Mathematics.

Prezentace na téma: "Mathematics."— Transkript prezentace:

1 Mathematics

2 Basic terminology - dictionary
alfa – aplha aritmetika – arithmetic C celá čísla – whole numbers Č číslice - digit číslo – number čtverec – square čtyřnásobek – quadruple D dělit - divide dvojitý - double E exponent - exponent L lichý J jmenovatel - denominator K konstanta – constant kořen - root kvocient - quotient M mínus - minus míra - measurement N násobek – multiple násobit - multiply neracionální - irrational nerovnost – inequality nula – zero O odčítání - subtraction P plus - plus počítat – count podíl – ratio prostý - simple prvotní - prime průměr - average přenost – accuracy přesnost - precision převrácený – inverse přímka - line přirozený - neutral R racionální – rational racionální číslo – rational number rovnost - equality rozdíl – difference Ř řadová číslovka – ordinal number řecká abeceda – Greek alphabet S sčítání - adding smíšený – mixed součet - sum správný - proper sudý – even T teorém – theorem těžnice – median trojitý - triple V významný - significant vzorec - formula Z základní číslovky – cardinal numbers zaokrouhlení – rounding zápis - notation záporný - negative závorka – bracket, parenthesis zbytek - remainder zlomek – fraction zmenšit – reduce 2 + 2 Two plus two 6 – 4 Six minus four 5 x 3 OR 5 * 3 Five times three = equals 2 + 2 = 4 Two plus two equals four. 7 < 10 Seven is less than ten. 12 > 8 Twelve is greater than eight. 4 + 1 ≤ 6 Four plus one is less than or equal to six. 5 + 7 ≥ 10 Five plus seven is equal to or greater than ten. 12 ≠ 15 Twelve is not equal to fifteen. 4 / 2 OR 4 ÷ 2 four divided by two 1/2 one half 1 ½ One and one half 1/3 one third 3 1/3 Three and one third 1/4 one quarter 2 ¼ Two and one quarter 5/9, 2/3, 5/6 five ninths, two thirds, five sixths 4 2/3 Four and two thirds 98% Ninety eight percent

3 DISCUSSION What is maths good for? Why did you choose to study it? Is maths a popular subject? Why yes? Why not? What kind of mathematical operations can you name? Can you read these numbers? , , ½ $ Can you read these numbers? Write the number six hundred thirty six ____________ forty thousand, eighty six ____________ one hundred six thousand, four ____________ four million, seven thousand, three hundred twenty eight ____________ thirteen billion, twelve ____________ six tenths ____________ forty five hundredths ____________ thirty thousand, forty two and seventy five thousandths ____________ seven hundred and 5 hundredths ____________ one thousand five hundred twenty six and three hundred twenty five thousandths ____________ DICTATE – teacher says the numbers and students write them down... ______________________ 2. _____________________ ______________________ 4. _____________________ 5. ______________________ 6. _____________________

4 14 12 minutes 7 cents 4 388,5 Can you solve these problems?
Suzanne has 8 pairs of white socks and 6 pairs of blue socks. Her sister has 12 pairs of white socks. How many pairs of socks does Suzanne have? Kurt spent 7 minutes studying for his spelling test. He took a 3 minute snack break. Then he studied for 5 more minutes. How long did Kurt study altogether? David spent 74 cents at the school store. He bought a notebook for 35 cents, a ruler for 18 cents, and 3 pencils. What is the cost of one pencil? 12 friends plan to order pizza for dinner. They assume that everyone can eat 1/3 of a pizza. How many pizzas should they order? The Money Hungry bank pays 5% interest annually. Selena put $370 in a savings account at the bank. At the end of one year, how much money will Selena have in her account? 14 12 minutes 7 cents 4 388,5 Can you write an example of... DIVISION _____________________________________________ ADDING _____________________________________________ MULTIPLYING _____________________________________________ SUBTRACTION _____________________________________________ FUNCTION _____________________________________________ Explain the use of these areas of mathematics ALGEBRA GEOMETRY COMBINATORICS LOGIC GAME THEORY PROBABILITY STATISTICS ROBOTICS TRIGONOMETRY APPLIED MATHEMATICS - EQUATIONS

5 Basic terminology – links
- základní matematické termíny - seznam matematických pojmů - kartičky se jmény pojmů / použitelné pro hry - velký rozcestník pro učitele nejen matematiky - matematický rozcestník - matematický online slovník pro děti – velice pěkné - matematické online hry a aktivity - matematické aktivity podle věku dětí - matematické aktivity dle složitosti - matematické aktivity od 1. třídy - matematika hrou - matematická cvičení pro starší - materiály pro učitele matematiky - seznam matematických témat a odvětví

6 History of mathematics - dictionary
antický – ancient argumentace - reasoning aritmetika – arithmetic artefakt - artifact C civilizace - civilization D datovat - date deduktivní – deductive desítkový - decimal dosažení - attainment důkaz – proof E elipsa – ellipse exponenciální - exponential G geometrie – geometry H hodina - hour I interpretace - interpretation J jazyk - language K kalendář – calendar koncept - concept kreativita – creativity kruh – circle krychlový - cubic L lunární - lunar M metoda – method minulost – past minuta - minute N nápad – idea nedostatek - defect nesporný - undisputed O období - period objev – discovery odlišnost - distinction operace - operation P památník - monument papyrus – papyrus pokus - attempt poznání – cognition pravidlo – rule průkopník - pioneer předmět – object přeměnit - convert psaný - written Pythagorejci - Pythagoreans původ - origin R ranný - early rozsah – extend S sekunda - second sled - sequence sloupec - column stagnace - stagnation T tempo - pace text – text tvrdit - claim U učenec - scholar ukázka - demonstration úvod - introduction V vědění – knowledge velikost, rozsah – magnitude vyřezat - crave vývoj – development význam - meaning Z zahrnout - incorporate zápis – notation zdroj - source značka – mark zpochybnit - dispute

7 Discussion Why did people start to count? How did they use to express number one or two? Which method did they use to „save“ their data? Which material did they use for saving their data? Could they count to 50? Why yes? Why not? Was the invention of numbers connected to the weather and climate? In what other everyday activities did the people use numbers? Did people know cicles and squares in the early ages? What kind of structures did the people built? Which purpose did most structures serve? What do you know about Mesopotanian mathematics? Where was Mesopotamia and what was invented there? What is it pictographic system of writing? What did the people of Mesopotamia use maths for? How do you understand this statement „their system was based on number 60“? The Babylonians in Mesopotamia invented „ZERO“ – how did it influence the development of mathematics? How do you think maths was used in metrology? What did people think about the position of the Sun, moon and the stars? How did maths influence trade? How did maths influence farming? Did the Babylonians know „our“ numbers? How did they write? multiplication multiplication with the use of squares division cubic equation quadratic equation The Babylonians were using these formula – do you know what they mean and what they were used for? ab = [(a + b)2 - a2 - b2]/2 ___________________________________ ab = [(a + b)2 - (a - b)2]/4 ___________________________________ a/b = a × (1/b) ___________________________________ ax3 + bx2 = c ___________________________________ x2 + bx = c and x2 - bx = c ___________________________________ Can you explain these words? CRAVE EQUATION SQUARE STARS CALENDAR CAVE CIRCLE METROLOGY ZERO SECOND DECIMAL PAPYRUS MONUMENT

