November 30, 2017

Introducing Place Value System

How do you introduce place value system to a child for the first time?

What is place value system?

Why is it only 1, 10s, 100s, 1000s and not any other grouping?

How do you meaningfully convey the concept and its usage? Why do we use it, in the first place?

From the wiki:

Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations (such as Roman numerals) for its use of the same symbol for the different orders of magnitude (for example, the "ones place", "tens place", "hundreds place"). This greatly simplified arithmetic, leading to the rapid spread of the notation across the world.
With the use of a radix point (decimal point in base-10), the notation can be extended to include fractions and the numeric expansions of real numbers.
The Babylonian numeral system, base-60, was the first positional system developed, and its influence is present today in the way time and angles are counted in tallies related to 60, like 60 minutes in an hour, 360 degrees in a circle. The Hindu–Arabic numeral systembase-10, is the most commonly used system in the world today for most calculations. The binary numeral system, base-2, is straightforwardly implemented in digital electronic circuitry and used by almost all computer systems and electronics for calculations and representations.

Much earlier to even talking about the place value system, I saw myself answering to DD1's questions like 'How do we write 42?' 'How do we write 67?' etc as just telling out the number 4-2 and 6-7 out. This was the time when I was thinking of how should the child be introduced to number system so that she herself will know how to write numbers with more than 1 digit?

I could recall my childhood at school, where all of us used to recite hundreds of times the following:

1-1  Eleven
1-2 Twelve
1-3 Thirteen

2-1 Twenty One
2-2 Twenty Two
2-3 Twenty Three 

and so on

Somewhere inside my mind, I knew this kind of recitation and rote learning about what the numbers actually signify was going against the philosophy of self-discovery. 

And, I didn't think much about it then. 

Recently, we took up the study of Place Value System. Let's see what is needed from a perspective of child's ability to understand the PVS.

1) Counting/writing 0-10
2) Grouping objects in 10s
3) Counting 10, 20, 30, 40 objects
4) Simple Addition/Subtraction

Let's talk more about each of the points:

1) Counting/Writing 0 - 10 
Knowing the names to numbers and ability to write 0 to 10 is the minimum prerequisite and for this, there are various tools that can be used to introduce writing to child. Tracing in sand, flour, rawa, on sandpaper and last comes pen on paper.

2) Grouping objects
Grouping can be introduced with any number of objects. You could use sticks, toys, seeds, stones as tools for this. This can be taken up as a fun game and count the number of groups of each number in the end. Some examples:
  1. Make groups of 2
  2. Make groups of 4
  3. Make groups of 7
  4. Make groups of 10
  5. Count number of each of the groups
  6. Just writing down the count 
3) Counting 10, 20, 30, 40 objects

4) Familiarity of where we write what

This is, in general, knowing that we read/write from left to right.

Now, what is the main aim of using the place value system? Why are we even introducing it to children?

PVS was introduced to make counting easier. To have a system in place of how objects can be represented in numbers. Remember all this while, the child did not know the way to write double digit numbers. So, this, in a way, is introducing the concept of representing objects, in number,  whose count is more than 10.

Before even starting to introducing PVS, the child has to be introduced to lot of fun games like, grouping, counting, simple addition/subtraction and the like.

The following is the way I did with DD1:

We had a box full of seeds beside us.

I asked DD1 to pick like a handful of seeds and keep them in another box 2.

Now, let's count the seeds in box 2.

DD1 began counting and reached the number Thirty Six.

I wrote Thirty Six in words and said, now, let us see how we can write thirty six using numbers. 

Group the seeds in 10s, each group placed in a small cup.

Group the remaining seeds in groups one 1, i.e., placed each one separately.

Place the cups containing groups of 10 in the square shown below.

Place the individual seeds (groups of 1) in the corresponding square below.

The first time we did this, we wrote and drew using up the entire floor around us. Couldn't click pics as I got too much involved and forgot about clicking pictures. 😇😇😇

10 (groups of 10)
1 (groups of 1)

Next count the number of groups (or cups) present in the square corresponding to 10. ---> 3

count the number of seeds present in the square corresponding to 1 ----> 6


This is the number that represents the total quantity of seeds, that was earlier counted to be Thirty Six. In other words, a quantity of Thirty Six is represented as 3-6, that is, 36.

Following this, lot of other maths could also be done, like:

  1. Counting the total seeds that were grouped as 10 = 30
  2. Counting seeds in each cup = 10
  3. Counting the number of cups = 3
  4. Understanding that 10 + 10 + 10 = 30 
  5. Understanding that 10 * 3 = 30
  6. Understanding that when you add 10 three times, you get 30

DD1 just loved to do this activity and wanted to play another time. 

After couple of times, you can just sit back and watch as your child explains to you the concept. She becomes the teacher and you the student!!



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