Visualizing Place Value 1

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Place Value Concept is Very Abstract

We have seen that the Place Value System is a very sophisticated system which requires a certain mental maturity.

This is because of 2 reasons - first the abstract nature of the concept &amp; second because students in lower primary school are not developmentally ready for understanding abstract concepts.

Hence children should be presented with this concept with concrete materials which mirror the concept.

Ineffective Teaching of Place Value

Place Value is usually not taught in a way so that the concept behind it becomes clear to the children. It is usually taught as a formula to be memorised; 23 means 2 in the Ten's Place and 3 in the One's Place.

These multiple and similar-sounding words One; Ten, One's & Ten's confuse children.

They may be able to orally repeat the pattern with any other number like "46 has 4 in the Ten's place and 6 in the One's place". But they do not get an understanding of the idea behind the Place Value System.

If students do not have a clear understanding of the PVS, they will have difficulties with all many number properties and arithmetic operations. Hence it is very necessary that the PVS be clearly understood.

We will see the relation between PVS and the ease of arithmetic operations in Chapter 6.11.

Visualizing Place Value

Several visual ways of presenting the place value idea are available. Many of these ideas can be graded as proceeding from the concrete to abstract. We present ideas which in actual practice have been found very effective.

Two-digit numbers - Bundles & Sticks

One way of making this concept understandable to children is to represent 23 as 2 bundles (of ten sticks) and 3 sticks.

It can be explained that the right most number, here 3, can be thought of as sticks and the next left number can be thought of 2 bundles. Hence 45 becomes 4 bundles and 5 sticks.

The difference between 4 & 5 in 45 becomes easy to understand; 4 stands for bundles and 5 for sticks, though on the blackboard they look similar!

Forty (40) is just 4 bundles. The fact there are no sticks is represented by 0 in the Unit's place. The presence of 0 conveys the meaning that 4 stands for bundles (tens).

This representation also makes it easy for children to visualise the difference between 32 and 23. In bundles & sticks it is easy to see that 32 is bigger than 23.

Three Digit Numbers – Sheets, Strips &amp; Pieces or Flats, Longs & Pieces

What do we do for numbers greater than 99?

For representing numbers more than Ninety-Nine, we need suitable materials which can represent Hundreds, Tens & Ones. Using a large bundle of hundred is not very effective as children may not be able to differentiate between tens (small bundle) and hundreds (large bundle). It is time for a step towards greater abstraction.

Rather than using large bundles to represent Hundred, we can use Sheets, Strips & Pieces as illustrated below. They can be cut out of chart paper.



The small square piece (Piece) can represent One, the long rectangular piece (Strip) can represent Ten and the large square piece (Sheet) can represent Hundred.

The Strip is usually equal to the length of ten pieces.

The side of the "square" Sheet is equal to the length of a Strip.

Hence geometrically the FLPs maintain the arithmetic relation between them.

These materials are known as FLPs in the west; Flats, Longs & Pieces or Base Ten Blocks.

This representation has the advantage of being used later to introduce concepts of algebra. We will see this in Section 28 on basic algebra.

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