## Quantifying numbers description

Although number is an abstract concept which can be represented by a word, a symbol (numeral) or an image, it is central to quantitative thinking.

This sub-element describes how a student becomes increasingly able to count, recognise, read and interpret numbers expressed in different ways. It outlines key understandings needed to process, communicate and interpret numerical information in a variety of contexts.

Within this sub-element, place value is taken to mean more than being able to read, write and state the positional value of a digit. Place value relies on understanding the relationship between digits in a numeral, which then enables the numeral to be renamed in multiple ways. In addition to the base-ten positional value property, the __place value system__ has both additive and multiplicative properties. That is, the quantity represented by a numeral is the sum of the values represented by its individual digits (326 = 300 + 20 + 6) and the value of a digit is determined by multiplying its face value by the value assigned to its position in the numeral (326 = 3 x 100 + 2 x 10 + 6 x 1).

The *Quantifying numbers* sub-element underpins learning of number sense, measuring and using data.

*Some students will communicate using augmentative and alternative communication strategies to demonstrate their numeracy skills. This may include digital technologies, sign language, braille, real objects, photographs and pictographs.*

*Each sub-element level has been identified by upper-case initials and in some cases lower-case letters of the sub-element name followed by ascending numbers. The abbreviation for this sub-element is QuN. The listing of indicators within each level is non-hierarchical. Subheadings have been included to group related indicators. Where appropriate, examples have been provided in brackets following an indicator.*

### QuN1

**Producing number names**

- produces number words that relate to students’ lives, which could involve the use of augmentative and alternative communication (AAC)

**Counting items**

- responds to a request for a different amount by increasing or decreasing a quantity
- recognises the effects of adding to and taking away from a collection of objects

**Number recognition and identification**

- recognises small quantities (<4) as being the same or different without counting (
__subitises__) - compares two quantities and states which group has more and which less
- matches one numeral with another (matches to a sample)
- recognises some numerals, such as those associated with age or home address

### QuN2

**Producing number names**

- produces a
__rote__count to at least 12[*] - produces a rote count down from 10

**Counting items**

- counts a small number of items (typically less than 4)

**Numeral recognition and identification**

- indicates the correct numeral from a range of different symbols for most numerals up to 10 (‘which is 3?’)
- produces the matching number word for most numerals up to 10

[*] Reference to a rote count to at least 12 rather than 10 is because approximately 87% of children start school being able to produce an oral count at least to 10. For most children, the first major hurdle in learning to count occurs at 12, with the start of the ‘teen’ sequence.

### QuN3

**Producing number names**

- produces the number word just after a given number word in the range 1–10 (but drops back to 1 when doing so)
- produces the number word just before a given number word in the range 1–10 (but drops back to 1 when doing so)

**Counting items**

- recognises that the last number word said in a count answers ‘How many?’
- matches the count (up to 10) to objects, using the
__one-to-one principle__

**Numeral recognition and identification**

- recognises and identifies all numerals in the range 1–10
- selects the largest numeral from an unordered group of 3 or more, in the range 1–10

### QuN4

**Producing number names**

- produces the number word just after a given number word in the range 1–10 (without dropping back to count from 1)
- produces the number word just before a given number word in the range 1–10 (without dropping back)

**Counting items**

- matches number words within the current known counting range to quantities of items
- correctly indicates the larger or smaller of two numerals in the range from 1 to 10

**Numeral recognition and identification**

- recognises and identifies all numerals in the range 1–10 as well as 20, 30, 40, 50, 60, 70, 80, 90 and 100
- orders numerals to at least 10

### QuN5

**Producing number names **

- counts to at least 20
- continues a count from a number other than 1
- counts forwards by tens to 100

**Counting items **

- counts groups of up to 20 items

**Numeral recognition and identification **

- points to the correct numeral in response to a verbal request, for numerals up to 20 as well as 30, 40, 50, 60, 70, 80, 90 and 100

### QuN6

**Producing number names**

- counts to at least 30
- produces the number word just after a given number in the range 1–30 (without dropping back)
- produces the number word just before a given number word in the range 1–30 (without dropping back)
- counts forwards and backwards by tens to and from 100

**Counting items**

- matches known numerals (to 20) to quantities

**Numeral recognition and identification**

- identifies all numerals up to 30 as well as 40, 50, 60, 70, 80, 90 and 100 (is shown the numeral 17 and produces its name)
- orders numbers to at least 20 (determines the largest number in a group of numbers selected from 1 to 20)

