Foundation
Mathematics
ASMATFY
Foundation Mathematics Achievement Standard
11 statements aligned to content descriptors and elaborations
Achievement standard (as ACARA publishes it)
Achievement standard
Click any sentence to jump to its statement and linked content descriptors.
By the end of Foundation Year, students make connections between number names, numerals and position in the sequence of numbers from zero to at least 20. They use subitising and counting strategies to quantify collections. Students compare the size of collections to at least 20. They partition and combine collections up to 10 in different ways, representing these with numbers. Students represent practical situations that involve quantifying, equal sharing, adding to and taking away from collections to at least 10. They copy and continue repeating patterns.
Students identify the attributes of mass, capacity, length and duration, and use direct comparison strategies to compare objects and events. They sequence and connect familiar events to the time of day. Students name, create and sort familiar shapes and give their reasoning. They describe the position and the location of themselves and objects in relation to other objects and people within a familiar space.
Students collect, sort and compare data in response to questions in familiar contexts.
The 11 achievement standard statements
Open a statement to see the content descriptors ACARA links to it, then open a descriptor's elaborations.
By the end of Foundation Year, students make connections between number names, numerals and position in the sequence of numbers from zero to at least 20.
Content descriptorAC9MFN01 Number
name, represent and order numbers including zero to at least 20, using physical and virtual materials and numerals
Elaborations (5)
- Elaboration responding to a request to collect a quantity of objects or reading a numeral and selecting the associated quantity of items from a collection to match the number required; for example, collecting 9 paint brushes after hearing the word ‘nine’
- Elaboration recognising the order in the sequence of numbers to 20 and identifying the number that is “one less” than a given number and the number that is “one more”; for example, playing instructive card games that involve reading and ordering number cards; using counting songs, story books and rhymes to establish the forwards and backwards counting sequence of numbers in the context of active counting activities
- Elaboration understanding and using terms such as “first”, “second”, “third”, … “fifth”… to indicate ordinal position in a sequence; for example, creating a number track using cards with the numerals zero to 20 and describing positions using terms such as first, last, before, after, between
- Elaboration recognising, writing and reading numerals written on familiar objects; for example, in images, text or illustrations in story books; writing a numeral on a container as a label to show how many objects it contains
- Elaboration connecting quantities to number names and numerals when reading and reciting stories and playing counting games or determining and reasoning about the size of sets of objects within First Nation Australians’ instructive games; for example, Segur etug from Mer Island in the Torres Strait region
They use subitising and counting strategies to quantify collections.
Content descriptorAC9MFN02 Number
recognise and name the number of objects within a collection up to 5 using subitising
Elaborations (2)
- Elaboration recognising how many objects are in a collection or in images on a card with a quick look and saying the associated number without counting
- Elaboration playing instructive card games that rely on the recognition of numbers represented in different ways; for example, playing memory games, matching pairs of quantities on dot cards or similar where the arrangement on each is different; using subitising to compare and order collections and to say who has more when sharing items in a game
Content descriptorAC9MFN03 Number
quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning
Elaborations (5)
- Elaboration establishing the language and process of counting, understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the question of “How many?”; for example, saying numbers in sequence while playing and performing actions
- Elaboration using counting to compare the size of two or more collections of like items to justify which collection contains more or less items
- Elaboration using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
- Elaboration discussing how different cultures may have alternative ways of representing the count; for example, discussing how people of the Asia region use an abacus or Chinese hand gestures
- Elaboration using body-tallying that involves body parts and one-to-one correspondence from counting systems of First Nations Peoples of Australia, to count to 20
Content descriptorAC9MFN04 Number
partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts
Elaborations (4)
- Elaboration recognising numbers represented in physical or virtual ten-frames, and describing their reasoning: “It’s 7 because there is 5 there and 2 more”
- Elaboration partitioning collections of up to 10 objects in different ways and saying the part-part-whole relationship; for example, partitioning a collection of 6 counters into 4 counters and 2 counters and saying, “6 is 4 and 2 more, it’s 2 and 4”, then partitioning the same collection into 5 and one or 3 and 3
- Elaboration representing part-part-whole relationships in numbers up to 10 using physical or virtual materials; for example, identifying numbers represented by dots in standard number configurations such as dominos and dice by recognising parts that form the whole
- Elaboration exploring number groupings in First Nations Australians’ counting systems and the different ways of representing these groupings to form and partition numbers, applying this to quantify collections of objects in the environment on Country/Place up to 10
Content descriptorAC9MFN05 Number
represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies
Elaborations (4)
- Elaboration using role-play and materials to represent mathematical relationships in stories; for example, “Eight kangaroos were drinking at the river and 3 hopped away”; drawing a picture and using materials to represent the situation, discussing, and recording the result of the action with a numeral
- Elaboration role playing or actively engaging in situations that involve quantifying or comparing collections of items or simple money transactions; for example, “Do we have enough scissors for our group so that each person has their own pair?”; role-playing using \$1 coins to pay for items in a shop where items are priced in whole dollars
- Elaboration representing situations expressed in First Nations Australians’ stories, such as “Tiddalick, the greedy frog”, that describe additive situations and their connections to Country/Place
- Elaboration representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory
Students compare the size of collections to at least 20.
