Representing Numbers 0 – 999

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We have seen how numbers up to 99 can be represented, starting from concrete form gradually becoming more and more abstract. We give below a sequence of representing numbers greater than 99 in the same manner.

Children should be able to represent numbers from 0 to 999 in all these representations. They should be able to match one representation with another.
 * 1) Sound Representation &amp; counting 				First learn to count in Sheets using following words– One Hundred, Two Hundred ..etcCombining strips (representing tens) and pieces (representing Units) we can build a visual &amp; spoken representation of all numbers up to 999.
 * 2) Sheets, Strips &amp; Pieces Representation 				Presenting a 3 digit number using sheets, strips &amp; pieces.
 * 3) Picture Representation – pictures of sheets, strips &amp; pieces representing the number.
 * 4) Numeral Representation – 125,263,378,409 etc. Numerals have different shapes which vary from language to language. When a child is learning 2 languages then numbers could be represented with numerals of both languages.
 * 5) Number Line – drawing a number line divided into tens and/or hundreds and marking the number on the line as a point.
 * 6) Word Representation – One, Two, Three etc. Number words are also written in various ways from language to language. When a child is learning 2 languages then numbers could be written in both languages. 				Following the logic of Place Value, the following 29 &ldquo;word cards&rdquo; would be sufficient to build all numbers up to Thousand.
 * 7) Arithmetic Representation – 415 as 300+115 etc. Arithmetic representation continues up to High School in terms of more complex ways of representing numbers.

Relative Sizes of Sheets, Strips &amp; Pieces

Initially the Sheets, Strips &amp; Pieces can be made such that 1 Sheet = 10 Strips &amp; 1 Strip = 10 Pieces. Here students can actually place Pieces on the Strip and find that ten of them fit.

Later the sheets, strips and pieces need not be to scale. Sheet can be a large square, Strip a long rectangle and Piece a small square.

At an even higher level of abstraction, all three can be replaced with tokens of different colours.

Numbers greater than 999

When students can represent numbers &amp; their operations with materials, they would reach a stage when they can deal with number purely in numeral form.

Most of the difficulties which students have with numbers &amp; their operations results because they have not been given a firm foundation of visualising numbers using the place value concept.

Word Representation of 3 Digit Numbers

Has been dealt separately in chapter 7.5.

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