FRAGMENTS FROM THIS BOOK ABOUT
Kindness in Mathematics: page 1 of 6
School Subjects can be FUN with a correct approach!
Stories from Part 3: Addition and Subtraction
WHY WE NEED TO ADD?
A little frog was born in a bog. When it began to rain, she started quacking merrily : ‘Quack-quack-quack, what lovely rain!'
And when the sun came out again, the little frog quacked :
‘Quack-quack-quack, hello lovely sun!'
‘Be quiet. This is a bog and there's nothing lovely here . You'd do better to hide in the slime and not let anyone see you,' the older frogs shouted at the little frog.
The frog didn't want to be quiet, so she left the bog . She hopped merrily around the meadow, and soon the young frog bumped into some very strange creatures.
‘Hello, are you big meadow frogs?' the traveller asked boldly.
‘No, we're not frogs at all – we're numbers . We come to the meadow every day to count and add up all the lovely things.'
‘I don't understand what you mean,' the young frog replied timidly.
‘Counting and adding up means finding out how many good things there are all around you. You start with one, and add one each time. Look, I put one apple into my basket. Then I added another one to it. 1+1=2 , so I have two apples,' the Number Two explained.
‘I was born in a bog, but there was nothing lovely there,' the frog sighed.
‘There are lovely things everywhere. Have a look, yesterday there were two buds growing on this bush.
Today there's another one. So there are now three flowers in total, because 2+1=3 ,' Number Three explained.
The happy little frog started to hop around the meadow after the numbers, counting: ‘Quack-quack-quack. First there were three bees, and then another one flew up. 3+1=4 : quack-quack-quack-quack – four little bees.'
‘You see how much fun life can be when you know how to count,' the numbers said to the frog, and she hopped off home.
From that day onwards, the little frog's life completely changed. In spring, she counted her frogspawn: quack-quack-quack – three tadpoles will grow in the meadow, among the reeds, and another three under the water lilies. 3+3=6 , so I'll have 6 new tadpoles in total.'
Surprisingly, all of the happy frog's babies could count and add up from the moment they were born, and from dawn till dusk, a merry ‘quack-quack-quack' rang out above the bog .
Questions and tasks :
- Why do some people count all the good things in life, whereas others count the bad things?
- Say lots of kind things to your friends and family . Find a way of adding them up, and find out how many kind words you have said.
- Try to do as many kind things as possible . Find a way of adding them up, and calculate how many kind things you do in a day .
WHO IS MORE GENEROUS?
One rich Khan has accumulated ten thousand gold coins. From this sum he took one hundred coins to feed all hungry people in his area. His cooks begun to prepare a tasty dish from rice and meat, while the khan's servants went to invite poor men for this lunch. On the way these servants met in the forest one poor woodcutter and ordered him to come for the khan's feast.
"The generosity of our Khan is boundless," servants have told.
"Thanks, but I used to live by my own work," the poor man answered.
Servants become angry, seized the woodcutter and have led him to their khan.
"Today I spent ten gold coins and with this money I managed to feed more
than one thousand persons, and what great deeds did you do?" the Khan
proudly asked the poor woodcutter.
"Well, today I have earned only four copper coins and on this money I was
able to feed only four persons, this is what I've done. I fed my wife,
myself and two sick old men, my neighbours," modestly answered the
At these words the Khan's face changed. "Who is more generous: me or this
woodcutter?" thought the Khan to himself.
Questions and tasks to the fairy tale on Kindness in Mathematics:
- What part of the money was spent on the people by the Khan, and what part – by the woodcutter? Try to compare it.
- What do you think, who is more generous, the Khan or the woodcutter?
- Imagine, that you have six sandwiches. What part of the whole amount will you give to your hungry friend, your hungry brother or sister, and to a hungry dog?
HEIGHT OF THE DATE PALM TREES
(moral entertaining story about proportions -
from the book "Kindness in Mathematics")
The lonely traveller was crossing the desert. All food supplies that he took with him had finished (come to an end, and he only could hope for a miracle
that could save him. Then, in a short while he seemed to notice a tiny oasis
ahead. The young man thought restlessly: whether "the owner would be so kind
to give him some water and a handful of dates?"
His fears appeared to be totally vain. The owner happily opened a gate
before him: "Welcome, welcome. Please come in! Any traveller is my respected
guest. Pity that I don't have anything to offer you".
The young man's glance fell at a palm tree near the hut. Its heavy branches
bent under the weight of ripe dates. The owner of the oasis, having caught
the traveller's sight, explained: "When I came to this oasis, here was nothing
except for this palm tree, and I often had to starve. Just imagine, how long
I waited, for the dates to ripen. Every day they were becoming more
and more sweeter so that I, at last, forgot about the famine.
Just at that time three travellers appeared in front of my door.
"They will eat my dates," thought I in a fright and decided not to let them
come into my oasis.
Next morning I noticed the palm tree became higher - so high that I
could not get the dates. Having become angry, I knocked its trunk with my stick,
hoping that the dates will fall on the ground. Suddenly to my amazement I
heard a roaring terrible voice: "You will be punished. I, the spirit of this
tree, shall allow you to eat my fruits only when the height of this palm
tree in meters will be equal to the quantity of the years lived by you in the
"Thus, I live here for ten years already, but I never tried any of these
"The moment when they ripen, birds arrive and carry all dates away. Now the
palm tree became so high, that nobody can get on it to measure its
"It is possible to measure the height of a palm tree without getting
on it," grinned the young man.
"Yes, it might be possible, if you are the magician or are able to
fly," sadly sighed the hermit.
I'm not the magician, but I studied mathematics. Just look. The length
of my stick is two meters, and, knowing this, I can measure the length of
its shadow on the sand. It has turned out to be four meters. The shadow from
a stick is twice as long, than a stick itself. Thus, the shadow from a palm
tree twice longer than the palm. In mathematics it is called proportion.
The young man quickly measured with the help of his stick the shadow of this
palm tree on the sand and joyfully informed: "The Length of the shadow
is equal to twenty meters, means the height of your palm tree..."
The young man didn't finish his speech yet as the heavy cluster of dates
with a noise fell to the sand!
"My palm tree forgave me," with tears on his eyes whispered the old man.
Questions and tasks to the fairy tale:
- What was the height of the palm tree?
- Where else this way of height measurement can be useful?
- How do you think, why the small sizes of people and buildings on a film turn
to big images on the screen?
- Divide children into groups and give them photos with the image of people
and objects of different height, for example: a person and a house. Ask
children to measure and count, how many times in their picture is the height
of the person less than height of the house. Explain to children that in a
photo and in the real world the correlation of height of the person to
height of the house are equal and calls 'proportion'. Then ask them to
measure the height of the house if the height of the person is equal
to two meters.
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read stories on mathematics online
Fragments from the book "Kindness in Mathematics"
Fragments from the book "Magic Mathematics"