Content descriptorAC9MFN03 Number
quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning
Elaborations (5)
- Elaboration establishing the language and process of counting, understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the question of “How many?”; for example, saying numbers in sequence while playing and performing actions
- Elaboration using counting to compare the size of two or more collections of like items to justify which collection contains more or less items
- Elaboration using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
- Elaboration discussing how different cultures may have alternative ways of representing the count; for example, discussing how people of the Asia region use an abacus or Chinese hand gestures
- Elaboration using body-tallying that involves body parts and one-to-one correspondence from counting systems of First Nations Peoples of Australia, to count to 20
They partition and combine collections up to 10 in different ways, representing these with numbers.
Content descriptorAC9MFN02 Number
recognise and name the number of objects within a collection up to 5 using subitising
Elaborations (2)
- Elaboration recognising how many objects are in a collection or in images on a card with a quick look and saying the associated number without counting
- Elaboration playing instructive card games that rely on the recognition of numbers represented in different ways; for example, playing memory games, matching pairs of quantities on dot cards or similar where the arrangement on each is different; using subitising to compare and order collections and to say who has more when sharing items in a game
Content descriptorAC9MFN04 Number
partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts
Elaborations (4)
- Elaboration recognising numbers represented in physical or virtual ten-frames, and describing their reasoning: “It’s 7 because there is 5 there and 2 more”
- Elaboration partitioning collections of up to 10 objects in different ways and saying the part-part-whole relationship; for example, partitioning a collection of 6 counters into 4 counters and 2 counters and saying, “6 is 4 and 2 more, it’s 2 and 4”, then partitioning the same collection into 5 and one or 3 and 3
- Elaboration representing part-part-whole relationships in numbers up to 10 using physical or virtual materials; for example, identifying numbers represented by dots in standard number configurations such as dominos and dice by recognising parts that form the whole
- Elaboration exploring number groupings in First Nations Australians’ counting systems and the different ways of representing these groupings to form and partition numbers, applying this to quantify collections of objects in the environment on Country/Place up to 10
Students represent practical situations that involve quantifying, equal sharing, adding to and taking away from collections to at least 10.
Content descriptorAC9MFN03 Number
quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning
Elaborations (5)
- Elaboration establishing the language and process of counting, understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the question of “How many?”; for example, saying numbers in sequence while playing and performing actions
- Elaboration using counting to compare the size of two or more collections of like items to justify which collection contains more or less items
- Elaboration using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
- Elaboration discussing how different cultures may have alternative ways of representing the count; for example, discussing how people of the Asia region use an abacus or Chinese hand gestures
- Elaboration using body-tallying that involves body parts and one-to-one correspondence from counting systems of First Nations Peoples of Australia, to count to 20
Content descriptorAC9MFN05 Number
represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies
Elaborations (4)
- Elaboration using role-play and materials to represent mathematical relationships in stories; for example, “Eight kangaroos were drinking at the river and 3 hopped away”; drawing a picture and using materials to represent the situation, discussing, and recording the result of the action with a numeral
- Elaboration role playing or actively engaging in situations that involve quantifying or comparing collections of items or simple money transactions; for example, “Do we have enough scissors for our group so that each person has their own pair?”; role-playing using \$1 coins to pay for items in a shop where items are priced in whole dollars
- Elaboration representing situations expressed in First Nations Australians’ stories, such as “Tiddalick, the greedy frog”, that describe additive situations and their connections to Country/Place
- Elaboration representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory
Content descriptorAC9MFN06 Number
represent practical situations that involve equal sharing and grouping with physical and virtual materials and use counting or subitising strategies
Elaborations (3)
- Elaboration using materials to role-play equal sharing; for example, sharing pieces of fruit or a bunch of grapes between 4 people and discussing how you would know they have been shared equally; when playing card games where each player is dealt the same number of cards, and counting the number of cards after the deal to ensure they have the same amount
- Elaboration representing situations that involve counting several items; for example, 9 beads or 6 \$1 coins, and sharing them equally between 3 people by subitising or counting each group by ones to decide how many beads or coins each person will receive
- Elaboration exploring instructive games of First Nations Australians that involve sharing; for example, playing Yangamini of the Tiwi Peoples of Bathurst Island to investigate and discuss equal sharing
They copy and continue repeating patterns.
