Maths topic
Counting and number sense
What children learn in counting and number sense, from their first year of school to the end of primary, and the lessons to watch together.
Sheets only, lesson coming
- Counting forwards: Saying the numbers in order, and knowing what comes next.
- Counting backwards: Counting down, and knowing what comes before a number.
- Skip counting: Counting in 2s, 5s and 10s, the first step to times tables.
What's taught, year by year
The steps in counting and number sense, in the order children usually meet them. Years are named as in Australia; the ages are a guide.
Before school ages 3–5
- Match objects one to one. Pair each object in one group with one object in another to see if they match.
- Say number names in order to 10. Recite the counting words from 1 to 10 in order, then keep going past 10.
- Show amounts to 5 on fingers. Show a number up to 5 on fingers and say how many fingers are up.
- See how many at a glance (up to 3). Say how many objects there are, up to 3, without counting them one by one.
- The last number counted tells how many. Count a small group (up to 5) and know the last number said is the total.
- Compare groups: more, fewer, the same. Decide which of two small groups has more, fewer or the same by matching or counting.
- Match numerals to amounts up to 5. Link the written numerals 1 to 5 to groups with that many objects.
Foundation ages 5–6
- See how many at a glance (up to 5). Recognise dot, dice and ten-frame patterns up to 5 instantly.
- See a number as two smaller parts. Spot small groups inside a larger pattern, such as 6 as 3 and 3, to say how many.
- Count objects to 10. Touch and count up to 10 objects, saying one number for each.
- Count objects in any arrangement. Count objects in a line, a circle or scattered and get the same total.
- Count out a given number of objects. Take exactly the number of objects asked for from a larger pile (to 20).
- Count actions and sounds. Count claps, jumps or drum beats that cannot be touched or seen together.
- Read and write numerals 0 to 10. Read and write the numerals 0 to 10 and match each to a quantity.
- Zero means none. Know that 0 is the number for an empty set and that it comes before 1.
- One more and one less (within 20). Say the number that is one more or one less than a given number.
- Count and write numbers to 20. Count objects to 20 and write the matching numerals.
- Count on from any number. Start counting from a number other than 1, such as 6, 7, 8...
- Count backwards from 20. Count back in ones from 10 and then from 20 to 0.
- Compare two numbers to 10. Say which of two numerals is greater or smaller.
- Order numbers to 20. Put a set of numbers up to 20 in order from smallest to largest.
Year 1 ages 6–7
- Numbers before, after and between. Name the number just before, just after, or between two numbers to 100.
- Count to 100 in ones and tens. Count forwards and backwards to 100 in ones, and in tens from 0.
- Count, read and write numbers to 120. Continue the counting sequence past 100 and read and write numbers to 120.
- Read and write number words to twenty. Read and spell the number words one to twenty and match them to numerals.
- Ordinal numbers: first to tenth. Use first, second, third... to tenth to describe position in a line.
- Skip count by 2s, 5s and 10s. Count forwards and backwards in twos, fives and tens and spot the pattern.
- Count a large group by making tens. Count a big collection quickly by grouping it into tens or other equal groups.
Year 2 ages 7–8
- Write number words to 100 and beyond. Read and write numbers to 100, then 1000, in words.
- Estimate how many, then count to check. Make a sensible guess of the size of a collection and count to check it.
- Skip count by 3s. Count forwards and backwards in threes from 0.
Year 3 ages 8–9
- Skip count by 4s, 8s, 50s and 100s. Count in steps of 4, 8, 50 and 100 from 0.
Year 4 ages 9–10
- Skip count by 6s, 7s, 9s, 25s and 1000s. Count in steps of 6, 7, 9, 25 and 1000 from 0.