8 Discussion Where was the Egyptian civilization? Why were they so famous? What did they build? How did they build it? Why did they build such monumental pieces? What is the „10 numeration system“? What mathematical operations do you think the Egyptians were capable of? Who do you think had the biggest influence on Egyptian mathematicians? Can you describe these pictures and comment them from the mathematical point of view? Which shapes do you see? What did they have to take into account when they were building these statues and pyramides? Can you compare our system or writing numbers and the Egyptian system? Do you think people are still able to build something like this? Quess the word __________ it´s a table showing months, weeks and days in at least one specific year. __________ it´s a massive monument of ancient Egypt having a rectangular base and four triangular faces culminating in a single apex, built over or around a crypt or tomb. __________ it´s something having an equal-sided rectangular form. __________ it´s something, such as a ring, shaped like such a plane curve. __________ it´s a star that is the center of a planetary system. __________ it´s one of the 24 equal parts of a day. __________ it´s an expression that indicates the quotient of two quantities. __________ it´s the operation of determining how many times one quantity is contained in another.

9 History of mathematics - links
- matematický archív - historie matematiky - archív knih (i matematických) - historie matematiky - poslech – video o historii matematiky - matematika od počátku do současnosti - archív okazů na matematické organizace a společnosti - časová linka a důležité události v matematice - matematika po letech a staletích - historie psaní čísel - historie čísel - největší matematici všech dob

10 Great Greek mathematicians – dictionary
aparát - apparatus astronom – astronomer D deduktivní - deductive F filozof – philosopher fyzika - physics G geometrie - geometry H hmota - substance hypotéza – hypothesis I induktivní - inductive K kilometrovník - odometer kosmologický – cosmological koule - sphere L logika - logic M metoda - method měřit - measure možnost - option mytologie – mythology N nehmotný - immaterial O odhad - approximation odmítnutí - rejection P pád – downfall pákový efekt - leverage parabola - parabola poskytnout – provide pozorování - observation princip – principle předpoklad – premise převodové ústrojí - gear příroda - nature přírodní – natural pyramida – pyramid R růst - growth S sklon – slope sluneční svit – sunlight spirála - spiral student - student svislý – vertical Š škola – school šroub - screw T trigonometrie - trigonometry trojúhelník - triangle U úhel – angle úspěch - achievement V válec - cylinder vynálezce - inventor vysvětlení - explanation vysvětlit – explain výška – height vývoj – evolution vzdálenost - distance Z zapříčinění - causation zatmění – eclipse závěr – conclusion zmenšení - diminution

11 Discussion Which areas of maths did Thales contribute to? Thales believed in the principles of water, air, earth and fire. Why? Why were these elements so important in Greek philosophy? Thales invented the word „electron“. What is it? Thales was interested in angles and triangles – what do you know about them? What is trigonometry? What is it good for? How did they used to measure the distances between ships? Who was Pythagoras? What is the Pythagorean theorem? Who is an astronomer? Why are people interested in the stars? How is maths used in astrology? Who was Aristotle? What was he interested in? Which areas of interest did he have? What is the difference between qualitative and quantitative approach? What did the ancient mathematicians think about movement? Which ways did they use for counting the speed and movement in general? Who was Archimedes? What is a sphere? What is a cylinder? What was a catapult? Can you answer these questions? What comes after a million, billion and trillion? What are the other names for ZERO? What was Abacus? Which numbers have always been considered lucky? Which numbers have always been considered unlucky? What is a „Palindrome number“? Greek alphabet – what do these symbols mean? Ω Χ Σ Κ Φ Δ Ψ Θ 9. Μ

12 Solve these word games There were 24 boys in the Athenian School. One day half of them wore blue tunics. How many children wore blue? There are 50 spears in 5 boxes. How many spears are there in each box? The Greek Gymnasium has 18 large training balls. Half of them need mending. How many can be used? Ariadne had 19 bunches of grapes. She can fit 5 bunches on a tray. How many full trays did she have? The Spartan Army has to march 27 miles. They can march 5 miles a day. How many days did it take them? A Greek Farmer had 18 goats. He could fit 4 goats in each of his pens. How many pens did he need? Describe the picture What do you see in this picture? Can you name she shapes you see? Do you understand the formulas you see? What do they mean? Which of these is the most difficult for your students and why? Why is it important to be able to use these formulas? Presentation Each student will choose one of the objects from the picture above and then he/she will try to tell the others everything about the object – including the formula and terms. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

13 Great Greek matematicians - links
- starověkké Řecko - starověkké Řecko (i pro děti) - Řecko, legendy, rozcestník - řečtí matematici - otázky a odpovědi k řecké matematice - rozcestník matematiků - matematika starého Řecka - vývoj matematiky v Řecku chronologicky - Řecko (mapa, města, matematici, apod.) - Řecká abeceda - vliv starého Řecka na současnou společnost - starověké Řecko v dnešním světě

14 Maths in astronomy and astrology – dictionary and phrases
analytický - analitic Č čas - time D dimenze - dimension důkaz - proof E energie – energy exponent – exponent G geometrie – geometry graf - diagram H hvězda – star hyperbola - hyperbola K kalkulačka – calculator kilometr - kilometre koeficient – coeficient křivka - curve kulovitý – spherical kužel - cone M masa – mass N navigace - navigation O objevit – discover obloha – sky observatoř – observatory orbitální - orbital osa - axis P parabola - parabola počítač – computer pohyb - motion poloměr - radius použití – usage pozorování – observation program - program proměnná - variable přístup (někam – access přístup (k něčemu) – attitude R rotace - rotation rozhodnutí – decision rozměr – dimension rychlost - velocity S složitý - complex Slunce – Sun solární – solar spojitost – relation světlo - light svítivost – luminosity Š škála - range V váha - weight velikost – magnitude výkon – output výpočet - computation Z zákon – law zápis - notation zdroj – source Země – Earth

