Knowing Our Numbers - How Large Can Numbers Get?

One fine morning Mr. Gulati was reading a ‘News Paper’ and was enjoying his morning tea in his Lawn. All of a sudden his son Hitesh and daughter Anju interrupted him by saying:

Anju: Dad ! we are arguing with each other saying for the last 5 minutes to decide which of the following two numbers is larger and how these numbers can be read:

Hitesh presented the two cut outs:

r. Gulati expressed his ignorance and joined them to continue the discussion by posing another question:

Have you noticed that the two numbers quoted above, both comprise of all the ten digits of our number system?

Can we say that either of the two numbers is the largest of the counting numbers?

In case you are given a chance to join this interactive session of Mr. Gulati’s family, how will you react?

Oh! Look at Anju and see how she has reacted:

Anju: No, Dad, I do not agree with you. Let us see what we shall get by adding ‘1’ to the number 1234567890.

We have 1234567890 + 1 = 1234567891 and clearly 1234567891 is a successor of 1234567890 and so 1234567890 > 1234567891

Mr. Gulati immediately clapped for Anju and made them understand:

“There is no largest number! Numbers get larger and larger by adding 1to a number and getting its successor. This process of getting the successors never stop and we never stop getting larger and larger numbers.

The reason for that is: if you had a really big number, say:

987 654 321 000 000 000 000 000 000 000 000 000 000

then you could create an even bigger number by simply adding 1 to the monster above:

987 654 321 000 000 000 000 000 000 000 000 000 000 + 1

= 987 654 321 000 000 000 000 000 000 000 000 000 001

and then you could make a bigger number again:

987 654 321 000 000 000 000 000 000 000 000 000 001 + 1

=987 654 321 000 000 000 000 000 000 000 000 000 002

and again:

987 654 321 000 000 000 000 000 000 000 000 000 002 + 1

= 987 654 321 000 000 000 000 000 000 000 000 000 003

and so on...

So, you see? Numbers just keep getting bigger and there's no stopping them. There is no one out there who can tell you what the biggest number of all is, because if someone comes up with the "biggest" number, you can always make it bigger by just adding one.

Hitesh still expressed his anxiety to know that how we can read the large numbers like the ones quoted by dad.

Mrs. Gulati who was busy with her kitchen work also enjoyed their discussion and got tempted to answer Hithesh’s quarry and joined them in the lawn.

She uttered:

“Very Large numbers with all its digits can be a pain to write out or to pronounce. So, our ancestors have invented names for these numbers to make life simpler. Some of these names are already known to you. Just recall the place value table which you have already learned.

Both – Anju and Hitesh framed the following place value table

Ten Thousands (Th)	Thousands (Th)	Hundreds(H)	Tens(T)	Ones (O)
10000	1000	100	10	1

Mrs Gulati extended this table and reproduced the same as follows:

-------	Crores		Lakhs		Thousands		Units
-------	Ten Crores	Crores	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
-------	100000000	100000000	1000000	100000	10000	1000	100	10	1

She further said, “Units, hundreds, thousands, lakhs and crores etc. are called the periods in Indo – Arabian system of writing numbers. First three places from the right of a number form the unit’s period. Next two places i.e. 4^th and 5^th places thousands period and so on.”

Incidentally one of the neighbor’s guests also reached their and interrupted “I believe that we may read large numbers by referring to the following place value chart:

Mr. Gulati took the ball in his court and said, “Yes, in the International numeration system, we use ones, tens, hundreds, thousands, millions and billions etc. In this system, commas are put after every three digits from the right. In other words, each period consists of three digits and the place value chart is:

-------	Billions	Millions			Thousands			Units
-----	-----	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
----	-----	100000000	10000000	1000000	10000	10000	1000	100	10	1

In order to conclude with the interactive session, Mr. Gulati expressed his gratitude for his family members and extended a special vote of thanks to the American Guest for making this morning session interesting and fruitful. He further asked Anju and Hitesh to write all the numbers which appeared during to day’s discussions in words, in figures in International as well as in Hindu Arabic Systems of numeration.

What about you? Would also like to do the assignment given by Mr. Gulati to his children?

For practice, work on the following assignment too:

Assignment 1.1

1. Next number in the sequence 24683, 35794, 46805, 57916, --------- is ------------.

2. Write the number obtained in question 1 above in

a. Figures in (i) Hindu Arabic system, separating different periods by using commas

(ii) International System, separating different periods by using commas

b. Words in (i) Hindu Arabic system (ii) International System

c. Expanded form in (i) Hindu Arabic system (ii) International System
3. First 20 odd natural numbers in the sequence of all 6 digit numbers are:

Recall: (i) Numbers not divisible by 2 are odd numbers and numbers divisible by 2 are

even numbers.

(ii) Numbers having 0 , 2 or a multiple of 2 in its unit’s place is divisible by 2.

4. What is the sum of the first 5 natural even numbers starting with 543210?

3. Find the 7^th number in the series 1, 30, 500, 7000 ____________

4. How many counting numbers are there between 567890 & 589543

5. A certain amount of money was shared by 3 people equally. Each of them spent Rs. 40000 and the sum of the remaining amount was equal to the initial share each had got. What was the initial sum of money each had?

