Materials for language lessons

Archive for September, 2013

Medieval brain teasers

I have found these medieval brain teasers on pedagonet, maybe you will like them, too:
 
 
The Amulet
.

A strange man was one day found loitering in the courtyard of the castle, and the retainers, noticing that his speech had a foreign accent, suspected him of being a spy.

So the fellow was brought before Sir Hugh, who could make nothing of him. 

He ordered the varlet to be removed and examined, in order to discover whether any secret letters were concealed about him. 

All they found was a piece of parchment securely suspended from the neck, bearing this mysterious inscription:

To-day we know that Abracadabra was the supreme deity of the Assyrians, and this curious arrangement of the letters of the word was commonly worn in Europe as an amulet or charm against diseases. 

But Sir Hugh had never heard of it, and, regarding the document rather seriously, he sent for a learned priest.
“I pray you, Sir Clerk,” said he, “show me the true intent of this strange writing.”

“Sir Hugh,” replied the holy man, after he had spoken in a foreign tongue with the stranger, “it is but an amulet that this poor wight doth wear upon his breast to ward off the ague, the toothache, and such other afflictions of the body.”

“Then give the varlet food and raiment and set him on his way,” said Sir Hugh.
“Meanwhile, Sir Clerk, canst thou tell me in how many ways this word ‘Abracadabra’ may be read on the amulet, always starting from the A at the top thereof?”

Place your pencil on the A at the top and count in how many different ways you can trace out the word downwards, always passing from a letter to an adjoining one.

The Amulet
Answer
The puzzle was to place your pencil on the A at the top of the amulet and count in how many different ways you could trace out the word “Abracadabra” downwards, always passing from a letter to an adjoining one.

“Now, mark ye, fine fellows,” said Sir Hugh to some who had besought him to explain, “that at the very first start there be two ways open: whichever B ye select, there will be two several ways of proceeding (twice times two are four); whichever R ye select, there be two ways of going on (twice times four are eight); and so on until the end. 

Each letter in order from A downwards may so be reached in 2, 4, 8, 16, 32, etc., ways. 

Therefore, as there be ten lines or steps in all from A to the bottom, all ye need do is to multiply ten 2’s together, and truly the result,1024, is the answer thou dost seek.”

 

The Four Princes

The dominions of a certain Eastern monarch formed a perfectly square tract of country.
It happened that the king one day discovered that his four sons were not only plotting against each other, but were in secret rebellion against himself. After consulting with his advisers he decided not to exile the princes, but to confine them to the four corners of the country, where each should be given a triangular territory of equal area, beyond the boundaries of which they would pass at the costof their lives.Now, the royal surveyor found himself confronted by great natural difficulties, owing to the wild character of the country.
The result was that while each was given exactly the same area, the four triangular districts were all of different shapes, somewhat in the manner shown in the illustration.

The puzzle is to give the three measurements for each of the four districts in the smallest possible numbers—all whole furlongs.
In other words, it is required to find (in the smallest possible numbers) four rational right-angled triangles of equal area.

The Four Princes
Answer :When Montucla, in his edition of Ozanam’s Recreations in Mathematics, declared that “No more than three right-angled triangles, equal to each other, can be found in whole numbers, but we may find as many as we choose in fractions,” he curiously overlooked the obvious fact that if you give all your sides a common denominator and then cancel that denominator you have the required answer in integers!Every reader should know that if we take any two numbers, m and n, then m2 + n2m2 – n2, and 2mn will be the three sides of a rational right-angled triangle.
Here m and n are called generating numbers.
To form three such triangles of equal area, we use the following simple formula, where m is the greater number:

mn + m2 + n2 = a
m2 – n2 = b
2mn + n2 = c

Now, if we form three triangles from the following pairs of generators, a and ba and ca and b + c, they will all be of equal area. This is the little problem respecting which Lewis Carroll says in his diary (see his Life and Letters by Collingwood, p. 343), “Sat up last night till 4 a.m., over a tempting problem, sent me from New York, ‘to find three equal rational-sided right-angled triangles.’ I found two … but could not find three!”

The following is a subtle formula by means of which we may always find a R.A.T. equal in area to any given R.A.T.
Let z = hypotenuse, b = base, h = height, a = area of the given triangle; then all we have to do is to form a R.A.T. from the generators z2 and 4a, and give each side the denominator 2z (b2 – h2), and we get the required answer in fractions.
If we multiply all three sides of the original triangle by the denominator, we shall get at once a solution in whole numbers.