15 1C 2E 3A 4B 5D 2A 3D Discussion What is the universe?
What can I find in there? Why are people so fascinated by it? Would you like to fly to the Moon? Do you think that one day people will be able to travel to other planets? What are the biggest problems the scientists are solving right now? How would you count the distance between the Sun and the Moon? What is a black hole? Does it exist? How fast do the spaceships fly? What are some activities of the people in the spaceship? What can you say about the Sun? Can you say something about the other planets? What is the Milky way? What is a comet? What is a meteor? What kind of shapes can be found in the space? 1C 2E 3A 4B 5D 2A 3D Can you match these numbers? Neutral numbers a) -2, 2/3, 1,21 Integers b) –e, √2, π Rational numbers c) 1,2,3,... Real numbers d) 2i, -2+3i Complex numbers e) -2,-1,0,1,2,... Can you match these equations,read them aloud and draw the image next to the equation? Circle a) x y2 = 1 a b2 2. Ellipse b) x y2 = 1 Parabola c) x2 + y2 = a2 Hyperbola d) y2 = 4ax

16 Do you know the answer? What did people think about the shapes of the Earth? Did they always know the Earth was a sphere? Do you know any famous astronomers? Why did they have problems with the Church? What did people think about the Sun? What do people know about other planets and other galaxies? How do people find new planets? Where can people go to observe planets? What is gravitation? What is gravitation good for? Would life exist without it? What is an orbit? Does the universe finish anywhere? How did it start? What happened at the beginning? Do you think the universe will collapse one day? Do we need the Moon for anything? What is the eclipse? Do you like movies about „meteor falling on the Earth“? Is such a disaster possible? Can you comment these statements and facts? The geocentric model entered Greek astronomy in the 4th century BC. During this period, educated Greeks thought that Earth was at the center of the universe and the Sun, Moon, stars and other planets surrounded Earth. The application of the telescope by Galileo Galilei in 1609 questioned the very foundation of geocentrism. With the help of his telescope, Galileo defended, corrected and expanded the heliocentric model challenging Ptolemy’s geocentrism. Isaac Newton devised the law of gravitation in The law of gravitation explained the motion of planets. On a clear night, the naked eye can only perceive about 3000 stars. Our galaxy alone has an estimated 1011 to 1012 stars and there are probably more than 1012 galaxies in the universe. With this simple calculation, there might be more than 1024 stars in the universe. Even if you had the most sophisticated spacecraft that travels at the speed of light (speed of light=186,000 miles per second), it would take approx. 105 (one hundred thousand) years to cross the galaxy.

17 Maths in astronomy and astrology - links
- matematická astrologie - matematika v astrologii - kniha - matematické metody v astronomii - definice matematické astrologie - nejznámější astronomové - 7 nejznámějších astronomů - astronomie pro děti - astronomie pro děti, projekty a hry - základní odpovědi pro děti - Mléčná dráha - informace, obrázky a rozcestník naší galaxie

18 Units of measurement – dictionary and phrases
ampér – ampere C centimetr - centimeter Č čas - time D délka – lenght dioptrie - dioptre E elektrický proud – electric current G galon - gallon gram - gram H hodina - hour K kalorie – calorie karát - carat kelvin - kelvin kilogram – kilogram kostka - cube L libra - pounds litr - liter M metr – meter metr čtverečný – meter square míle – mile milimetr - milimetre minuta – minute O objem - volume P panec - inch pinta – pint pravítko - ruler přepona – prefix R rychlost – speed S sekunda – second stopa - feet T tekutina - liquid teplota – temperature teploměr – termometer tloušťka - thikness tuna - ton U unce – ounce Y yard - yeard Z zkratka – abbreviation zrychlení - acceleration Large number prefixes Name deca hecto kilo mega giga tera peta exa zetta yotta Symbol da h k M G T P E Z Y Factor 101 102 103 106 109 1012 1015 1018 1021 1024 Small number prefixes Name deci centi milli micro nano pico femto atto zepto yocto Symbol d c m n p f a z y Factor 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 10-21 10-24

19 Do you know the answer? The prefix 'kilo' means ___________ The prefix 'milli' means ___________ What is one trillion as a power of 10? Can you think of anything that is only 1 milimeter thick? Can you think of anything that is about 1 meter long? The length of a ruler is 30 cm. How many millimeters is that? Can you think of anything that is about one yard long? How would you describe square meter? When and how are square meters used? What is a cubic meter? Can you think of things that would weigh 1000g? How do people express their weight and height? Can you use the American way of measurement as well? How many miles in one kilometer? How many centimetres in one feet? Can you write these numbers? trillion __________________ billion __________________ million __________________ hundred __________________ thousand __________________ ten __________________ tenth __________________ hundredth __________________ thousandth __________________ millionth __________________ Can you comment these facts? Water boils at 100 degrees Celsius or 212 degrees Fahrenheit 1 mile = 1,760 yards = 5,280 feet = 63,360 inches One meter equals roughly one long step of an adult man. One kilometer equals about 12 minutes' walk.

20 Can you match these units of measurement with their definition?
AMPERE a) unit for measuring sound intensity 2) DECIBEL b) unit of frequency equal to one cycle per second 3) FARAD c) unit of force that accelerates 1 kilogram to 1 meter / second / second 4) CALORIE d) unit of x-radiation or gamma radiation 5) HERTZ e) unit for measuring amount of electrical current 6) KARAT f) unit of electrical resistance of circuits 7) NEWTON g) unit of power equal to one joule per second 8) OHM h) unit of fineness of gold equal to 1/24 part of pure gold 9) ROENTGEN i) unit measuring electrical capacitance 10) WATT j) unit of heat or heat-producing value 1E 2A 3i 4J 5B 6H 7C 8f 9D 10 Can you solve these mathematical problems? 3.83 cm = ___________ mm 2) kg = ___________ g 351 ml = ___________ L 4) 1,576 ml = ___________ L 2.6 L = ___________ ml 6) 3,557 ml = ___________ L 6.3 kg = ___________ g 8) m = ___________ cm 1.62 m = ___________ cm 10)  29.6 cm = ___________ mm mm = ________ cm 12) dam = ________ dm 13) Farmer Brendan has just bought a new herd of cows, and needs to fence off one of his fields for them to live in. The field is square and one side of the field measures 450m. What distance of fencing does he need to buy? I am wrapping christmas presents. I have 2m of ribbon, and I need 25cm for each present. How many presents will I be able to wrap? The perimeter of a regular hexagon is 36cm. How long is each side? Mr. Martin's Spanish class is 45 minutes long. If it starts at 3:30, what time does it end? Lois wants to send a box of oranges to a friend by mail. The box of oranges cannot exceed a mass of 10 kg. If each orange has a mass of 200g, what is the maximum number she can send?   A box contains 4 bags of sugar. The total mass of all 4 bags is 6 kg. What is the mass of each bag in grams? David has a lot of homework to do. He starts his reading homework at 3:45 and ends at 4:30. Then he does math from 4:30 until 5:00. Lastly, he studies for a science test from 5:00-5:30. How much total time did David spend on his homework and studying?