6. Which of the following are prime numbers?

(a) 20019 (b) 115024 (c) 1275555 (d) none

Recall: (i) Counting Numbers other than 1which are not divisible by any number other than 1 and number it self are called prime numbers and numbers other than 1 which are divisible by at least one number other than 1 are called composite numbers.

(ii) Numbers having sum of the digits divisible by 3 are divisible by 3.

(iii) Numbers having 0, or 5 in its unit’s place are divisible by 5.

7). The sum of any seven consecutive numbers is divisible by

a) 2 b) 7 c) 3 d) 11

8. Number 500000 is divided into 2 parts such that their difference is 302550. Find the 2 parts.

9. There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. Find the first number.

10. The sum of two times one natural number and three times another natural number is less than 24. If the first natural number is less than or equal to eight, the highest value of the second natural number is:

(a) 5 (b) 6 (c) 7 (d) 8 (e) 9

Our lives are ruled by numbers which set our Destiny. Knowing these Numbers that influence and rule our lives, we can find Success and build Wealth.

Activities for Class I students _ Maths.

Book 1

Let us play

Sorting Activity: To recognize Shapes

Group Size: 4 Students on each table.

Material Required: 4 paper mats divided in to 4 Squares of same size.

A large bowl, number of snacks of solid shapes viz Cubes, Spheres, and Cones

(May be cheese dry grapes & biscuits of different shapes)

Instructions to be given

1. Take your seats.

2 .Put the scattered snacks in the bowl.

3. Who can find two snacks?

of same shape?

4. Who can find two

Snacks of different shape?

5. Place the like shapes in

one part of your mat. Snacks

of different shape in the other

Parts of your mat.

6. Encourage the children to repeat

the activity till all the snacks are

Exhausted.

Winners: Group which will take least time to complete

the round correctly will be given FIRST PRIZE ART WORK: 4 children

In each group, the child having maximum snacks around a table having

in his mat will be declared FIRST in his Group. Bowl, skater snacks & 4 mats

ACTIVITY 2

Venue: Play Ground Objective: Sorting

Group Size: Whole Class.

Material required: Number of circles, rectangles & triangles drawn on the ground with sufficient gaps& proper size with lime powder.

ART WORK

Musical Instrument with music to play.

Instructions to be given: Children stand any where you like but not very far off so that you may listen to me & the music

Which will be played shortly.

Start dancing when music is on & go to the block of the shape, which will be announced by the musical instrument before it announces STOP.

Child failing to occupy the proper place will be out.

The activity will be repeated after crossing one or two blocks.

Last three children will be declared First, Second & Third.

Class II Topic: Time (Clock) Unit: 13

Objective: To make children the concept of time.

Group size: Whole Class divided in to groups of 4 to 5 children.

Material required: Glass Cylinder, Paper Cone, Fine clean sand, electric bell with automaticrigig device to make the bell ring after equal intervals regularly, other similar timers, chart papers, markers & empty boxes etc.

Preplanning: Keep the sand timer ready by keeping the paper cone with a mall whole at the bottom closed with a rubber band, fitted in the glass cylinder& filling the paper cone with fine clean sand.

Start: Interact with children by asking the questions of the type:

Can we see time? Expected answer: yes.

How can we know the time? Expected answer: Using

Watches/Clocks.

What we would do to know the time if we do not have a watch/clock? Expected answer: By different events at home e.g. Chanting of birds early in the morning, ringing of call bell by the milk man, Voice coming from nearby religious places of worship, Radio /TV programes etc.

OR

Different events of the School e.g. Ringing of the bell for morning assembly or different periods etc.

OR

Natural events such as rising of sun/ setting of the sun etc.

(Encourage the children to give as many alternate answers as they can.)

Start the game: Set different timers ready to start the game.

Help the children making time estimates by asking the questions of the type:

How many times you can jump before the sand in the time sander run out?

Record children estimates recorded on the chart papers.

Start the timer & ask the children start jumping simultaneously. Art Work: jumping children teacher children, teacher,

Chart etc

.

Ask some children to start recording the number of jumps taken by the children in schedule time.

This activity should be performed in groups of 4 to 5 children.

S.No	Name	Estimated number of jumps	Actual number of jumps
1	Sandeep	10	7
2	Noor jahan	12	10
3	Gagan Deep	8	9
4	Victor	13	10

Help children to understand that timers can be used to measure time taken in completing an activity.

Ask the groups of children to choose a timer & measure how long it takes them to build a tower with blocks, paint a picture, sing a song etc.

(Children may be encouraged to answer the time taken to perform the above activities as: 3 bells time rounds of sand timer etc.)

Now ask the questions of the type:

(a) Which activities of your daily routine take maximum time?

(b) Which activity of your daily routine takes minimum time?

(c) List some activities in decreasing? Increasing order.

(d) What would have happened if there were two wholes in the sand timer?

(e) What people might have been doing when they did not have watches?