Mathematics
Basic terminology - dictionary
A
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
12 > 8
4+1≤6
Seven is less than ten.
Twelve is greater than eight.
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
1½
1/3
3 1/3
1/4
2¼
5/9, 2/3, 5/6
4 2/3
one half
One and one half
one third
Three and one third
one quarter
Two and one quarter
five ninths, two thirds, five
sixths
Four and two thirds
DISCUSSION
1.
2.
3.
4.
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?
36
366
36 ½
360
3 600
3,6
3600000
36,6
36$
Can you read these numbers?
1.
2.
3.
4.
5.
6.
7.
8.
36 585
29 472
21 999
98 654
78 555
36 851
14 441
59 952
9.
10.
11.
12.
13.
14.
15.
16.
104 258
258 589
888 754
587 723
1 258 778
5 879 587
9 587 111
10 587 998
Write the number
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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
____________
11. DICTATE – teacher says the numbers and students write them down...
1. ______________________
2. _____________________
3. ______________________
4. _____________________
5. ______________________
6. _____________________
Can you solve these problems?
1.
2.
3.
4.
5.
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?
Can you write an example of...
1.
2.
3.
4.
5.
DIVISION
ADDING
MULTIPLYING
SUBTRACTION
FUNCTION
_____________________________________________
_____________________________________________
_____________________________________________
_____________________________________________
_____________________________________________
Explain the use of these areas of mathematics
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ALGEBRA
GEOMETRY
COMBINATORICS
LOGIC
GAME THEORY
PROBABILITY
STATISTICS
ROBOTICS
TRIGONOMETRY
APPLIED MATHEMATICS - EQUATIONS
Basic terminology – links
1) http://www.basic-mathematics.com/basic-math-glossary.html základní matematické termíny
2) http://dorakmt.tripod.com/mtd/glosmath.html - seznam
matematických pojmů
3) http://www.flashcardmachine.com/basic-math-termsshortlist.html -
kartičky se jmény pojmů / použitelné pro hry
4) http://www.spellingcity.com/math-vocabulary.html - velký rozcestník
pro učitele nejen matematiky
5) http://www.math.com/ - matematický rozcestník
6) http://www.amathsdictionaryforkids.com/dictionary.html matematický online slovník pro děti – velice pěkné
7) http://www.softschools.com/math/games/ - matematické online hry
a aktivity
8) http://www.ixl.com/ - matematické aktivity podle věku dětí
9) http://www.math-exercises-for-kids.com/ - matematické aktivity dle
složitosti
10) http://www.mathabc.com/ - matematické aktivity od 1. třídy
11) http://www.sheppardsoftware.com/math.htm - matematika hrou
12) http://www.math-drills.com/ - matematická cvičení pro starší
13) http://www.schoolexpress.com/funtime/math_generator/ materiály pro učitele matematiky
14) http://en.wikipedia.org/wiki/Lists_of_mathematics_topics - seznam
matematických témat a odvětví
History of mathematics - dictionary
A
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
Discussion
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
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?
The Babylonians were using these formula – do you know what they mean and
what they were used for?
1.
2.
3.
4.
5.
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
CAVE
EQUATION
SQUARE
CIRCLE
METROLOGY
DECIMAL
PAPYRUS
STARS
CALENDAR
ZERO
SECOND
MONUMENT
Discussion
1.
2.
3.
4.
5.
6.
7.
8.
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.
History of mathematics - links
1) http://www-history.mcs.st-and.ac.uk/ - matematický archív
2) http://www.math.tamu.edu/~dallen/masters/hist_frame.htm historie matematiky
3) http://archive.org/details/AHistoryOfMathematics - archív knih (i
matematických)
4) http://www.bbc.co.uk/podcasts/series/maths - historie matematiky poslech
5) http://www.youtube.com/watch?v=cy-8lPVKLIo – video o historii
matematiky
6) http://fclass.vaniercollege.qc.ca/web/mathematics/about/history.ht
m - matematika od počátku do současnosti
7) http://archives.math.utk.edu/topics/history.html - archív okazů na
matematické organizace a společnosti
8) http://www.timetoast.com/timelines/8517 - časová linka a důležité
události v matematice
9) http://en.wikipedia.org/wiki/Timeline_of_mathematics matematika po letech a staletích
10) http://en.wikipedia.org/wiki/History_of_writing_ancient_numbers historie psaní čísel
11) http://www.wolframscience.com/reference/notes/901d - historie
čísel
12) http://fabpedigree.com/james/mathmen.htm - největší matematici
Great Greek mathematicians – dictionary
A
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
Discussion
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
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?
