Whole number place value:
key ideas and important concept knowledge
Key ideas
The overarching key ideas of estimation, benchmarks, visualisation, equality and equivalence, language and strategies need to be considered when developing units of work in place value. The specific key ideas in place value are: quantity, number triad, digit position, base-10 system, place-value partitioning and comparison.
Quantity
A quantity is an amount of something which is determined using a number and a unit.
Number triad
A number triad represents the relationship between words, symbols and materials or diagrams of a quantity.
Digit position
The place of a digit in a number determines its value.
There are three ways to interpret a single digit within a whole number: face value, place value and total value.
Zero can be a placeholder and a digit representing a quantity.
Base-10 system
The base-10 system is a number system that is based on grouping and equally partitioning quantities by tens.
Each place has a value that is 10 times greater than the place to its right, and one-tenth of the value of the place to its left.
Place-value partitioning
Place-value partitioning is breaking a whole number into place-value units.
Comparison
The relative size of two quantities can be compared, either to each other or a benchmark.
Important concept knowledge
Rounding
Rounding is a context-driven approximation used to make numbers easier to calculate. It is useful for estimation.
The convention for rounding is that numbers are rounded up when the digits to the right of the nominated ‘place’ are equal to or greater than 5, and numbers are rounded down when these digits are less than 5.
