More or Less? Need to Guess!

Gayathri Tirthapura

"Ranju, can you get me two
coconuts from that basket?"
Ranjita raced to the other
side of the room. She returned in an instant with the two coconuts.
Amma was pleased. "Thank
you, darling! You are such a help."
Ranjita glowed with pride. It
was a BIG day today - her uncle Mahesh Chikkappa's wedding! And she
had a BIG responsibility - to hand over mithai boxes to the 100
guests after lunch.

But where were the mithai
boxes?
"Oh no!" cried
Amma. "The boxes are still in the room upstairs! Run and bring
them down quickly, Ranju. The guests have almost finished their
lunch."
"Amma, you never ask ME for
help!" said a small, whiny voice. "And I'm hungry."
"You can help Akka,
Vikky," said Amma soothingly. "Ranju, take him with you,
please?"
Ranjita frowned. Why did Amma
always do this? Her little brother Vikram was SO annoying! But there
was no time to argue.

"You have to listen to me and do exactly as I say, Vikky!" she warned him, making her eyes big and stern.
Vikram nodded. "I will, Akka! Promise!"

The two of them ran to the
room upstairs.

Upstairs, in a corner, were a pile of
cloth bags. Ranjita pulled open a bag. There were several small
mithai boxes inside.
"It will take too long to
empty all the bags and count out 100 boxes, Akka!" Vikram was very
worried. "And I'm very hungry."
"Shhhh!" said
Ranjita fiercely. "Let me think!"

Ranjita thought hard. Vikram
was right. It would take too long to actually count out 100 boxes.
They couldn't take all the bags down either. There were too many of
them.
Vikram looked longingly at
the mithai boxes. "Can I open one? I'm VERY hungry."

"NO!" said Ranjita.
Then she smiled. "Idea! We don’t need to take EXACTLY 100
mithai boxes! We can take APPROXIMATELY 100. That will be much
quicker."
"Approximately?"
Vikram looked puzzled. "What does that mean, Akka?"
"It means a few MORE than, or a few LESS than, the exact number," said Ranjita.
"Bu-ut," Vikram said slowly, "If we take less than 100, there won't be enough for everyone."

"So we take more!"
said Ranjita.
"Ok, let’s do it!"
Vikram grabbed a few bags. "Quick! I'm very, VERY hungry!"
"Wait, silly! Let me tell
you HOW to approximate first!" said Ranjita.
She poured out all the boxes
from one bag onto the floor and counted them. "See, Vikky," she
said. "There are 10 mithai boxes in this bag." Vikram
nodded.

Ranjita pointed to the other
bags. "All the bags are approximately, more or less, the same
size. What does that tell you?"
Vikram shrugged.
"It tells you that each
bag has approximately, more or less, 10 mithai boxes!" said
Ranjita.
"Oh THAT!" said
Vikram airily. "I knew THAT."

Ranjita hid her grin. "Tell
me this, then. How many mithai boxes in two bags?"
"Approximately-more-or-less
20*," said Vikram instantly.
"And in three bags?"
"Approximately-more-or-less
30**!" Vikram began to smile. He was getting the hang of this.
"And in five?"
"Approximately-more-or-less
50***!" yelled Vikram. "And 50 is half**** of all the mithai
boxes we need!"
*(10 x 2 = 20),
**(10 x 3 = 30)
***(10 x 5 = 50)
**** (Half of 100 = 100 / 2 = 50)

"That's very good,
Vikky!" said Ranju admiringly.
Vikram turned red with
delight. He loved it when his Akka praised him. "Now can I open
a mithai..." Ranjita glared.
"I mean," Vikram
said quickly, "I will take 5 bags with
approximately-more-or-less 50 boxes, and you take 5. Okay?"

"Not so fast!" said Ranjita. "We haven't counted the boxes in every bag. What if one or two bags have only 8 boxes? We won't have enough for everyone then."

Vikram paused. As usual, Akka
was right.
"So we take 11 bags,
then?" he asked slowly. "With approximately-more-or-less
110 mithai boxes?"
"Exactly!" said
Ranjita. "You take 5 bags, and I will take 6. Come on!"
The children ran down the
stairs with the bags. Amma was waiting anxiously. She was very
relieved to see them.
"That was quick!"
said Amma. "Are you sure we have enough for everyone?"
"Yes, Amma," said
Vikky. "I am very, very sure. AND... I'm very, very, VERY
hungry."

When all the guests had left,
Amma hugged Ranjita and Vikram. "You both saved the day!"
she said.
Then she narrowed her eyes.
"I've never seen you both work so well together," she said.
"Does that mean you finally like each other?"
Ranjita and Vikram laughed.
"Approximately-more-or-less!" they said, as they ran to
lunch.

THE GUESSING GAME
Ranjita and Vikram used a clever mathematical trick to get their job
done quickly. They called it 'Approximately More or Less';
mathematicians call it 'Estimation'.
So what is Estimation? Is it like guessing? Sort of, but estimation
is 'intelligent' guessing.
Why is estimation important?
Estimation helps you identify wrong answers quickly.
For instance, let's say you have just 30 seconds to answer this
question:
1. What is 17 x 9?
a. 172
b. 153
c. 186
d. 89
You know that 17 x 10 = 170 (anything into ten is the same number
with a zero at the end). So 17 x 9 should be LESS than that. That
means Options (a) and (c) are wrong. Option (d) seems too small to be
the right answer - 17 x 9 should be closer to 170. So you pick Option
(b). See how estimation has helped you pick the right option, simply
by identifying the wrong ones?

Estimation helps alert you to real-life errors. When the
shopkeeper totals your bill, you can tell instantly if it is wrong
because you have estimated approximately how much it should be.
Estimation helps you calculate distances. If you know that you
cover 30 cm with each step, and that you take 1800 steps to walk from
home to the library, you can estimate the distance between the two
(1800 x 30 cm = 54000 cms = 540 m, which is about half a kilometre).
Estimation is fun. How many peas inside half a kilo of
unshelled pods? How many elephants should you stand on top of each
other to make the height of your flagpole? You can find out answers
to all kinds of wacky questions using estimation!