1.
2.
3.
4.
5.
6.
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?
1.
4.
7.
Ω
Κ
Ψ
2. Χ
5. Φ
8. Θ
3. Σ
6. Δ
9. Μ
Solve these word games
1.
2.
3.
4.
5.
6.
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
1.
What do you see in this picture?
2.
Can you name she shapes you see?
3.
Do you understand the formulas you
see? What do they mean?
4.
Which of these is the most difficult for
your students and why?
5.
Why is it important to be able to use
these formulas?
Presentation
1.
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.
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
Great Greek matematicians - links
1) http://www.ancientgreece.com/s/Main_Page/ - starověkké Řecko
2) http://www.bbc.co.uk/schools/primaryhistory/ancient_greeks/ starověkké Řecko (i pro děti)
3) http://greece.mrdonn.org/ - Řecko, legendy, rozcestník
4) http://en.wikipedia.org/wiki/Chronology_of_ancient_Greek_mathe
maticians - řečtí matematici
5) http://www-history.mcs.st-and.ac.uk/Indexes/Greeks.html - otázky a
odpovědi k řecké matematice
6) http://atschool.eduweb.co.uk/sirrobhitch.suffolk/portland%20state
%20university%20greek%20civilization%20home%20page%20v2/do
cs/7/it.html - rozcestník matematiků
7) http://www.crystalinks.com/greekmath.html - matematika starého
Řecka
8) http://www.mlahanas.de/Greeks/TLMathematics.htm - vývoj
matematiky v Řecku chronologicky
9) http://aleph0.clarku.edu/~djoyce/mathhist/greece.html - Řecko
(mapa, města, matematici, apod.)
10) https://en.wikipedia.org/wiki/Greek_alphabet - Řecká abeceda
11) http://anonemuss.hubpages.com/hub/Greek-Influences-today - vliv
starého Řecka na současnou společnost
12) http://www.britannica.com/EBchecked/topic/369194/mathematics/
65989/Survival-and-influence-of-Greek-mathematics - starověké
Maths in astronomy and astrology –
dictionary and phrases
A
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
Discussion
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
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?
Can you match these numbers?
1.
2.
3.
4.
5.
Neutral numbers
Integers
Rational numbers
Real numbers
Complex numbers
a) -2, 2/3, 1,21
b) –e, √2, π
c) 1,2,3,...
d) 2i, -2+3i
e) -2,-1,0,1,2,...
Can you match these equations,read them aloud and draw the image next to the
equation?
1.
Circle
a) x2 + y2 = 1
a2
b2
2.
Ellipse
b) x2 - y2 = 1
a2
b2
3.
Parabola
c) x2 + y2 = a2
4.
Hyperbola
d) y2 = 4ax
Do you know the answer?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
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?
1.
2.
3.
4.
5.
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 1678. 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.
Maths in astronomy and astrology - links
1) http://www-history.mcs.st-and.ac.uk/Indexes/Astronomy.html matematická astrologie
2) http://space.about.com/od/astronomydictionary/g/mathastronomy.