The answer to our puzzle in smallest possible numbers is as follows:

First Prince 518 1320 1418
Second Prince 280 2442 2458
Third Prince 231 2960 2969
Fourth Prince 111 6160 6161

The area in every case is 341,880 square furlongs.
I must here refrain from showing fully how I get these figures. I will explain, however, that the first three triangles are obtained, in the manner shown, from the numbers 3 and 4, which give the generators 37, 7; 37, 33; 37, 40.
These three pairs of numbers solve the indeterminate equation, a3b – b3a = 341,880.
If we can find another pair of values, the thing is done. These values are 56, 55, which generators give the last triangle.
The next best answer that I have found is derived from 5 and 6, which give the generators 91, 11; 91, 85; 91, 96.
The fourth pair of values is 63, 42.

The reader will understand from what I have written above that there is no limit to the number of rational-sided R.A.T.’s of equal area that may be found in whole numbers.

The Crescent and the Cross

When Sir Hugh’s kinsman, Sir John de Collingham, came back from the Holy Land, he brought with him a flag bearing the sign of a crescent, as shown in the illustration.
It was noticed that De Fortibus spent much time in examining this crescent and comparing it with the cross borne by the Crusaders on their own banners.One day, in the presence of a goodly company, he made the following striking announcement:

“I have thought much of late, friends and masters, of the conversion of the crescent to the cross, and this has led me to the finding of matters at which I marvel greatly, for that which I shall now make known is mystical and deep.

Truly it was shown to me in a dream that this crescent of the enemy may be exactly converted into the cross of our own banner. Herein is a sign that bodes good for our wars in the Holy Land.”

Sir Hugh de Fortibus then explained that the crescent in one banner might be cut into pieces that would exactly form the perfect cross in the other.

It is certainly rather curious; and I show how the conversion from crescent to cross may be made in ten pieces, using every part of the crescent.
The flag was alike on both sides, so pieces may be turned over where required.

The Crescent and The Cross
Answer :”By the toes of St. Moden,” exclaimed Sir Hugh de Fortibus when this puzzle was brought up, “my poor wit hath never shaped a more cunning artifice or any more bewitching to look upon.
It came to me as in a vision, and ofttimes have I marvelled at the thing, seeing its exceeding difficulty.
My masters and kinsmen, it is done in this wise.”

The worthy knight then pointed out that the crescent was of a particular and somewhat irregular form—the two distances a to b andc to d being straight lines, and the arcs ac and bd being precisely similar.
He showed that if the cuts be made as in Figure 1, the four pieces will fit together and form a perfect square, as shown in Figure 2, if we there only regard the three curved lines.
By now making the straight cuts also shown in Figure 2, we get the ten pieces that fit together, as in Figure 3, and form a perfectly symmetrical Greek cross.
The proportions of the crescent and cross in the original illustration were correct, and the solution can be demonstrated to be absolutely exact and not merely approximate.

I have a solution in considerably fewer pieces, but it is far more difficult to understand than the above method, in which the problem is simplified by introducing the intermediate square

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Kids’ songs 3.

Six Little Ducks

letöltés (2)

Six little ducks
That I once knew
Short ones, fat ones,
Skinny ones, too.

But the one little duck
With the feather on his back
He ruled the others
With his quack, quack, quack

Down to the river
They would go
A wibble wobble wibble wobble
To and fro
But the one little duck
With the feather on his back
He ruled the others
With his quack, quack, quack.

Into the water they would dive
The little one first and then the other five
But the one little duck
With the feather on his back
He ruled the others
With his quack, quack, quack.

Out of the river they would go
A wibble wobble wibble wobble
To and fro
But the one little duck
With the feather on his back
He ruled the others
With his quack, quack, quack

Twinkle, Twinkle, Little Star

Twinkle, twinkle, little star,
How I wonder what you are!
Up above the world so high,
Like a diamond in the sky.
Twinkle, twinkle, little star,
How I wonder what you are!

letöltés (3)

This Old Man

This old man, he played one,
He played knick-knack on my thumb.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played two,
He played knick-knack on my shoe.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played three,
He played knick-knack on my knee.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played four,
He played knick-knack on my door.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played five,
He played knick-knack on my hive.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played six,
He played knick-knack on my sticks.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played seven,
He played knick-knack up in heaven.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played eight,
He played knick-knack on my gate.
With a knick-knack, paddy whack,
Give a dog a bone,
This old man came rolling home.

This old man, he played nine.
He played knick-knack on my spine.
With a knick-knack, paddy whack,
Give a dog a bone.
This old man came rolling home.

This old man, he played ten.
He played knick-knack once again.
With a knick-knack, paddy whack,
Give a dog a bone.
This old man came rolling home.

Kids’ songs 2.

