Place Value Systems

Just as we need the alphabet to write down words and sentences, so we need a notation to write down numbers. Place value is core to our understanding of so many areas of mathematics. As students build their understanding of counting and additive properties, they must develop the capacity for multiplicative thinking in order to work flexibly and efficiently with a range of whole numbers, fractions and decimals.

Hindu-Arabic numerals exhibit some of the qualities that make mathematics so powerful, namely
• they can be used by understanding a small number of ideas, and
• they can be generalized beyond the original setting for which they were devised.
(The notation was developed to express whole numbers, but it extends to the representation of fractions and decimals.)

Hindu-Arabic numerals are a decimal, or base-ten, place-value number system with the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 as fundamental building blocks.

Hindu-Arabic notation is a place value system based on bundles of 10; so it is a decimal system.
The key to a place value system is the use of a place marker.
A place value system using 9 digits and a space or the word kha (for emptiness) as place marker was used in India the 6th century.

By the 9th century the system had made its way to the Arab world (including Persia and Al-Andalus in what is now Spain).
The digit 0 evolved from “·” and was used in both Madhya Pradesh (Northern India) and the Arab world by the 10th century.
Leonardo Fibonacci learned to use the notation from merchants in Africa when he was a boy and wrote a book, Liber Abaci, in 1202 which popularized the system.

Once the numbers below ten are established, the next goal is to look at the numbers from ten to twenty.
We want students to:

• see the importance of ten
• start to use ten as a countable unit.

Students are encouraged to use a variety of materials in building their understanding of counting in tens:

From here, students can start to understand more complex numbers and ideas – for instance, what does one hundred look like?

Students can now start to build on their knowledge of tens as the base of the place value system:

For more information and activities focusing on place value, please see our free models:
http://www.amsi.org.au/teacher_modules/Counting_and_place_valueK-4.html and
http://www.amsi.org.au/teacher_modules/Using_place_value4-7.html