Students in Kindergarten/Prep/Reception investigate Number concepts informally – no symbols used! This is for 2 reasons:
i. students in Kindergarten/Prep/Reception learn 10 symbols for numbers, 26 symbols for lower case letters, and 26 symbols for upper case letters – that’s a huge 62 symbols!
ii. students need to be able to understand and explain the concepts behind the symbols +, -, x, ÷, and = before they begin to use the symbols.

Students initially investigate counting, before moving on to investigating grouping in a concept sequence we call “Early Counting and Grouping’. (See the diagram below!) (For Professional Learning on Early Counting and Grouping, select Professional Learning above, Learn by Concept, Number and Algebra, Early Counting and Grouping Professional Learning.)

Students begin investigating non-mathematical counting including the forward and backward number sequences, writing numerals and recognising numerals in 2 ways – when their name is spoken and when seeing its numeral. They name the number before and the number after (ECG 1, 2, 3, 4). These are non-mathematical because we all just agree on the sequence and the numerals! However knowing these is essential to begin to investigate mathematical counting.

Students begin investigating mathematical counting as they count with one-to-one correspondence. explaining that the last number they said is the total, and that the number after is one more and the number before is 1 fewer. They explain that counting forwards is adding one each time, while counting backwards is taking away one each time. Students subitise the number in a small collection (without counting). (ECG 5, 6, 7, 8, 9)  

Before students can investigate joining groups (informal adding) and taking away from a group (informal subtracting), they need to be able to explain groups flexibly. This means explaining that they started with a group, then made 2 groups, made 1 group again, then made 3 groups – all from the same group of counters! Students estimate the number is a group, explain that numbers are inclusive (2 is inclusive of 1, 3 is inclusive of 2 and of 1) (ECG 10, 11, 12).

Once students can explain groups flexibly, they begin to join groups to make a group and to take away a group from a group to leave a group. They also investigate finding the difference between 2 groups by adding to the smaller group to make the larger group, or taking away from the larger group to make the smaller group (ECG 13, 14, 15)