21 Units of measurement - links
- systém jednotek - převody jednotek online - seznam jednotek (matematické i fyzikální) - systém SI - zkratky používané v převodech a pro vyjádření čísla - jednotky pro děti + vysvětlení - jednotky pro děti, videa a vysvětlení – základní jednotky video - hry zaměřené na převody - spojovačky a hádanky zaměřené na převody jednotek - rozcestník pro děti zaměřený na převody a matematiku - všeobecný matematický rozcestník

22 Fractions and Percents – dictionary and phrases
absolutní hodnota – absolute value C celé číslo – integer celý - whole Č čitatel – numerator D dělení – division desetinné číslo - decimal E ekvivalent – equivalent F faktor – factor G grafický - graphical H hodnota – value I iracionální - explicit J jmenovatel – denominator K kvocient – quotient M metoda – method mimořádný – special množství - amount N násobení – multiplication nezmenšitelný – irreducible O oboustranný - reciprocal P pár – pair počáteční - initial pole - field poměr - ratio porovnat – compare proces - procedure procento – percentage průměr - average přeměnit – convert přesný - precise R racionální – rational radikál - radical rozdělit – divide Ř řešení - solution řešit - solve S sčítání – addition složitý – complex statistika - statistics stejný – equal svah - slope U úroková sazba – interest rate V velikost – size vzor - pattern Z zlomek – fraction zlomková čára – vinculum, fraction bar zmenšit – decrease, reduce zvětšit – increase MÍSTA ZA DESETINNOU ČÁRKOU – DECIMALS desetina – tenth setina – hundredth tisícina – thousandth desetitisícina – ten thousandth stotisícina – hundred thousandth miliontina – millionth desetimiliontina – ten millionth stomiliontina – hundred millionth

23 Discussion What is a fraction? Can you give an example? What are fractions good for? How do you explain them to your students? Is it easy for children to understand fractions? How would you explain „addition of fractions“? How would you explain „subtraction of fractions“? How would you explain „multiplication of fractions“? How would you explain „division of fractions“? How do you explain percents to your students? Is it difficult for them? Can you read and solve these problems? 4 3/7+ 4 1/2 = 2) /3+ 2 3/7 = 3 1/8+ 3 7/11 = 4) /3 = 3 1/ /15 = 6) 2 2/5- 2 5/14 = 7) /9 = 8) 9 1/4- 2 5/11 = 9) 4 1/4× 2 5/6 = 10) 9 1/2× 8 = 11) 8 3/4× 1 8/13  12) 2 7/15× 3 1/11 = 13) 2 5/14÷ 2 2/5 = 14) 9÷ 1 4/9 9 = 15) 2 5/11÷ 9 1/4 = 16) 3 2/11÷ 1 1/3 = 17) Jana is making chocolate milkshakes for Petra´s birthday party. There will be fourteen people at the party. It takes a third of a cup of milk to make one chocolate milkshake. How many cups of milk will it take to make fourteen milkshakes? 18) One-third of the class grew peas, one-third grew carrots, and one-third grew beans. The class consisted of 63 students of which five-sevenths were girls. The teacher chose the three groups to be as equal in their boy-girl composition as possible. How many boys and girls were assigned to each team? 19) The Novak family went to a ice-hockey game last weekend. They spent $12 on food, $41 on souvenirs, and $9 on drinks. What fraction of their expenditures was spent on drinks?

24 Percent – word problems and games
What number is 112% of 2053? 168 is what percent of 420? Clara ran the 100-meter dash in seconds yesterday at track practice. Her twin sister Destiny ran it in seconds. Clara´s time differed from her sister's by what percent? Round your answer to the nearest hundredth of a percent. Marianne is a good scorer for her soccer team. She scored 9 goals during regular play, and she scored 4 on penalty kicks. What percent of her goals did not result from penalty kicks? Round your answer to the nearest tenth of a percent. A soil sample from the nearby power plant has 189 grams of sand in every kilogram of soil. What percent of the soil is made up of sand? Monica deposited $22,000 at a bank that pays 10% interest. John deposited $16,000 at a bank that pays 16% interest. Who will receive more interest in a year, and by how much more? John deposited $15,000 in an account that pays 6.4% interest each year. The amount of interest is paid at the end of each year. How much will the account have after 3 years? Andrew borrowed $26,000 for 210 days at 9% annual interest. However, Peter received a bonus from his boss and was able to repay the loan in 60 days. How much interest did Peter save by paying the loan early? Match these words with their correct translation DENOMINATOR A) MNOŽSTVÍ INCREASE B) POROVNAT AMOUNT C) ROVNÝ DECIMAL D) JMENOVATEL COMPARE E) PRŮMĚR AVERAGE F) DĚLENÍ DEVISION G) DESETINNÉ ČÍSLO EQUAL H) ZLOMKOVÁ ČÁRA REDUCE J) ZVÝŠIT FRACTION BAR K) ZMENŠIT Task Each students makes up his/her own fraction or percent task and gives it to the others. Then the student explains the solution to the others.

25 Fractions and Percents - links
- vysvětlení zlomků - zlomky pro děti, rozcestník - vysvětlení zlomků pro děti - zlomky a cvičení - online hry na zlomky - hry se zlomky pro děti - procenta - vysvětlení - procenta vs. zlomky - procentní kalkulátor - hry s procenty - procenta, zlomky a desetinná čísla - rozcestník na cvičení online – procenta, zlomky a desetinná čísla

26 Time – dictionary and phrases
absolutní - absolute astronomy – astronomie C cyklický - cyclical Č čas – time D den - day dochvilnost – timekeeping E efekt - effect G gravitace - gravity H hodina - hour hodiny – clock CH chronometr - chronometer I interval – interval inženýr - engineer K kalendář – calendar kalibrovat – calibrate kauzalita - causality L lineární - linear M mechanika - mechanics měsíc - month minuta – minute místní – local moment - moment N navigace - navigation P platný – applicable povědomí – awareness pravděpodobnost - expectancy pravidlo - rule prostor – space prostorový – spatial pozorovatel - observer předpovědět - predict přesný - accurate přesýpací hodiny – hourglass příčina - cause R realita - reality relativita - relativity rok – year rotace - rotation rozměr – dimension rozšíření - dilatation rychlost – velocity S sekunda - second síla – power slunce - Sun sluneční hodiny – sundial souměrnost - symmetry stín – shadow světlo - light T teorie - theory trvání – duration týden – week U ukazovat - indicate V vnímat - percieve vynálezce – inventor vzdálenost - distance Z zařízení – device zmatený - chaotic zvonec - bell

27 Discusstion How do we read time in English? Why do people need to know time? What would happen if people didn´t know time? What kind of clock do you know? How do we read dates in English? How do we read years and centuries in English? What is a calendar? What parts does it have and why do some years have 366 days? Can you read these times? 12: :20 3. 5: :30 8: :58 7. 12: :00 9: The teacher dictates the times and the students write: _______________ 2) ______________ _______________ 4) ______________ 5) _______________ 6) ______________ What do you think about these statements? Time on Earth is actually slowing down. Dinosaurs had to fit a full day’s work into just 23 hours. Cultural background affects our perception of time. The Soviet Union experimented with 5 and 6-day weeks between 1929 and 1931. Like all good things, time will come to an end….maybe? There is no time like the present. Until the 1800s, every village lived in its own little time zone, with clocks synchronized to the local solar noon. Time has not been around forever. Most scientists believe it was created along with the rest of the universe in the Big Bang, 13.7 billion years ago. Everyone experiences time differently. The past and future are equally real.