Content descriptorAC9MFA01 Algebra
recognise, copy and continue repeating patterns represented in different ways
Elaborations (4)
- Elaboration recognising, copying and describing different repeating patterns using materials, shapes, sounds and movements during activities and play; for example, making a bead necklace and describing the pattern they have created, such as, “red, blue, green, red, blue, green, red, blue, green”; copying repeating patterns of drumbeats or dance moves during music activities
- Elaboration recognising repeating patterns used at home and in daily activities to help make tasks easier or to solve problems; for example, setting the table to eat
- Elaboration recognising and discussing repeating patterns in images created using dynamic geometric software or a generative artificial intelligence tool, describing what has been repeated in the pattern
- Elaboration recognising and describing repeating patterns that can be observed on Country/Place and in First Nation Australians artwork, cultural performances and material cultures; for example, shell and seed necklaces, dances and songs
Students identify the attributes of mass, capacity, length and duration, and use direct comparison strategies to compare objects and events.
Content descriptorAC9MFM01 Measurement
identify and compare attributes of objects and events, including length, capacity, mass and duration, using direct comparisons and communicating reasoning
Elaborations (4)
- Elaboration using language to describe the measurement attributes of length, mass, capacity and duration, and connecting the words with the appropriate attribute; for example, using words like “tall”, “short”, “wide”, “long”, “high” to describe the attribute of length
- Elaboration directly comparing pairs of objects to say which is longer/shorter, and explaining or demonstrating how they know; for example, standing back-to-back to determine who is taller; choosing to line up the bases of a spoon and fork to decide which is longer and explaining why
- Elaboration starting 2 events at the same time to decide which takes longer; for example, putting on a pair of sandals with buckles or Velcro, describing the duration using familiar terms and reasoning, “I took a longer time because I’m still learning to do up my buckles”
- Elaboration directly comparing pairs of everyday objects from the kitchen pantry to say which is heavier/lighter; for example, hefting a tin of baked beans and a packet of marshmallows; comparing the same pair of objects to say which is longer/shorter and discussing comparisons
They sequence and connect familiar events to the time of day.
Content descriptorAC9MFM02 Measurement
sequence days of the week and times of the day including morning, lunchtime, afternoon and night time, and connect them to familiar events and actions
Elaborations (5)
- Elaboration ordering images of daily events on a string line across the room, and justifying the placement by referring to morning, lunchtime, afternoon, and night time
- Elaboration distinguishing between the days of the school week and weekends, and recognising that the days of the week form a sequence that repeats, with Monday always following on from Sunday
- Elaboration sequencing the events from a story in the order in which they occurred using language like, “This happened first” then “This happened next”
- Elaboration creating, interpreting and discussing classroom rosters; for example, a roster for watering the classroom garden and asking, “Who watered the garden yesterday?” or “Whose turn is it today?”
- Elaboration creating a pictorial diary to show the important events that happen on the various days of the week
Students name, create and sort familiar shapes and give their reasoning.
Content descriptorAC9MFSP01 Space
sort, name and create familiar shapes; recognise and describe familiar shapes within objects in the environment, giving reasons
Elaborations (5)
- Elaboration sorting a collection of shapes into groups based on different features such as the number of sides, colour or size, and describing how they have been sorted
- Elaboration creating a picture using a variety of shapes and a range of materials, including objects to trace around, describing the shapes they have created or used and sharing why they chose each shape in their picture
- Elaboration creating familiar shapes using groups of people; for example, holding hands and creating a circle
- Elaboration recognising and naming shapes that are (close to) rectangles, squares, triangles and circles in component parts of everyday items; for example, on bicycles, toy vehicles or kitchen pantry items
- Elaboration describing and naming shapes within objects that can be observed on Country/Place, recreating and sorting into groups based on their shape
They describe the position and the location of themselves and objects in relation to other objects and people within a familiar space.