htm - matematika v astrologii
3) http://www.ams.org/journals/bull/1948-54-11/S0002-9904-194809089-9/S0002-9904-1948-09089-9.pdf - kniha - matematické
metody v astronomii
4) http://www.britannica.com/EBchecked/topic/369194/mathematics/
65972/Mathematical-astronomy - definice matematické astrologie
5) http://cnr2.kent.edu/~manley/astronomers.html - nejznámější
astronomové
6) http://science.discovery.com/famous-scientists-discoveries/7-
famous-astronomers-you-should-know.htm - 7 nejznámějších
astronomů
7) http://www.kidsastronomy.com/ - astronomie pro děti
8) http://www.sciencekids.co.nz/astronomy.html - astronomie pro děti,
projekty a hry
9) http://osr.org/articles/astronomy-basics-for-children/ - základní
odpovědi pro děti
10) http://www.space.com/19915-milky-way-galaxy.html - Mléčná dráha
11) http://science.nationalgeographic.com/science/photos/galaxiesgallery/ - informace, obrázky a rozcestník naší galaxie
Units of measurement – dictionary and phrases
A
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
Symbol
Factor
deca hecto kilo mega giga
da
h
k
M
G
1
2
3
6
10
10
10
10
109
tera peta exa zetta yotta
T
P
E
Z
Y
12
15
18
21
10
10
10
10
1024
Small number prefixes
Name
Symbol
Factor
deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
µ
10-6
nano
n
10-9
pico
p
10-12
femto
f
10-15
atto
a
10-18
zepto
z
10-21
yocto
y
10-24
Do you know the answer?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
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?
13. How many miles in one kilometer?
14. How many centimetres in one feet?
Can you write these numbers?
trillion
million
thousand
tenth
thousandth
__________________
__________________
__________________
__________________
__________________
billion
hundred
ten
hundredth
millionth
__________________
__________________
__________________
__________________
__________________
Can you comment these facts?
1.
2.
3.
4.
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.
Can you match these units of measurement with their definition?
1)
2)
3)
AMPERE
DECIBEL
FARAD
4)
5)
6)
7)
8)
9)
10)
CALORIE
HERTZ
KARAT
NEWTON
OHM
ROENTGEN
WATT
a) unit for measuring sound intensity
b) unit of frequency equal to one cycle per second
c) unit of force that accelerates 1 kilogram to 1 meter /
second / second
d) unit of x-radiation or gamma radiation
e) unit for measuring amount of electrical current
f) unit of electrical resistance of circuits
g) unit of power equal to one joule per second
h) unit of fineness of gold equal to 1/24 part of pure gold
i) unit measuring electrical capacitance
j) unit of heat or heat-producing value
Can you solve these mathematical problems?
1)
3)
5)
7)
9)
11)
3.83 cm = ___________ mm
351 ml = ___________ L
2.6 L = ___________ ml
6.3 kg = ___________ g
1.62 m = ___________ cm
238.94 mm = ________ cm
2)
4)
6)
8)
10)
12)
22.9 kg = ___________ g
1,576 ml = ___________ L
3,557 ml = ___________ L
0.84 m = ___________ cm
29.6 cm = ___________ mm
9.7 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?
14) 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?
15) The perimeter of a regular hexagon is 36cm. How long is each side?
16) Mr. Martin's Spanish class is 45 minutes long. If it starts at 3:30, what time does it
end?
17) 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?
18) 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?
19) 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?
Units of measurement - links
1) http://www.convert-me.com/en/ - systém jednotek
2) http://www.convertunits.com/ - převody jednotek online
3) http://phrontistery.info/unit.html - seznam jednotek (matematické i
fyzikální)
4) http://physics.nist.gov/cuu/Units/ - systém SI
5) http://www.jbc.org/site/misc/itoa.TI.xhtml - zkratky používané v
převodech a pro vyjádření čísla
6) http://www.ducksters.com/kidsmath/units_of_measurement_glossa
ry.php - jednotky pro děti + vysvětlení
7) http://www.neok12.com/Measurements.htm - jednotky pro děti,
videa a vysvětlení
8) http://www.youtube.com/watch?v=7vT-988yH3M – základní
jednotky video
9) http://www.onlinemathlearning.com/measurement-games.html hry zaměřené na převody
10) http://www.learninggamesforkids.com/1st-grademath/measurements-1st.html - spojovačky a hádanky zaměřené na
převody jednotek
11) http://www.kidskonnect.com/subjectindex/17educational/math/293-measurement.html - rozcestník pro děti
zaměřený na převody a matematiku
12) http://www.helpingwithmath.com/by_subject/geometry/geometry.
Fractions and Percents – dictionary and phrases
A
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
Discussion
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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?