28 Can you read these dates and answer these questions?
What day was it yesterday? What day was it 3 days ago? What date was it 2 days ago? What date will it be tomorrow? READ READ READ READ READ READ 80´s, 70´s, 90´s READ 19th century, 20th century What are ordinal numbers? Can you count from 1 – 20 (in ordinal numbers)? What is the second season? What is the 6th month of the year? What is the 11th month of the year? What is the 3rd day of the week? When do we use ordinals in other everyday situations? What in an anniversary? Which anniversaries do we celebrate? What is a reunion? Which reunions do we celebrate? How often do they repeat? How do we use ordinals in sports? Which sports are based on time? How do you use ordinals at school? Do you need ordinals to find out the best students in the class? Can you name any things that are/were the first in some area/field? Can you name any people who were the best in their branch? What is a second hand shop? Can you name 3 biggest countries of the world? Can you name 3 smallest countries in the world? Who was the first woman and man? What is the first aid? What is „first class“? How do people feel when they finish last in a game? Who was the first one to come to this lesson? What is the name of the 4th chapter of this book? What is your last day of this course? What is the first thing that you ate today?

29 Time - links http://math.about.com/od/countin1/a/time.htm – čtení času
- sčítání a odčítání času - hry s časem online - hry s časem pro děti - pracovní sešity pro děti na téma čas - vysvětlení času, pracovní listy a testy - matematické hry dle třídy - matematický převodník – způsoby měření času - novinky ze světa matematiky - historie měření času – historie času – video - typy hodin - chápání času

30 Geometry – dictionary and phrases
prostor – space protínat - intersect pyramida - pyramid R rovina křivky – plane curves rovnice – equation S sedmiúhelník - septagon spirála - spiral stavebnictví - construction symetrie – symmetry Š šestihran - hexahedron šestiúhelník – sextagon šroubovice - helix T tečna – tangent topologie – topology trojrozměrný prostor – three dimensional space trojúhelník – triangle tupý - obtuse tvar – shape U úhel - angle V válec – cylinder vektor – vector veličina - ratio velikost - size B bod – point Č čára – line časoprostor – space-time čtverec - square čtyřstěn - tetrahedron čtyřúhelník - quadrilateral D definice - definition délka – length desetiúhelník - decagon dimenze - dimension diskrétní geometrie – discrete geometry E elipsa - ellipse F funkce - function G geometr – geometer grafika - graphics K kombinatorika - combinatorics konvexní geometrie – convex geometry koule - sphere kruh – circle kružnice - circle křivka – curve kužel - cone kuželosečka – conic section L lichoběžník - trapezium M mnohoúhelník - polygon N nástroj – instrument, tool nekonečná řada – infinite series O obdélník - rectangle objem – volume oblouk - arc obvod – circumference ostrý - acute osmiúhelník - octagon otázka – question P parabola – parabole pětiúhelník - pentagon plocha – area podobnost – similarity poloměr – radius projektivní geometrie – projective geometry

31 Discussion What is geometry? What do we use it for? Do children usually understand it? Which shapes can you name? What tools do I need for geometry at school? What is 2D and 3D? Is there anything like 4D or 5D? What is it? Do you have problems seeing 3D pictures? Have you ever seen a 3D movie? What kind of shapes can you see around you right now? Discussion What do you see in the picture? Can you comment each image and say its formula? Which one is the easiest for children? Which one is the most problematic for children? Can you find examples of all these images in the world around us? In which jobs do we need to be good at geometry? What kinds of geometry do you know? Translate ČTVEREC _________________ OBDÉLNÍK _________________ TROJÚHELNÍK _________________ KOULE _________________ KRUH _________________ BOD _________________ LINKA _________________ HYPERBOLA _________________ KRYCHLE _________________ VÁLEC _________________

32 1e 2a 3c 4f 5d 6b Match the formula with the correct shape SQUARE A) ½ (b x h) TRIANGLE B) ½ h (a x b) RECTANGLE C) a x b CIRCLE D) πxr1 x r2 ELLIPSE E) a2 TRAPEZOID F) πr2 Pythagoras theorem – Can you comment it, explain it and draw an image? The  area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides. 1d 2h 3b 4g 5a 6f 7c 8e Try to match the definitions POINT a) An angle that measures less than 90° LINE b) Line segements that never intersect (they are always the same distance apart) PARALEL LINES c) Distance (line segment) from center of a circle to any point on that circle's circumference. RIGHT ANGLE d) A location in space - a dot on a piece of paper ACUTE ANGLE e) A line segment (or length) joining two points on a circles circumference and passes through the circle's center (twice the length of the radius) OBTUSE ANGLE f) An angle that measures more than 90° RADIUS g) An angle that measures 90° DIAMETER h) Connects two points via the shortest path and continues indefintely (forever) in both directions TRUE or FALSE Triangle has 4 sides. A square is formed by 4 angles. The length and width of a rectangular are the same. π is needed for counting the sphere. Right angle triangle means that one of the angles measures 80o. Symmetry means that both sides are the exact same when split in half. Similarity means that the objects look the same but might have different lenght and width. A vector is needed for counting triangles.

33 Geometry - links - vysvětlení geometrie pro děti - jednoduchá vysvětlení a aktivity - matematický rozcestník - geometrie - vysvětlení, obrázky - geometrické hry pro děti – základní geometrie – video - geometrické vzorce - matematické problémy a vzorce - geometrická fakta a vysvětlení - praktická geometrie - matematický rozcestník a cvičení - moderní geometrie

34 Equations- dictionary and phrases
algoritmus - algorithm analogie - analogy B bilance - balance binární – binary bod – point C celočíslo – integer Č čtvrtá odmocnina – fourth foot D derivate - derivation dimenze – dimension disekce - dissection doména – domain dotýkat se - touch druhá odnocnina – square root E ekvivalentní – equivalent extrapolace – extrapolation G graf - graph H hodnota – value J jednorozměrný - univariate K koeficient – coefficient konečný - finite konstanta - constant kruh – circle L levá strana – right side linka – line M matice - matrix N nekonečný - infinite nerovnost - inequality neznámá – unknown O omezený – limited operátor - operator P pravá strana – right side prohlášení - statement proměnná – variable protnout – cross průsečík - intercept předpokládat – assume přepsat – rewrite přesnost - accuracy přidat - add R racionální číslo – rational number relace – relation rovina - plane rovnoběžný – parallel rovnost – equality rozhodnutí - decision Ř řešení – solution S skalár - scalar sklon - slope souřadnice – coordinates soustava – system of equations společný – common strana - side T třetí odmocina – cube root tvrzení – proposition U unikátní - unique V vektor – vector vlastnosti - properties výraz – expression vzniknout - arise vzorec – formula vztah - relation Z zápis - notation