Content descriptorAC9MFSP02 Space
describe the position and location of themselves and objects in relation to other people and objects within a familiar space
Elaborations (4)
- Elaboration describing the position of an item in relation to other items in the space using language like “inside”, “underneath” and “on top of”; for example, when asked “Where are the scissors kept?”, responding with “They are in a box, on the bottom shelf at the back of the classroom”
- Elaboration describing where they have moved themselves and items in relation to other items within a space, using familiar terms; for example, playing a hiding game and when asked “Where did you hide the ball?”, responding, “I hid it behind the garbage bin over there near the bench”
- Elaboration describing the position of a robotic toy in relation to other objects as it moves around a familiar space; for example, describing the position of a robotic car as being under the desk or next to the chair
- Elaboration exploring First Nations Australians’ instructive games; for example, Thapumpan from the Wik-Mungkan Peoples of Cape Bedford in north Queensland, describing position and movement of self in relation to other participants, objects or locations
Students collect, sort and compare data in response to questions in familiar contexts.
Content descriptorAC9MFN03 Number
quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning
Elaborations (5)
- Elaboration establishing the language and process of counting, understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the question of “How many?”; for example, saying numbers in sequence while playing and performing actions
- Elaboration using counting to compare the size of two or more collections of like items to justify which collection contains more or less items
- Elaboration using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
- Elaboration discussing how different cultures may have alternative ways of representing the count; for example, discussing how people of the Asia region use an abacus or Chinese hand gestures
- Elaboration using body-tallying that involves body parts and one-to-one correspondence from counting systems of First Nations Peoples of Australia, to count to 20
Content descriptorAC9MFST01 Statistics
collect, sort and compare data represented by objects and images in response to given investigative questions that relate to familiar situations
Elaborations (7)
- Elaboration collecting, and sorting data collected through everyday activities or events; for example, sorting toys into categories, such as “toys that move” and “toys that don’t move”
- Elaboration collecting and deciding how to organise data to answer “Yes/No” questions; for example, “Do more people in our class today have shoes with laces than without?”; explaining that lining up, and matching shoes with and without laces one-to-one will answer the question
- Elaboration creating classroom charts and rosters using stickers to represent data; comparing and interpreting representations
- Elaboration role-playing being a robot that sorts objects into groups based on a set of instructions; for example, imitating a robot designed to pack things away in the classroom or an industrial robot programmed to sort products on an assembly line by colour or shape
- Elaboration role-playing, as a class, at training an artificial intelligence system to recognise objects, asking yes/no questions to gather data to make the best guess about the identification of a mystery object
- Elaboration investigating statistical contexts after reading a story, such as "The Waterhole" by Graeme Base; asking and responding to questions like “What different animals did you see?”, “How many different types of animals were there?” or “Were there more tigers or kangaroos?”
- Elaboration exploring what and how information from the environment is collected and used by First Nations Australians to predict weather events
This achievement standard describes the expected learning for Foundation Mathematics. Use it to plan teaching and assessment with the Australian Curriculum v9.
At a Glance
| Strand | Substrand | CDs | Elaborations |
|---|---|---|---|
| Algebra | — | 1 | 4 |
| Measurement | — | 2 | 9 |
| Number | — | 6 | 23 |
| Space | — | 2 | 9 |
| Statistics | — | 1 | 7 |
| Total | 12 | 52 | |
Frequently Asked Questions
What should students know by the end of Foundation Mathematics?
By the end of Foundation Year, students make connections between number names, numerals and position in the sequence of numbers from zero to at least 20. They use subitising and counting strategies to quantify collections. Students compare the size of collections to at least 20. Read the full standard
How many Content Descriptors support this standard?
12 Content Descriptors support this Achievement Standard (Algebra: 1, Measurement: 2, Number: 6, Space: 2, Statistics: 1).
Is this from the latest Australian Curriculum?
Yes, this Achievement Standard is from the Australian Curriculum version 9.0 (AC v9), the most current version published by ACARA.