Big Ideas in Number

Counting is one of the very first skills that children learn in mathematics. In many cases, it begins before students even enter the classroom but needs to be carefully taught in their first year using eight explicit methods. When learning to count, students will need exposure and practise in eight key principles.

Trusting the count is a teaching approach that emphasises the importance of children understanding the meaning of numbers, rather than just memorising them. It encourages children to count objects and group them in different ways, to understand that numbers represent a quantity and that they can be broken down into smaller parts.

Subitising is the ability to recognise quantities without counting. This foundational skill lays the groundwork for more complex number concepts, facilitating a deeper understanding of addition, subtraction, and beyond, as students learn to quickly identify and manipulate numbers without reliance on sequential counting.

An early understanding of place value involves the idea that whole numbers can be seen as countable units. This understanding of numbers as countable units lays a strong foundation for more advanced mathematical concepts children will encounter not just in place value but also in later mathematical concepts.

Unitising is a concept that involves breaking numbers down into smaller units, such as ones, tens, and hundreds. One way to teach unitising is through the use of the phrase "one of these is ten of these". This phrase helps children understand the relationship between different place values, such as how one group of ten units is equivalent to ten individual units.

Our base-10 number system has developed around the ten digits 0 – 9. The term 'base' means a collection and in our number system, 10 is the value that determines a new collection (Reys, 2022). From a multiplicative perspective, our place value numeration system increases and decreases by a factor of 10.