35 Discussion What is the equation good for? Can you mention some typical everyday situations when equation could be used? Are there many types of equations? Why are there letters used in equations? Is it difficult to make children understand equations? Do you think your maths books are good at explaining things to children or would you like to have another books or change something in them? Can you read and solve these equations? x + 2 = 17 – 4x _______________________________________________ 6 + 10n – 4n = n + 1 _______________________________________________ 10 – 8x = -2x + 4x _______________________________________________ -7p – 10 = -8p – 4p _______________________________________________ | 3+k | = 8 _______________________________________________ | k – 5 | = 0 _______________________________________________ | 1 + v | = 4 _______________________________________________ | t + 5 | = 6 _______________________________________________ 15 – w = 22 _______________________________________________ 6 30 = m _______________________________________________ 3 Can you find the correct answer? What is a proportion? Are equations used for counting proportions? What is the difference between the square equation and quadratic equation? What kind of curves do you know? What are they good for? What are parentheses? What is the function of zero in equations? Are there any famous equations you can mention and explain a bit? a) ________________________________________________________ b) ________________________________________________________ c) ________________________________________________________ d) ________________________________________________________

36 PLANE MATRIX SIDE FRACTION
38 22 3,16 46 Can you solve these mathematical problems? Gabriela sold half of her comic books and then bought 15 more. Now she has 34. With how many did she begin? Jack won 71 lollipops playing basketball. At school he gave 3 lollipops to each student in his maths class. Now he has 5 remaining lollipops. How many students are there in his class? Jane bought a magazine for 5.76$ and 3 erasers. She spent a total of 12.24$. How much did each eraser cost? For a trip 17 students rode in cars and the rest filled 6 buses. How many students were in each bus when 293 students were on the trip? What can you see in the image? Can you explain the use of each equation? Which of these images are not equations? Why? Which of the equations is the most difficult for the children to understand? Can you comment these words, use them in a sentence and explain them? POINT LINE SQUARE ROOT EQUAL VALUE GRAPH DIMENSION VECTOR SOLUTION FORMULA UNKNOWN COEFFICIENT FINITE INFINITE CUBE ROOT RATIONAL NUMBER IRRATIONAL NUMBER PLANE MATRIX SIDE FRACTION

37 Equations - links - základní informace o rovnicích a druzích rovnic - vysvětlení rovnic pro děti - úvod do rovnic, příklady a vysvětlení - řešení rovnic - video – úvod do rovnic, video pro děti - pracovní sešity a aktivity pro děti - pracovní aktivity pro děti – rovnice - procvičení rovnic, různá obtížnost - velký rozcestník matematických materiálů - zajímavá fakta o rovnicích – 17 nejdůležitějších rovnic

38 Famous mathematicians - dictionary and phrases
analytický – analytical Č černá díra – black hole D definice – definition diferenciální geometrie – differential geometry doměnka – conjecture dvourozměrný – 2-dimensional dymanika - dynamics důkaz – proof E ekonomika – economics etika - ethics G geodezie – geodesy geofyzika - geophysics graf - graph K kalkulačka – calculator kartografie - cartography klíčová postava – key figure klíčový - pivotal kontinuita - continuity L logaritmus - logarithm M mechanika – mechanics metafyzika - metaphysics N nebeský - celestial O obrana – defense optika - optics osoba – person P platnost - validity pohyb – motion pochyba – doubt povrch - surface pravděpodobnost - probability princip – principle předmět - subject příspěvek - contribution publikovat – publish R racionalismus - rationalism realizace - implementation rychlost zvuku – speed of sound S sloupec - column spisovatel – writer statistika - statistics T teorie – theory trojrozměrný – 3-dimensional tvrzení - statement V vědec – scientist vynálezce - intentor Z základy – foundation zakřivení - curvature zákon – law zhoršení - deterioration

39 ISAAC NEWTON When did he live? What was he interested in? What did he found and invent? What are his „law of motion“? He invented one of the first telescopes. What is a telescope good for? Newton was interested in gravitation. What is it and how does it affect us? BLAISE PASCAL When did he live? Where did he live? What was he interested in? He was interested in fluids? Why is it important to understand the qualities of fluids? He invented the first calculator. What can you say about calculators in general and what do you know about their history? He combined mathematics and philosophy. How is maths and philosophy connected? LEONHARD EULER When did he live? Where did he live? He invented the graph theory. What are the graphs good for in our lives. Where can we see them and do you personally use them? He was interested in cartography. What is it? Why is it useful? Euler spent his live in Russia and Germany. Which were some other countries and places where mathematicians and philosophers lived and studied? Euler was interested in general analysis. What in maths can be analysed and why do we need to analyse things?

40 http://www. shutterstock
CARL GAUSS Do you know him? What do you know about him? He was interested in geophysics and geodesy, what are they about? A few things and places were named after Gauss. Can you think of any of them? He was fond of differencial geometry? What is it used for? Do you understand it? GOTTFRIEND WILHELM LEIBNIZ Who was he? What has his field of interest? He wrote the „Law of continuity“. What is it? He added multiplication and division to Pascals calculator – why did the people need these functions? What for and in which areas was the calculator used? He was one of those who invented the binary number system – where is it used and why was this invention important? PIERRE SIMON LAPLACE Do you know this matematician? He was an astronomer and one of the first ones to mention „black holes“. What is it? How is it formed? What do people think about them? And do they really exist? He was also interested into the speed of sound. Why is it important to understand it? When and for what is it used? What do you think that all the matematicians thought about religion and God? What did they believe in and what do you think that people thought about them? Was the life of a matematician a hard life?