1)
3)
4 3/7+ 4 1/2 =
3 1/8+ 3 7/11 =
2)
4)
9 1/3+ 2 3/7 =
2+ 4 2/3 =
5)
7)
3 1/3- 1 14/15 =
9- 1 4/9 =
6)
8)
2 2/5- 2 5/14 =
9 1/4- 2 5/11 =
9)
11)
4 1/4× 2 5/6 =
8 3/4× 1 8/13
10)
12)
9 1/2× 8 =
2 7/15× 3 1/11 =
13)
15)
2 5/14÷ 2 2/5 =
2 5/11÷ 9 1/4 =
14)
16)
9÷ 1 4/9 9 =
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?
Percent – word problems and games
1.
2.
3.
4.
5.
6.
7.
8.
What number is 112% of 2053?
168 is what percent of 420?
Clara ran the 100-meter dash in 13.12 seconds yesterday at track practice. Her
twin sister Destiny ran it in 14.62 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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
DENOMINATOR
INCREASE
AMOUNT
DECIMAL
COMPARE
AVERAGE
DEVISION
EQUAL
REDUCE
FRACTION BAR
A) MNOŽSTVÍ
B) POROVNAT
C) ROVNÝ
D) JMENOVATEL
E) PRŮMĚR
F) DĚLENÍ
G) DESETINNÉ ČÍSLO
H) ZLOMKOVÁ ČÁRA
J) ZVÝŠIT
K) ZMENŠIT
Task
1.
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.
Fractions and Percents - links
1) http://www.aaamath.com/fra.htm - vysvětlení zlomků
2) http://www.visualfractions.com/ - zlomky pro děti, rozcestník
3) http://www.mathsisfun.com/fractions.html - vysvětlení zlomků
pro děti
4) http://www.coolmath4kids.com/fractions/ - zlomky a cvičení
5) http://www.maths-games.org/fraction-games.html - online hry na
zlomky
6) http://www.math-play.com/math-fractions-games.html - hry se
zlomky pro děti
7) http://www.math.com/school/subject1/lessons/S1U1L7GL.html procenta - vysvětlení
8) http://www.mathgoodies.com/lessons/vol4/meaning_percent.html -
procenta vs. zlomky
9) http://www.math.com/students/calculators/source/3percent.htm procentní kalkulátor
10) http://www.maths-games.org/percentage-games.html - hry s
procenty
11) http://www.mathsisfun.com/decimal-fraction-percentage.html procenta, zlomky a desetinná čísla
12) http://www.bbc.co.uk/bitesize/ks3/maths/number/fractions_decim
als_percentages/revision/1/ - rozcestník na cvičení online –
procenta, zlomky a desetinná čísla
Time – dictionary and phrases
A
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
Discusstion
1.
2.
3.
4.
5.
6.
7.
8.
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?
1.
3.
5.
7.
9.
12:55
5:15
8:45
12:00
9:35
2.
4.
6.
8.
10.
3:20
6:30
1:58
24:00
11.05
The teacher dictates the times and the students write:
1) _______________
2) ______________
3) _______________
4) ______________
5) _______________
6) ______________
What do you think about these statements?
1.
2.
3.
4.
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.
5. Like all good things, time will come to an end….maybe?
6. There is no time like the present.
7. Until the 1800s, every village lived in its own little time zone, with clocks
synchronized to the local solar noon.
8. 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.
9. Everyone experiences time differently.
10. The past and future are equally real.
Can you read these dates and answer these questions?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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 25.8.1955
READ 18.12.914
READ 4.2.2018
READ 31.3.1578
READ 10.6.2000
READ 80´s, 70´s, 90´s
READ 19th century, 20th century
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
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?
Time - links
1) http://math.about.com/od/countin1/a/time.htm – čtení času
2) http://www.mathsisfun.com/time-add-subtract.html - sčítání a
odčítání času
3) http://resources.woodlands-junior.kent.sch.uk/maths/measures.htm
- hry s časem online
4) http://www.maths-games.org/time-games.html - hry s časem pro
děti
5) http://www.teachingideas.co.uk/maths/contents_time.htm pracovní sešity pro děti na téma čas
6) http://www.bbc.co.uk/bitesize/ks3/maths/measures/time/revision/
1/ - vysvětlení času, pracovní listy a testy
7) http://www.mathgametime.com/ - matematické hry dle třídy
8) http://www.easysurf.cc/tmadd.htm - matematický převodník
9) https://www.learningplace.com.au/deliver/content.asp?pid=49526 –
způsoby měření času
10) http://topics.nytimes.com/topics/news/science/topics/mathematics
/index.html - novinky ze světa matematiky
11) http://nrich.maths.org/6070 - historie měření času
12) http://www.youtube.com/watch?v=UK9NTS1FZbk – historie času –
video
13) http://www.time-for-time.com/clocks.htm - typy hodin
14) http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Time_1.html
Geometry – dictionary and phrases
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
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
Discussion
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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
1.