### QuN7

**Producing number names to at least 120***

- counts forwards and backwards to and from 120 and beyond
- continues counting from any number up to 120 and beyond
- counts forwards and backwards by fives

**Grouping and counting items by tens **

- counts items in groups of twos, fives and tens
- recognises that a count of one ten is the same as ten counts of one

**Numeral recognition and identification**

- identifies numerals from 0 to at least 100 (is shown the numeral 45 and produces its name)

recognises a numeral from a given range up to 100 (is shown the numerals 70, 38, 56 and 26 and when asked which is 38, indicates the numeral)

* Reference to producing number names to at least 120 rather than 100 is because of the higher proportion of students in the early years who encounter a hurdle at 109 compared to 100.

### QuN8

**Producing number names to at least 1000**

- counts forwards and backwards by 100s to 1000 (100, 200 … 1000)
- counts forwards and backwards by
__tens off the decade__to 100 (2, 12, 22, …)

**Numeral recognition and identification of place value**

- recognises and describes teen numbers as 1 ten and some more (16 is 1 ten and 6 more)
- represents and renames two-digit numbers as separate tens and ones (68 is 6 tens and 8 ones, 68 ones, or 60 + 8)
- applies an understanding of zero in place value notation when reading numerals that include
__internal zeros__(correctly recognises 101 as one hundred and one, not 1001)

### QuN9

**Producing number names of any size **

- counts forwards and backwards from any number
- produces and reads numbers to at least 1000

**Numeral recognition and identification of place value**

- recognises and identifies numerals from a given range up to 1000 (is shown the numerals 170, 318, 576 and 276 and when asked which is 276, points to the 276)

**Understanding place value**

- represents and flexibly renames three-digit numbers as counts of hundreds, tens and ones (247 is 2 hundreds, 4 tens and 7 ones, or 2 hundreds and 47 ones, or 24 tens and 7 ones)

**Understanding decimal place value**

- recognises that the
__place value system__can be extended to tenths and hundredths - uses an understanding of the magnitude of decimals to compare them to two decimal places (0.20 is smaller than 0.4)
- orders decimals to one decimal place by placing them on an interval between 0 and 1

### QuN10

**Numeral recognition and identification of place value**

- identifies numerals in the range 0–10 000 (is shown the numeral 2001 and responds
*two thousand and one*) - recognises a numeral from a given range of numerals up to 10 000 (when presented with the numerals 1701, 9318, 2050 and 2500 and when asked which is 2050, indicates the correct numeral)

**Understanding place value**

- reads and writes numbers beyond 1000 applying knowledge of the place value periods of ones and thousands
__partitions numbers__by their place value into thousands, hundreds, tens and ones

**Understanding decimal place value**

- locates and orders decimals between 0 and 1 up to two decimal places
- recognises that the
__place value system__can be extended to thousandths - compares the size of decimals (including
__ragged decimals__such as 0.5, 0.25, 0.125) - reads, compares and
__renames__decimal numbers (0.4 is greater than 0.355 because 0.4 has 4 tenths and 0.355 only has 3 tenths)

### QuN11

**Understanding place value**

- reads and writes numbers applying knowledge of the
__place value periods__of ones, thousands, millions (how numbers are written with the digits organised in groups of three – 10 000 is read as ten thousand, where thousand is the place value period) __partitions__numbers by their place value into tens of thousands, thousands, hundreds, tens and ones and beyond- recognises the relationship between adjacent positions in place value (200 is 10 times as large as 20, which is 10 times as large as 2)
- estimates whole numbers to the nearest hundred thousand, ten thousand, etc. (crowd numbers at a football match)

**Understanding decimal place value**

- compares and orders decimals beyond 1 including
__ragged decimals__(those expressed with unequal numbers of places) - recognises the relationship between adjacent positions in place value for decimals (0.20 is 10 times larger than 0.02)

### QuN12

**Understanding place value (directed numbers)**

- orders negative numbers (recognises that −10 °C is colder than −2.5 °C)

**Representing place value**

- recognises, reads and interprets very large and very small numbers
- expresses numbers as powers of 10 in
__scientific notation__and determines the__order of magnitude__of quantities (a__nanometre__has an order of magnitude of -9) - relates place value parts to
__indices__(1000 is 100 times larger than 10, and that is why 10^{1}x 10^{2}= 10^{3}and why 10^{3}divided by 10^{1 }is equal to 10^{2})