Representing Numbers 0 – 999

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.

1. Sound/ Spoken Representation & counting

   1. First learn to count in Sheets using following words– One Hundred, Two Hundred ..etc

   2. Combining strips (representing tens) and pieces (representing Units) we can build a visual & spoken representation of all numbers up to 999.

2. Sheets, Strips & Pieces Representation

   1. Presenting a 3 digit number using sheets, strips & pieces.

3. Picture Representation – pictures/ sketches of sheets, strips & 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.

   1. Following the logic of Place Value, the following 29 “word cards” 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.

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.

Relative Sizes of Sheets, Strips & Pieces

Initially the Sheets, Strips & Pieces can be made such that 1 Sheet = 10 Strips & 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 & 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 & 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.