2.
3.
4.
5.
6.
7.
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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ČTVEREC
OBDÉLNÍK
TROJÚHELNÍK
KOULE
KRUH
BOD
LINKA
HYPERBOLA
KRYCHLE
VÁLEC
_________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________
Match the formula with the correct shape
1.
2.
3.
4.
5.
6.
SQUARE
TRIANGLE
RECTANGLE
CIRCLE
ELLIPSE
TRAPEZOID
A) ½ (b x h)
B) ½ h (a x b)
C) a x b
D) πxr1 x r2
E) a2
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.
Try to match the definitions
1.
2.
POINT
LINE
3.
PARALEL LINES
4.
5.
RIGHT ANGLE
ACUTE ANGLE
6.
7.
8.
OBTUSE ANGLE
RADIUS
DIAMETER
a) An angle that measures less than 90°
b) Line segements that never intersect (they are always the
same distance apart)
c) Distance (line segment) from center of a circle to any
point on that circle's circumference.
d) A location in space - a dot on a piece of paper
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)
f) An angle that measures more than 90°
g) An angle that measures 90°
h) Connects two points via the shortest path and continues
indefintely (forever) in both directions
TRUE or FALSE
1.
2.
3.
4.
5.
6.
7.
8.
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.
Geometry - links
1) http://www.mathsisfun.com/geometry/ - vysvětlení geometrie pro
děti
2) http://www.aaamath.com/geo.htm - jednoduchá vysvětlení a
aktivity
3) http://www.freemathhelp.com/geometry.html - matematický
rozcestník
4) http://gogeometry.com/geometry/geometry_for_children_index.ht
ml - geometrie - vysvětlení, obrázky
5) http://www.kidsmathgamesonline.com/geometry.html geometrické hry pro děti
6) http://www.youtube.com/watch?v=15likNwNMjk – základní
geometrie – video
7) http://www.math.com/tables/geometry/ - geometrické vzorce
8) http://www.basic-mathematics.com/common-geometry-
formulas.html - matematické problémy a vzorce
9) http://www.geom.uiuc.edu/docs/reference/CRC-formulas/ geometrická fakta a vysvětlení
10) http://www.mathguru.com/result/practical-geometry.aspx praktická geometrie
11) http://cbse.meritnation.com/cbse-math/practicalgeometry/1/14/ncertsolutions.html - matematický rozcestník a
cvičení
12) http://vignonoussa.wordpress.com/modern-geometries-math-325/ -
Equations- dictionary and phrases
A
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
Discussion
1.
2.
3.
4.
5.
6.
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?
1.
2.
3.
4.
x + 2 = 17 – 4x
6 + 10n – 4n = n + 1
10 – 8x = -2x + 4x
-7p – 10 = -8p – 4p
_______________________________________________
_______________________________________________
_______________________________________________
_______________________________________________
5.
6.
7.
8.
| 3+k | = 8
|k–5|=0
|1+v|=4
|t+5|=6
_______________________________________________
_______________________________________________
_______________________________________________
_______________________________________________
9.
15 – w = 22
6
10. 30 = 10 + 4m
3
_______________________________________________
_______________________________________________
Can you find the correct answer?
1.
2.
3.
4.
5.
6.
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)
________________________________________________________
Can you solve these mathematical problems?
1.
2.
3.
4.