41 Famous matematicians - links
největších matematiků - známí matematikové nejznámějších matematiků včetně moderních - matematici a jejich vynálezy a názory - seznam matematiků a rozcestník na jejich stránky - ženy v matematice a informace o nich - obrázky známých matematiků - matematici dle národnosti - matematický rozcestník, kvízy a testy - kvíz (matematici) - kvíz pro děti

42 Graphs and charts - dictionary and phrases
aplikace – application B bublina - bubble Č časová osa - timeline číselný – numerical D dílek (koláče) - slice dílkování – graduation duální - dual G grafický – graphical H hodnota - value horizontální – horizontal J jev - phenomenon K kapacita - capacity konec – end konektivita - connectivitiy koncový bod – end point křivka - curve kvalitativní – qualitative M mřížka – grid N nepravidelný - irregular O obdélník – rectangle okraj - edge osa - axis P podskupina - subset popisek - legend porozumění - understanding poskytnout – provide pravidelný - regular procento – percentage proud - streem R radar - radar rodokmen – pedigree Ř řád – order S sdílet – share síť - network smyčka – loop sousedící - adjacent specifický – specific spojený – connected spojit - join struktura – structure stupeň - degree symbol – symbol Š šipka - arrow T tečka – dot teplota - temperature U účel - purpose údaje – data úrok – interest rate V velikost - size vertikální – vertical vrcholek – vertex všeobecný - universal výskyt - incidence význam – meaning vztah - relationship Z zobrazení - representation

43 Discussion What is a graph? What is it good use for? What kind of graphs do you know? What kind of information can I find in a graf? Look at the image below and try to quess what is each graph used for, how do you understand these graphs and which ones to do find easy to understand and which ones do you think are quite complicted. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

44 Can you answer these questions?
Can you draw an example of a ? HISTOGRAM BAR CHART PIE CHART LINE CHART Can you explain directed graphs? Can you explain indirected graphs? What is a mixed graph? 32 children voted for their favourite ice-cream flavour. How many children voted for chocolate? a) draw the graph and find out the correct answer b) ¼ vanilla, 1/8 strawberry, ¼ lemon, 3/8 chocolate A class of 30 voted for their favourite actor who played James Bond. How many voted for Sean Connery? How many did not vote for George Lazenby? How many more children voted for Pierce Brosnan than Roger Moore? How many children all together voted for Sean Connery and Roger Moore? WHEN 2/5 voted for Pierce Brosnan, 1/10 for Timothy Dalton, 1/5 Roger Moore, 1/5 Sean Connery, 1/10 George Lazenby Draw the graph and answer the questions. Which type of graph would you choose for showing how the price of gasoline changes each month over a year? Which type of graph would you choose for showing the attendence in your class? What is the name of the graph that uses pictures and symbols to show data?

45 Graphs and charts - links
- grafy pro děti a učitele - vytvoř si vlastní graf - grafy, matematický rozcestník – druhy grafů, video - statistika a grafy pro děti (moc hezké) - typy grafů - matematické hry pro školní děti - jak stvořit graf - jak učit děti grafy - složitější matemetické grafy a funkce - video - matematické funkce - matematické kvízy

46 Maths around us - dictionary and phrases
B bankovka - banknote C cesta – journey Č čas - time D délka – length den - day drahý - expensive drobné change H hodinky - watch hodiny – clock hra – game hrát – play K kalendář - calendar kilogram – kilogramme koupit - buy L lék - medicine levný – cheap litr - litre M měsíc - month množství – amount N nejmenší – the smallest největší – the biggest P peníze – money pilulka – pill platit - pay počasí – weather podobný - similar poplatek – fee, charge poražený – loser prodat sell přidat – add R roční období - season rychlost - speed S skóre – score směnárna – exchange office směnný kurz – exchange rate sport – sport statistika – statistics stejný – the same stupeň – degree symetrie – symmetry T týden - week V váha – scales (přístroj) váha – weight (člověka) vážit - weigh vítěz – winner výlet - trip výsledek – result vzdálenost – distance Jak dlouho to trvá? How long does it take? Kdo vyhrál? Who won? Kolik je hodin? What´s the time? Je pozdě. It´s late. Je brzy. It´s (too) soon. Má moc práce. He´s busy. Kolik to stojí? How much is it? Máte drobné? Do you have change? Kolik vám dlužím? How much do I owe you? Je to drahé. It´s expensive. Je to levné. It´s cheap. Kde je směnárna? Where is the exchange office? Máte eura? Do you have euros? Kolik je poplatek? How much is the free/charge? Kolik chcete kil? How many kilos do you want? Kolik stojí kilo? How much is one kilo? Kolik vody mám přidat? How much water shall I add? Kolik to váží? How much does it weigh? Kolik si toho mám vzít? How much shall I take? Jak často si to mámn brát? How often shall I take it? Jaké je počasí? What is the weather like? Jak rychle jedete? How fast do you go? Jak často jezdíte? How often do you know?

47 skóre plán výletu čas nakupování sports – bowling atd směnárna vaření
Can you name any individual sports? Can you name any team sports? Can you name any sports where the team has only 2 members? Can you name any sports in which the sportsmen need to score? Can you name any sports where time is very important? Can you name any sports with subjective evaluation? Which sport and system of evaluation is your favourite? TRAVELLING What does it mean to come late? What can you do not to come late? What is a delay? What means of transport do you know and which one is the most reliable? What can go wrong when it comes to different kinds of transport? Can you compare prices of various means of transport? What are emissions? What do they consist of? What can you use maths for during your holiday? TIME Why do people need to learn to tell the time? What would happen if people didn´t have any watches? Do you think that our lives are faster than they used to be? Why? Why does 5min sometimes seem so long and sometimes so short? Do you always come on time? How do you feel when you are late? What do you think about people who come late? What is a timetable? What is a schedule? Do you carefully plan your days? SHOPPING Do you like shopping? How often do you go shopping? How much do you usually spend? Is living in the Czech Republic getting more and more expensive? Why? Can you buy everything you want? Do you think some people buy more than they need? Should we plan our shopping? How should we plan our budget? skóre plán výletu čas nakupování sports – bowling atd směnárna vaření when we are sick kalendář počasí jízda dopr pr v přírodě peníze symetrie statistika opakovanost

48 EXCHANGE OFFICE When do go to the exchange office? What currencies can I get there? What is an exchange rate? What can you say about the changing exchange rate between EURO and THE CZECH CROWN? What is a „fee“? Why is it paid? COOKING Do we need maths in the kitchen? When? What gadgets help us with measuring in the kitchen? Why do I need to know exact numbers in the kitchen? MEDICINE What would happen if people didn´t use maths when it comes to mediation? What forms of medication do you know? What is a „dose“? What does it mean to overdose someone? Do you remember any case when someone overdosed other people on purpose? CALENDAR What is a calendar? What is it good for? Is there only one kind of calendar in the world? What kinds of calendar do you know? Which month and season are your favourite any why? REPETITION Is there anything that you do EVERY day? What do you do only ONCE a week? How OFTEN do you go on holiday? What would you NEVER do and why? Have you EVER tried any adrenalin sport? Is there any food that you have ALWAYS wanted to try? How OFTEN do you cook? How many times have you moved in your life? How many times have you been abroad? How many times have you tasted something really discusting? Have you EVER seen any accident? Have you EVER been to a bank abroad?

