2 Basic terminology - dictionary alfa – aplhaaritmetika – arithmeticCcelá čísla – whole numbersČčíslice - digitčíslo – numberčtverec – squarečtyřnásobek – quadrupleDdělit - dividedvojitý - doubleEexponent - exponentLlichýJjmenovatel - denominatorKkonstanta – constantkořen - rootkvocient - quotientMmínus - minusmíra - measurementNnásobek – multiplenásobit - multiplyneracionální - irrationalnerovnost – inequalitynula – zeroOodčítání - subtractionPplus - pluspočítat – countpodíl – ratioprostý - simpleprvotní - primeprůměr - averagepřenost – accuracypřesnost - precisionpřevrácený – inversepřímka - linepřirozený - neutralRracionální – rationalracionální číslo – rational numberrovnost - equalityrozdíl – differenceŘřadová číslovka – ordinal numberřecká abeceda – Greek alphabetSsčítání - addingsmíšený – mixedsoučet - sumsprávný - propersudý – evenTteorém – theoremtěžnice – mediantrojitý - tripleVvýznamný - significantvzorec - formulaZzákladní číslovky – cardinal numberszaokrouhlení – roundingzápis - notationzáporný - negativezávorka – bracket, parenthesiszbytek - remainderzlomek – fractionzmenšit – reduce2 + 2 Two plus two6 – 4 Six minus four5 x 3 OR 5 * 3 Five times three= equals2 + 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 two1/2 one half1 ½ One and one half1/3 one third3 1/3 Three and one third1/4 one quarter2 ¼ Two and one quarter5/9, 2/3, 5/6 five ninths, two thirds, five sixths4 2/3 Four and two thirds98% Ninety eight percent
3 DISCUSSIONWhat 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 numbersix 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?1412 minutes7 cents4388,5Can you write an example of...DIVISION _____________________________________________ADDING _____________________________________________MULTIPLYING _____________________________________________SUBTRACTION _____________________________________________FUNCTION _____________________________________________Explain the use of these areas of mathematicsALGEBRAGEOMETRYCOMBINATORICSLOGICGAME THEORYPROBABILITYSTATISTICSROBOTICSTRIGONOMETRYAPPLIED 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
7 DiscussionWhy 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?multiplicationmultiplication with the use of squaresdivisioncubic equationquadratic equationThe 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 DiscussionWhere 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
11 DiscussionWhich 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 ΣΚ Φ ΔΨ Θ 9. Μ
12 Solve these word gamesThere 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 pictureWhat 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?PresentationEach 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
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?1C2E3A4B5D2A3DCan you match these numbers?Neutral numbers a) -2, 2/3, 1,21Integers b) –e, √2, πRational numbers c) 1,2,3,...Real numbers d) 2i, -2+3iComplex 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 = 1a b22. Ellipse b) x y2 = 1Parabola c) x2 + y2 = a2Hyperbola 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
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 Fahrenheit1 mile = 1,760 yards = 5,280 feet = 63,360 inchesOne 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 intensity2) DECIBEL b) unit of frequency equal to one cycle per second3) FARAD c) unit of force that accelerates 1 kilogram to 1 meter / second / second4) CALORIE d) unit of x-radiation or gamma radiation5) HERTZ e) unit for measuring amount of electrical current6) KARAT f) unit of electrical resistance of circuits7) NEWTON g) unit of power equal to one joule per second8) OHM h) unit of fineness of gold equal to 1/24 part of pure gold9) ROENTGEN i) unit measuring electrical capacitance10) WATT j) unit of heat or heat-producing value1E2A3i4J5B6H7C8f9D10Can you solve these mathematical problems?3.83 cm = ___________ mm 2) kg = ___________ g351 ml = ___________ L 4) 1,576 ml = ___________ L2.6 L = ___________ ml 6) 3,557 ml = ___________ L6.3 kg = ___________ g 8) m = ___________ cm1.62 m = ___________ cm 10) 29.6 cm = ___________ mmmm = ________ cm 12) dam = ________ dm13) 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
23 DiscussionWhat 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 translationDENOMINATOR A) MNOŽSTVÍINCREASE B) POROVNATAMOUNT C) ROVNÝDECIMAL D) JMENOVATELCOMPARE E) PRŮMĚRAVERAGE F) DĚLENÍDEVISION G) DESETINNÉ ČÍSLOEQUAL H) ZLOMKOVÁ ČÁRAREDUCE J) ZVÝŠITFRACTION BAR K) ZMENŠITTaskEach 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 zlomkůpro 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
27 DiscusstionHow 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: :203. 5: :308: :587. 12: :009: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?READREADREADREADREADREAD 80´s, 70´s, 90´sREAD 19th century, 20th centuryWhat 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
31 DiscussionWhat 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?DiscussionWhat 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?TranslateČTVEREC _________________OBDÉLNÍK _________________TROJÚHELNÍK _________________KOULE _________________KRUH _________________BOD _________________LINKA _________________HYPERBOLA _________________KRYCHLE _________________VÁLEC _________________