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
Equations - links
1) http://en.wikipedia.org/wiki/Equation - základní informace o
rovnicích a druzích rovnic
2) http://www.mathsisfun.com/algebra/equation-formula.html -
vysvětlení rovnic pro děti
3) http://www.aaamath.com/equ.htm - úvod do rovnic, příklady a
vysvětlení
4) http://www.purplemath.com/modules/solveabs.htm - řešení rovnic video
5) http://www.youtube.com/watch?v=Bqn8p3f7p1Y – úvod do rovnic,
video pro děti
6) http://algebra4children.com/examples_simultaneous_equation_sub
stitution.html - pracovní sešity a aktivity pro děti
7) http://www.mathworksheets4kids.com/equations/one-step.html pracovní aktivity pro děti – rovnice
8) http://www.algebra4children.com/printables.html - procvičení
rovnic, různá obtížnost
9) http://www.superteacherworksheets.com/equations.html - velký
rozcestník matematických materiálů
10) http://www.files.chem.vt.edu/RVGS/ACT/notes/Types_of_Equations.
html - zajímavá fakta o rovnicích
11) http://www.businessinsider.com/the-17-equations-that-changedthe-world-2012-7?op=1 – 17 nejdůležitějších rovnic
Famous mathematicians - dictionary and phrases
A
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
ISAAC NEWTON
1.
2.
3.
4.
5.
6.
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
1.
2.
3.
4.
5.
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
1.
2.
3.
4.
5.
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?
CARL GAUSS
1.
2.
3.
4.
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
1. Who was he?
2. What has his field of interest?
3. He wrote the „Law of continuity“. What is it?
4. 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?
5. He was one of those who invented the binary
number system – where is it used and why was
this invention important?
PIERRE SIMON LAPLACE
1.
2.
3.
4.
5.
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?
Famous matematicians - links
1) http://fabpedigree.com/james/mathmen.htm - 30 největších
matematiků
2) http://www.kidsmathgamesonline.com/facts/famousmathematician
s.html - známí matematikové
3) http://listverse.com/2010/12/07/top-10-greatest-mathematicians/ 10 nejznámějších matematiků včetně moderních
4) http://www.gradeamathhelp.com/famous-math-people.html matematici a jejich vynálezy a názory
5) http://www.biography.com/people/groups/academics/mathematicia
ns - seznam matematiků a rozcestník na jejich stránky
6) http://www.agnesscott.edu/lriddle/women/alpha.htm - ženy v
matematice a informace o nich
7) http://www.kidsmathgamesonline.com/pictures/mathematicians.ht
ml - obrázky známých matematiků
8) http://www.buzzle.com/articles/famous-mathematicians.html matematici dle národnosti
9) http://www.dmoz.org/Kids_and_Teens/School_Time/Math/Mathem
aticians/ - matematický rozcestník, kvízy a testy
10) http://www.funtrivia.com/trivia-quiz/People/FamousMathematicians-114462.html - kvíz (matematici)
11) http://www.quia.com/quiz/104806.html - kvíz pro děti
Graphs and charts - dictionary and phrases
A
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
Discussion
1.
2.
3.
4.
5.
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.
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
____________
Can you answer these questions?
1.
Can you draw an example of a.........?
HISTOGRAM
BAR CHART
PIE CHART
LINE CHART
2.
3.
4.
5.
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
6.
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.
7.
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?
8.
9.
Graphs and charts - links
1) http://math.pppst.com/graphs.html - grafy pro děti a učitele
2) http://nces.ed.gov/nceskids/createagraph/ - vytvoř si vlastní graf
3) http://mathworld.wolfram.com/Graph.html - grafy, matematický
rozcestník
4) http://www.youtube.com/watch?v=HmQR8Xy9DeM – druhy grafů,
video
5) http://www.amathsdictionaryforkids.com/mathsCharts.html statistika a grafy pro děti (moc hezké)
6) http://www.bbc.co.uk/bitesize/standard/maths_i/relationships/data
_graphs/revision/1/ - typy grafů
7) http://www.turtlediary.com/kids-games/math-topics/graphsgames.html - matematické hry pro školní děti
8) http://www.readingrockets.org/article/43814/ - jak stvořit graf
9) http://homeschooling.about.com/od/chartsandgraphs/Understandin
g_Charts_and_Graphs.htm - jak učit děti grafy
10) http://library.thinkquest.org/20991/alg2/graphs.html - složitější
matemetické grafy a funkce
11) http://www.khanacademy.org/math/trigonometry/functions_and_g
raphs/function_introduction/v/functions-as-graphs - video matematické funkce
12) http://www.cliffsnotes.com/math/statistics/graphic-displays/quizpie-chart - matematické kvízy
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?