If You’re Happy And You Know It

If you’re happy and you know it clap your hands. (clap clap)
If you’re happy and you know it clap your hands. (clap clap)
If you’re happy and you know it then your face will surely show it.
If you’re happy and you know it clap your hands. (clap clap)

If you’re happy and you know it stomp your feet. (stomp stomp)
If you’re happy and you know it stomp your feet. (stomp stomp)
If you’re happy and you know it then your face will surely show it.
If you’re happy and you know it stomp your feet. (stomp stomp)

If you’re happy and you know it nod your head. (nod nod)
If you’re happy and you know it nod your head. (nod nod)
If you’re happy and you know it then your face will surely show it.
If you’re happy and you know it nod your head. (nod nod)

If you’re happy and you know it shout “Hooray!” (Hoo-Ray!)
If you’re happy and you know it shout “Hooray!” (Hoo-Ray!)
If you’re happy and you know it then your face will surely show it.
If you’re happy and you know it shout “Hooray!” (Hoo-Ray!)

If you’re happy and you know it do all four. (clap stomp nod Hoo-Ray!)
If you’re happy and you know it do all four. (clap stomp nod Hoo-Ray!)
If you’re happy and you know it then your face will surely show it.
If you’re happy and you know it do all four. (clap stomp nod Hoo-Ray!)

I’m a Little Teapot

I’m a little teapot
Short and stout
Here’s my handle
Here’s my spout

When I get all steamed up
Hear me shout
“Tip me over
and pour me out!”

Itsy Bitsy Spider

The itsy bitsy spider
Climbed up the waterspout

Down came the rain
And washed the spider out.

Out came the sun
And dried up all the rain

So the itsy-bitsy spider
Climbed up the spout again!

London Bridge Is Falling Down

London Bridge is falling down,
Falling down, falling down.
London Bridge is falling down,
My fair lady.

Build it up with iron bars,
Iron bars, iron bars,
Build it up with iron bars,
My fair lady.

Iron bars will bend and break,
Bend and break, bend and break,
Iron bars will bend and break,
My fair lady.

Build it up with gold and silver,
Gold and silver, gold and silver,
Build it up with gold and silver,
My fair lady.

letöltés (1)

Old MacDonald Had A Farm

Old MacDonald had a farm, E I E I O,
And on his farm he had some chicks, E I E I O.
With a chick chick here
and a chick chick there,
Here a chick, there a chick,
everywhere a chick chick.
Old MacDonald had a farm, E I E I O.

Old MacDonald had a farm, E I E I O,
And on his farm he had a cow, E I E I O.
With a moo moo here
and a moo moo there,
Here a moo, there a moo,
everywhere a moo moo.
Old MacDonald had a farm, E I E I O.

Old MacDonald had a farm, E I E I O,
And on his farm he had a pig, E I E I O.
With an oink oink here
and an oink oink there,
Here an oink, there an oink,
everywhere an oink oink.
Old MacDonald had a farm, E I E I O.

Old MacDonald had a farm, E I E I O,
And on his farm he had some geese, E I E I O.
With a honk honk here
and a honk honk there,
Here a honk, there a honk,
everywhere a honk honk.
Old MacDonald had a farm, E I E I O.

Old MacDonald had a farm, E I E I O,
And on his farm he had a horse, E I E I O.
With a neh neh here
and a neh neh there,
Here a neh, there a neh,
everywhere a neh neh.
Old MacDonald had a farm, E I E I O.

Old MacDonald had a farm, E I E I O,
And on his farm he had a mule, E I E I O.
With a hee haw here
and a hee haw there,
Here a hee, there a hee,
everywhere a hee haw.
Old MacDonald had a farm, E I E I O.

Old MacDonald had a farm, E I E I O,
And on his farm he had a duck, E I E I O.
With a quack quack here
and a quack quack there,
Here a quack, there a quack,
everywhere a quack quack.
Old MacDonald had a farm, E I E I O.

Kids’ songs

Animal Fair

I went to the animal fair,
The birds and the beasts were there,
The big baboon by the light of the moon
Was combing his auburn hair.
The monkey bumped the skunk,
And sat on the elephant’s trunk;
The elephant sneezed and fell to his knees,
And that was the end of the monk!
The monk!

images

Brother John

Are you sleeping,
Are you sleeping?
Brother John,
Brother John?
Morning bells are ringing,
Morning bells are ringing.
Ding Ding Dong,
Ding Ding Dong.

Five Little Monkeys

Five little monkeys jumping on the bed,
One fell off and bumped his head.
Mama called the Doctor and the Doctor said,
“No more monkeys jumping on the bed!”

Four little monkeys jumping on the bed,
One fell off and bumped her head.
Papa called the Doctor and the Doctor said,
“No more monkeys jumping on the bed!”