49 Maths around us - links - matematika v našem životě – prezentace - matematika okolo nás – obrázky a vysvětlení - hra - kolem světa za 80sekund - online matematická hra - přístup k výuce matematiky ve světě - matematika vs. svět kolem nás – videa – matematika a my - finanční povědomí - prezentace - matematiky kolem nás - prezentace - nejen matematické - praktické matematické aktivity ve třídě

50 Final revision, conversation, practical use of
mathematics, game and quizes – dictionary A absolutní - absolute Č čas - time číselný obor – numeric field D definice – definition dělit - divide důkaz – proof F frekvence - frequency H hodnota – field J jmenovatel - denominator K koeficient - coefficient kombinace - combination konjunkce – conjunction konstatní – constant korelace - corellation kvadratický - quadratic L levý - left lineární – linear linka – line M místo - place N náhodný - random negace – negation nereálný - unreal nezávislost - independency O operace – operation opečení - rotation P permutace – permutation počítání - counting podmínka - condition poměr - ratio posunutí – displacement pravděpodobnost - probability pravý - right proměnná – variable prostor – space R reálný - real relativní - relative rovina - plane rovnice – equation rovný – straight rozšíření – explansion Ř řešení - solution řešit - solve T teorie – theory transformace - transformation U úhel - angle úsečka - bar V vektor - vector vlastnost - property výraz - expression výrok - statement vztah - relationship Z základní – basic závislost – dependency zlomek - fraction znalost - knowledge

51 BASIC MATHEMATICS Can you explain these terms? Can you give an example as well? ELEMENT ______________________________________________ CONJUNCTION ______________________________________________ EQUIVALENCE ______________________________________________ DEFINITION ______________________________________________ PROOF ______________________________________________ NATURAL NUMBERS ______________________________________________ RATIONAL NUMBER ______________________________________________ IRRATIONAL NUMBERS ____________________________________________ NUMERIC FIELD ______________________________________________ SECOND AND THIRD SQUARE ROOT __________________________________ ESTIMATION ______________________________________________ ROUNDING ______________________________________________ RESULT ______________________________________________ PRIME NUMBERS ______________________________________________ ARITHMETIC ______________________________________________ QUESTIONS and ANSWERS What is algebra? What is a formula? Can you give examples of a few formulas and comment them? a) __________________________________________________________ b) __________________________________________________________ c) __________________________________________________________ d) _________________________________________________________ What is quadratic inequality? What is a parameter? When are they used? What is planimetry? How is planimetry used in everyday life? Is it easy or difficult to teach planimetry? What are the biggest problems for the students? What kinds of shapes do you know?

52 Discussion What is a function? What kinds of functions do you know? What are they used for? How do you explain functions to your students? What is goniometry about? Can you draw and example? 6. What is trigonometry about? Can you draw and example? 7. What is stereometry? Can you draw and example? What is the differential calculus? What is the integral calculus? Can you draw and example of a matrix? Can you give an example of a decimal number? Can you write a few fractions and read them aloud? What is a percentage? What is it good for? What is probability? Make a definition of one mathematical term and let the others guess what it is... ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

53 the teacher DOESN´T show this worksheet to the students
1000 2000 3000 4000 5000 ALGEBRA What s addition? What is subtraction? What is whole number? What is integer? What is division? DECIMALS Read 0,2 Read 0,258 Read 0,1582 Count 1 – 0,2585 = ? Count 2 – 0,5588 = ? EQUATIONS Give an example of a 1-step equation. Give an example of a 2-step equation. What kinds of equations do you know? Can you tell us some really famous equations? Can you name a mathematician and say what he is famous for? FRACTIONS What are the parts of a fraction? Explain the adding of fractions. Explain the subtraction of fractions. Explain the multiplication of fractions. Explain the division of fractions. GEOMETRY Name 5 different shapes. What is the difference between 2D and 3D? Is there anything like 4D? What is it? Name 2 formulas for counting the 2D shapes and explain them. Name 2 formulas for counting the 3D shapes and explain them. GRAPHS What is a graph? What kinds of graphs do you know? Draw a „pie“ graph. Draw a „bar“ graph. Draw your favourite type of graph and explain it. MEASUREMENT What are some units of weight? What are some units of lengh? What are some units of time? Say something about British units of measurement. Convert: 3m = ____ feet TIME How many seconds are there in one hour? How many months are there in one year? How many days are there in one year? What kind of calendars do you know? Is time relative? Explain it. JEOPARDY the teacher DOESN´T show this worksheet to the students each student chooses his/her own question, e.g. „Time for 3000“ – then the teacher asks the question and the students answers it. if the answer is correct – the the student gets the points if the answer is not correct – the student gets no points and another student can continue the teacher corrects the wrong answers – nobody gets points for those answers

54 1d 2i 3f 4j 5a 6h 7b 8e 9g 10c BIG PRESENTATION
Each student chooses one mathematical field and everyone gets time to prepare the presentation. The presentation will contain: a) explanation b) practical use c) a few example and exercises Quess the word ALGORITHM A) the branch of mathematics that deals with the logic and consistency of mathematical proofs, formulas, and equations. ANALOGISM B) the doctrines taught by Pythagoras CALCULUS C) the branch of mathematics that deals with the relationships between the sides and the angles of triangles and the calculations based on them, particularly the trigonometric functions GEOMETRY D) any methodology for solving a certain kind of problem METAMATHEMATICS E) the branch of algebra that deals with quadratic equations PLANIMETRY F) a system or method of calculation PYTHAGORISM G) the study of the properties of geometric figures QUADRATICS H) measurement of plane areas TOPOLOGY I) the construction of a proportion TRIGONOMETRY J) the mathematics of the properties, measurement, and relationships of points, lines, angles, surfaces, and solids 1d 2i 3f 4j 5a 6h 7b 8e 9g 10c

55 Famous maths quotes... what do you think about them?
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.  ~John Louis von Neumann Pure mathematics is, in its way, the poetry of logical ideas.  ~Albert Einstein The essence of mathematics is not to make simple things complicated, but to make complicated things simple.  ~S. Gudder Go down deep enough into anything and you will find mathematics.  ~Dean Schlicter Sometimes it is useful to know how large your zero is.  ~Author Unknown If there is a God, he's a great mathematician.  ~Paul Dirac Infinity is a floorless room without walls or ceiling.  ~Author Unknown One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers...  ~Heinrich Hertz You and maths When did you become interested in maths? Why did you decide to study it? What about your studies? Where did you study and how difficult was it? Why did you become a teacher? Say something about your school. Say something about maths in each grade – what do you teach there? Which fields of maths are the most popular and which ones are the least popular of all? Why do the children like / dislike maths? What kind of tool do you use during your lessons? How often do you test your students? What methods do you use to explain various fields of maths? What do you think about the „state maturitas“? Do you think everyone should take the state maturita from maths? Why is maths important for our future? How do you think young students should be attracted to mathematical universities? What jobs can the students do when they finish mathemtical universities? Which mathematical problems do you think scientists will be solving in the future? Do you think you will spend your life as a teacher of mathematics?

56 Online games and quizes – links
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