Kdo vyhrál?
Kolik je hodin?
Je pozdě.
Je brzy.
Má moc práce.
Kolik to stojí?
Máte drobné?
Kolik vám dlužím?
Je to drahé.
Je to levné.
Kde je směnárna?
Máte eura?
Kolik je poplatek?
Kolik chcete kil?
Kolik stojí kilo?
Kolik vody mám přidat?
Kolik to váží?
Kolik si toho mám vzít?
Jak často si to mámn brát?
Jaké je počasí?
Jak rychle jedete?
Jak často jezdíte?
How long does it take?
Who won?
What´s the time?
It´s late.
It´s (too) soon.
He´s busy.
How much is it?
Do you have change?
How much do I owe you?
It´s expensive.
It´s cheap.
Where is the exchange office?
Do you have euros?
How much is the free/charge?
How many kilos do you want?
How much is one kilo?
How much water shall I add?
How much does it weigh?
How much shall I take?
How often shall I take it?
What is the weather like?
How fast do you go?
How often do you know?
SPORTS
1.
2.
3.
4.
5.
6.
7.
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
1. What does it mean to come late?
2. What can you do not to come late?
3. What is a delay?
4. What means of transport do you know and which one is the most reliable?
5. What can go wrong when it comes to different kinds of transport?
6. Can you compare prices of various means of transport?
7. What are emissions? What do they consist of?
8. What can you use maths for during your holiday?
TIME
1. Why do people need to learn to tell the time?
2. What would happen if people didn´t have any watches?
3. Do you think that our lives are faster than they used to be? Why?
4. Why does 5min sometimes seem so long and sometimes so short?
5. Do you always come on time?
6. How do you feel when you are late?
7. What do you think about people who come late?
8. What is a timetable?
9. What is a schedule?
10. Do you carefully plan your days?
SHOPPING
1. Do you like shopping?
2. How often do you go shopping?
3. How much do you usually spend?
4. Is living in the Czech Republic getting more and more expensive? Why?
5. Can you buy everything you want?
6. Do you think some people buy more than they need?
7. Should we plan our shopping?
8. How should we plan our budget?
EXCHANGE OFFICE
1.
2.
3.
4.
5.
