

Solution, answer 187+100+142+83=512m Perimeter of the park Obilní trh is 512m. Yes,your answer is right.

Picture taken from: http://www.hd.cz/ajda/img/obilni-trh.jpg

Find out how many kilometers is it from Brno to Prague? How long does it take to travel from Brno to Prague if your speed is 130 km/h? Picture taken from: https://autotrip.cz/wpcontent/uploads/2017/04/D%C3%A1lniced1.jpg

From Brno to Prague is 205 km. 205/130=1.6h. It takes 1.6h Yes,your answer is right.

Calculate how high the Latvian Freedom Monument is when https://lv.wikipedia.org/wiki/Br% Everest is 211 times bigger? C4%ABv%C4%ABbas_piemin eklis

Freedom monument measures 42m.

2015: 1,978 millions 2016: 1,96 millions 2017: 1 941 300 millions The mass of the population has diminished of 18 700 peoples.

Picture taken from:

Calculate how many people increased or decreased from 2015 to 2017. Calculate the average population of Latvia.