Representing Numbers 1-9

Representing Numbers

Since we deal with numbers from very early in life, we tend to forget that they are abstract ideas. To communicate ideas about numbers, we need the skill to represent them in various ways suitable for the purpose in hand.

We are very familiar with numbers through "number sounds" and numerals. We are introduced to numbers by hearing our parents asking us to bring "two" spoons. We also see the the idea of two represented as "2" all around us in print & on TV screens.

What we do not realise is that these representations themselves are very abstract. Children understand them because they experience them continuously over a long period of time. For a person who does not speak our language the sound of "two" and the numeral "2" may not convey any meaning.

So schools should start introducing numbers in representations which proceed from the concrete to the abstract. Concrete representations are easiest to understand and abstract ones are the most difficult.

In Chapter 4.1 we have seen activities for strengthening the understanding of numbers 1 to 5. The same activities can also be used for understanding numbers from 1 to 9 and even introducing new concepts like number operations.

1. Tally Mark Representation - After some experience in representing bigger numbers with tally marks, the patterns made by these tally marks can also be interpreted to represent operations in visual ways.

   1. They can be recognised as different ways of writing any number in terms of smaller numbers. A dot pattern for 4 can be interpreted either as 1 + 3 or 2 + 2 leading to ideas of addition and subtraction.

   2. Ideas like Triangle Numbers and Square Numbers can be introduced visually

2. Arithmetic Representation - At later stages, a number can also be seen as the result of operation or operations; 4 as 1 + 3 or 5 -2, 2 X 2, 8 ÷ 2 etc.

   1. Arithmetic representations continues up to High School in terms of more complex ways of representing numbers using roots, exponents and functions.

Meaning of Understanding Numbers 1 to 9

With these understandings we can now describe fully what we mean when we say that a child has understood numbers from 1 to 9. The child should be able to

1. Represent numbers from 1 to 9 in various concrete/ semi concrete/ abstract representations.

2. Show numbers in different patterns using tokens.

3. Match or compare numbers represented in different ways

4. IArrange number representations in increasing or decreasing order of magnitude

Chapter 5.3 gives the various representations in the form of a graphic network, which will make it easier for a teacher to design activities where children would match any representation to any other representation. Chapter 5.4 gives the same information in a tabular format.

Avoid writing of numbers more than 9

In the pre-primary school it is better to avoid writing numbers more than 9 using numerals. This is because writing 2-digit numbers requires an understanding of place value which is too sophisticated for these children.

Children who are used to 2 and 3 being equal to 5, will find it difficult to grasp the idea that 2 and 3 can be put together into a number 23 which is much larger!

Section 6 - "Place Value Concept" deals with this issue in a detailed manner.

Oral Counting up to thirty

However oral counting of numbers can be practiced up to twenty or thirty, since it does not involve understanding of place value. Children will just learn them as different sounds called out in a particular sequence. This would help them practice counting.

Numbers from Eleven to Nineteen do not follow a logical pattern in the way they are pronounced. Hence these number words need to be memorised. From Twenty upwards there is a logical pattern in the pronunciation of numbers and hence children may find it easier to remember the sequence.

It is also better to give counting practice using strings of beads rather than just oral recitation. The teacher gives the student a string of beads and asks the student to find the quantity of beads. This will reinforce the meaning of the counted number to the quantity of beads.

Number Line

At this stage, children can also be introduced to the idea of a Number Line. Numbers 1 to 9 can be represented on a line with numbers increasing from 1 to 9 as we proceed to the right.

This reinforces the idea of increasing or decreasing order in numbers and comparison of numbers related to their position on the line. We can also introduce them to the term "Number Line"