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
1. Do we need maths in the kitchen? When?
2. What gadgets help us with measuring in the kitchen?
3. Why do I need to know exact numbers in the kitchen?
MEDICINE
1. What would happen if people didn´t use maths when it comes to mediation?
2. What forms of medication do you know?
3. What is a „dose“?
4. What does it mean to overdose someone?
5. Do you remember any case when someone overdosed other people on purpose?
CALENDAR
1. What is a calendar? What is it good for?
2. Is there only one kind of calendar in the world?
3. What kinds of calendar do you know?
4. Which month and season are your favourite any why?
REPETITION
1. Is there anything that you do EVERY day?
2. What do you do only ONCE a week?
3. How OFTEN do you go on holiday?
4. What would you NEVER do and why?
5. Have you EVER tried any adrenalin sport?
6. Is there any food that you have ALWAYS wanted to try?
7. How OFTEN do you cook?
8. How many times have you moved in your life?
9. How many times have you been abroad?
10. How many times have you tasted something really discusting?
11. Have you EVER seen any accident?
12. Have you EVER been to a bank abroad?
Maths around us - links
1) http://www.slideshare.net/kpunu2076/maths-in-daily-life matematika v našem životě – prezentace
2) http://pinterest.com/karenpinto/math-all-around-us/ - matematika
okolo nás – obrázky a vysvětlení
3) http://www.missmaggie.org/scholastic/roundtheworld_eng_launche
r.html - hra - kolem světa za 80sekund
4) http://mrnussbaum.com/aroundtheworld/ - online matematická hra
5) http://www.creativetallis.com/how-maths-is-taught-across-theworld.html - přístup k výuce matematiky ve světě
6) http://asiasociety.org/education/resources-schools/professionallearning/understanding-world-through-math - matematika vs. svět
kolem nás
7) http://www.youtube.com/watch?v=AYIQYZuQNMw – videa –
matematika a my
8) http://www.educationworld.com/a_curr/archives/math.shtml finanční povědomí
9) http://www.slideshare.net/mrsd8/math-is-all-around-us-8728078 prezentace - matematiky kolem nás
10) http://www.powershow.com/view1/1583e2MmFlY/Math_is_All_Around_Us_powerpoint_ppt_presentation prezentace - nejen matematické
11) https://sites.google.com/site/merit0910annettejuanita/activities -
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
BASIC MATHEMATICS
Can you explain these terms? Can you give an example as well?
1.
ELEMENT
______________________________________________
2.
CONJUNCTION
______________________________________________
3.
EQUIVALENCE
______________________________________________
4.
DEFINITION
______________________________________________
5.
PROOF
______________________________________________
6.
NATURAL NUMBERS ______________________________________________
7.
RATIONAL NUMBER ______________________________________________
8.
IRRATIONAL NUMBERS ____________________________________________
9.
NUMERIC FIELD
______________________________________________
10. SECOND AND THIRD SQUARE ROOT __________________________________
11. ESTIMATION
______________________________________________
12. ROUNDING
______________________________________________
13. RESULT
______________________________________________
14. PRIME NUMBERS
______________________________________________
15. ARITHMETIC
______________________________________________
QUESTIONS and ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
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?
Discussion
1.
2.
3.
4.
5.
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?
8. What is the differential calculus?
9. What is the integral calculus?
10. Can you draw and example of a matrix?
11. Can you give an example of a decimal number?
12. Can you write a few fractions and read them aloud?
13. What is a percentage? What is it good for?
14. What is probability?
15. Make a definition of one mathematical term and let the others guess what it is...
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
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 1step equation.
Give an
example of a 2step 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.
MEASUREM
ENT
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
BIG PRESENTATION
1.
Each student chooses one mathematical field and everyone gets time to
prepare the presentation.
2.
The presentation will contain:
a) explanation
b) practical use
c) a few example and exercises
Quess the word
1.
ALGORITHM
A) the branch of mathematics that deals with the logic and
consistency of mathematical proofs, formulas, and
equations.
2. ANALOGISM
B) the doctrines taught by Pythagoras
3. 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
4. GEOMETRY
D) any methodology for solving a certain kind of problem
5. METAMATHEMATICS E) the branch of algebra that deals with quadratic
equations
6. PLANIMETRY
F) a system or method of calculation
7. PYTHAGORISM
G) the study of the properties of geometric figures
8. QUADRATICS
H) measurement of plane areas
9. TOPOLOGY
I) the construction of a proportion
10. TRIGONOMETRY
J) the mathematics of the properties, measurement, and
relationships of points, lines, angles, surfaces, and solids
Famous maths quotes... what do you think about them?
1.
2.
3.
4.
5.
6.
7.
8.
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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
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?
Online games and quizes – links
1) http://www.mathplayground.com/games.html
2) http://www.maths-games.org/
3) http://www.primarygames.com/math.php
4) http://www.coolmath4kids.com/
5) http://www.mathsisfun.com/games/
6) http://www.hoodamath.com/
7) http://www.learninggamesforkids.com/math_games.html
8) http://www.coolmath-games.com/
9) http://mathematics.goodgame.co.in/
10) http://www.sheppardsoftware.com/math.htm
11) http://www.softschools.com/math/
12) http://www.multiplication.com/games
13) http://www.bbc.co.uk/bitesize/ks1/maths/
14) http://www.sumdog.com/
15) http://www.fun4thebrain.com/mult.html
16) http://www.aaamath.com/
17) http://www.kidzone.ws/math/ - pracovní sešity
18) http://edhelper.com/math.htm - pracovní sešity
19) http://www.kidslearningstation.com/math/ - pracovní sešity
20) http://math.about.com/od/worksheets/Math_worksheets_printable
s_Black_line_masters.htm - pracovní sešity
21) http://www.mathfactcafe.com/home/ - pracovní sešity