32 1e2a3c4f5d6bMatch the formula with the correct shapeSQUARE A) ½ (b x h)TRIANGLE B) ½ h (a x b)RECTANGLE C) a x bCIRCLE D) πxr1 x r2ELLIPSE E) a2TRAPEZOID F) πr2Pythagoras 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.1d2h3b4g5a6f7c8eTry to match the definitionsPOINT 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 paperACUTE 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 directionsTRUE or FALSETriangle 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
35 DiscussionWhat 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 _______________________________________________630 = m _______________________________________________3Can 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 38223,1646Can 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 NUMBERPLANE 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
39 ISAAC NEWTONWhen 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 PASCALWhen 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 EULERWhen 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 GAUSSDo 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 LEIBNIZWho 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 LAPLACEDo 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 matematikovénejznámějších 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
43 DiscussionWhat 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 CHARTCan 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 answerb) ¼ vanilla, 1/8 strawberry, ¼ lemon, 3/8 chocolateA 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 LazenbyDraw 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 Bbankovka - banknoteCcesta – journeyČčas - timeDdélka – lengthden - daydrahý - expensivedrobné changeHhodinky - watchhodiny – clockhra – gamehrát – playKkalendář - calendarkilogram – kilogrammekoupit - buyLlék - medicinelevný – cheaplitr - litreMměsíc - monthmnožství – amountNnejmenší – the smallestnejvětší – the biggestPpeníze – moneypilulka – pillplatit - paypočasí – weatherpodobný - similarpoplatek – fee, chargeporažený – loserprodat sellpřidat – addRroční období - seasonrychlost - speedSskóre – scoresměnárna – exchange officesměnný kurz – exchange ratesport – sportstatistika – statisticsstejný – the samestupeň – degreesymetrie – symmetryTtýden - weekVváha – scales (přístroj)váha – weight (člověka)vážit - weighvítěz – winnervýlet - tripvýsledek – resultvzdálenost – distanceJak 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?TRAVELLINGWhat 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?TIMEWhy 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?SHOPPINGDo 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?skóreplán výletučasnakupovánísports – bowling atdsměnárnavařeníwhen we are sickkalendářpočasíjízda dopr prv příroděpenízesymetriestatistikaopakovanost
48 EXCHANGE OFFICEWhen 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?COOKINGDo 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?MEDICINEWhat 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?CALENDARWhat 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?REPETITIONIs 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
51 BASIC MATHEMATICSCan 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 ANSWERSWhat 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 DiscussionWhat 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 10002000300040005000ALGEBRAWhat s addition?What is subtraction?What is whole number?What is integer?What is division?DECIMALSRead 0,2Read 0,258Read 0,1582Count 1 – 0,2585 = ?Count 2 – 0,5588 = ?EQUATIONSGive 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?FRACTIONSWhat 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.GEOMETRYName 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.GRAPHSWhat 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.MEASUREMENTWhat 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 = ____ feetTIMEHow 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.JEOPARDYthe teacher DOESN´T show this worksheet to the studentseach 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 pointsif the answer is not correct – the student gets no points and another student can continuethe 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) explanationb) practical usec) a few example and exercisesQuess the wordALGORITHM A) the branch of mathematics that deals with the logic and consistency of mathematical proofs, formulas, and equations.ANALOGISM B) the doctrines taught by PythagorasCALCULUS 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 functionsGEOMETRY D) any methodology for solving a certain kind of problemMETAMATHEMATICS E) the branch of algebra that deals with quadratic equationsPLANIMETRY F) a system or method of calculationPYTHAGORISM G) the study of the properties of geometric figuresQUADRATICS H) measurement of plane areasTOPOLOGY I) the construction of a proportionTRIGONOMETRY J) the mathematics of the properties, measurement, and relationships of points, lines, angles, surfaces, and solids1d2i3f4j5a6h7b8e9g10c
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 NeumannPure mathematics is, in its way, the poetry of logical ideas. ~Albert EinsteinThe essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~S. GudderGo down deep enough into anything and you will find mathematics. ~Dean SchlicterSometimes it is useful to know how large your zero is. ~Author UnknownIf there is a God, he's a great mathematician. ~Paul DiracInfinity is a floorless room without walls or ceiling. ~Author UnknownOne 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 HertzYou and mathsWhen 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 - pracovní sešity- pracovní sešity- pracovní sešity- pracovní sešity- pracovní sešity