1 Place value in the decimal number system

According to India’s National Council of Educational Research and Training (2008, p. 35):

• Understanding the concept of place value is an important aspect of number representation and a core requirement of mathematics.

The decimal system of numbering enables any number, small or big, to be written using only the ten digits from 0 to 9. It is based on the following principles:

• The system uses only the following ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
• The position of a digit within a number determines its value.
• The system uses 10 as a ‘base’ – a digit one place to the left of another is worth ten times its value.
• Zero is used as a placeholder to represent that, for example, in the number 205 there are no tens in the tens place.

Students do not need to know these principles explicitly. However, it is essential that they develop a sound understanding of how to use these principles, because they underpin so much of what follows in their mathematical learning. In particular, place value forms the basis of the methods that students are taught to use for calculations with larger numbers, but a secure understanding of place value is also crucial for ordering numbers, making measurements and handling money.

However, the concept of place value is very abstract. Students need lots of opportunities to develop their understanding through active approaches that make use of concrete and visual representations of the decimal number system. This unit explores the possibilities of several different representations, and also their limitations.

Pause for thought Think back to when you were at school, or perhaps even earlier. Can you remember learning to count, or how to write numbers? This may not be easy because, having learnt to do them when you were very young, they can seem like things that you ‘have always been able to do’. Consequently it is not necessarily easy to support students as they learn about numbers, especially those who encounter difficulties. Now that you are a teacher, have you noticed any student in your class who gets confused about naming numbers where the numerals are reversed (e.g. 64 and 46), or where a number includes a zero? What do you think might be the reason for this?