Three little monkeys jumping on the bed,
One fell off and bumped his head.
Mama called the Doctor and the Doctor said,
“No more monkeys jumping on the bed!”

Two little monkeys jumping on the bed,
One fell off and bumped her head.
Papa called the Doctor and the Doctor said,
“No more monkeys jumping on the bed!”

One little monkey jumping on the bed,
He fell off and bumped his head.
Mama called the Doctor and the Doctor said,
“Put those monkeys straight to bed!”

letöltés

Hickory Dickory Dock

Hickory dickory dock,
The mouse ran up the clock.
The clock struck one,
The mouse ran down,
Hickory dickory dock.

Riddles

If our students speak English well, we can give them some more difficult riddles as well:

1, If you break me
I do not stop working,
If you touch me
I may be snared,
If you lose me
Nothing will matter.

2, My life can be measured in hours,
I serve by being devoured.
Thin, I am quick
Fat, I am slow
Wind is my foe.

gyertya

3, You heard me before,
Yet you hear me again,
Then I die,
‘Till you call me again.

4, I build up castles.
I tear down mountains.
I make some men blind,
I help others to see.
What am I?

5, Soft and fragile is my skin
I get my growth in mud
I’m dangerous as much as pretty
For if not careful, I draw blood.

6, It cannot be seen, it cannot be felt,
Cannot be heard, cannot be smelt,
Lies behind stars and under hills,
And empty holes it fills.
Comes first follows after,
Ends life kills laughter.

7, If you have it, you want to share it.
If you share it, you don’t have it.
What is it?

Solutions:

1, heart, 2, candle, 3, echo, 4, sand, 5, thorn, 6, darkness, 7, secret

Irregular verbs

base past past participle
cut cut cut
fit fit fit
hit hit hit
let let let
put put put
quit quit quit
set set set
shut shut shut
split split split
upset upset upset
burst burst burst
cast cast cast
cost cost cost
hurt hurt hurt
spread spread spread
knit knit/knitted knit/knitted
sit sat sat
spit spat/spit spat/spit
begin began begun
swim swam swum
ring rang rung
sing sang sung
spring sprang sprung
cling clung clung
fling flung flung
sling slung slung
sting stung stung
swing swung swung
wring wrung wrung
hang hung/hanged** hung/hanged
drink drank drunk
shrink shrank shrunk
stink stank stunk
think thought thought
bring brought brought
buy bought bought
seek sought sought
fight fought fought
catch caught caught
teach taught taught
creep crept crept
keep kept kept
sleep slept slept
sweep swept swept
weep wept wept
bleed bled bled
breed bred bred
feed fed fed
flee fled fled
lead led led
speed sped/speeded sped/speeded
meet met met
bend bent bent
lend lent lent
send sent sent
spend spent spent
deal dealt dealt
feel felt felt
kneel knelt knelt
dream dreamt/dreamed dreamt/dreamed
mean meant meant
spill spilt/spilled spilt/spilled
build built built
burn burnt/burned burnt/burned
hold held held
sell sold sold
tell told told
find found found
grind ground ground
wind wound wound
break broke broken
choose chose chosen
freeze froze frozen
speak spoke spoken
steal stole stolen
wake woke woken
weave wove woven
arise arose arisen
drive drove driven
ride rode ridden
rise rose risen
write wrote written

Idioms

 DSC_1021

Here you can find some idioms and their meanings:

Achilles’ heel A metaphor for a fatal weakness in spite of overall strength.
All ears Listening intently; fully focused or awaiting an explanation.
Barking up the wrong tree Looking in the wrong place.
A bitter pill A situation or information that is unpleasant but must be accepted.
A dime a dozen Anything that is common, inexpensive, and easy to get or available any where.
Ace in the hole A hidden or secret strength, or unrevealed advantage.
Beat around the bush To treat a topic, but omit its main points, often intentionally or To delay or avoid talking about something difficult or unpleasant.
Bite the dust Euphemism for dying or death.
Call it a day To declare the end of a task.
Cat nap Short sleep.
Fit as a fiddle In good physical health.
For a song Almost free. Very cheap.
From A to Z Covering a complete range; comprehensively.
Hit the road ” To leave.
Hit the sack ”/sheets/hay To go to bed.
Let the cat out of the bag ” To reveal a secret.
Kick the bucket Euphenism for dying or death.
Piece of cake ” A job, task or other activity that is pleasant – or, by extension, easy or simple.
Pull somebody’s leg To tease or to joke by telling a lie.
Spill the beans Reveal someone’s secret.
Through thick and thin Both good and bad times.
Under the weather Feel sick or poorly

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