This page contains the Learning and Assessment Framework (LAF). The LAF has eight zones: Primitive Modelling, Intuitive Modelling, Sensing, Strategy Exploring, Strategy Refining, Strategy Extending, Connecting and Reflective Knowing.
In the descriptors of each of these zones, reference is made to the assessment tasks that are contained in Booklets 1 and 2 of the original SNMY. These may be accessed here.
In the table below the LAF, the zones are mapped to the Australian Curriculum: Mathematics. It can be seen that there is a broad alignment between the zones and the year levels.
The updated version of the National Numeracy Learning Progression (NNLP) has not yet been published. After publication, we will include a mapping between the LAF and the NNLP.
Learning and Assessment Framework
Primitive Modelling
Can solve simple multiplication and division problems involving relatively small whole numbers.
For example, Butterfly House parts a and b. Tends to rely on drawing, models and countall strategies.
For example, draws and counts all pots for part a of Packing Pots. May use skip counting (repeated addition) for groups less than 5.
For example, to find number of tables needed to seat up to 20 people in Tables and Chairs. Can make simple observations from data given in a task.
For example, Adventure Camp a. Can reproduce a simple pattern.
For example, Tables and Chairs, parts a to e. Multiplicative Thinking (MT) not really apparent as there is no indication that groups are perceived as composite units, dealt with systematically, or that the number of groups can be manipulated to support a more efficient calculation.
Intuitive Modelling
Trusts the count for groups of 2 and 5, that is, can use these numbers as units for counting.
For example, Tables & Chairs part j, Butterfly House part d. Counts large collections efficiently and systematically keeps track of count (for example, may order groups in arrays or as a list) but needs to ‘see’ all groups.
For example, Tiles, Tiles, Tiles part a, Butterfly House part e. May use list and/or doubling as follows: 2 butterflies 5 drops 4 butterflies 10 drops 6 butterflies 15 drops … 12 butterflies 30 drops Can share collections into equal groups/parts.
For example, Pizza Party parts a and b. Recognises small numbers as composite units.
For example, can count equal group and skip count by twos, threes and fives Recognises multiplication is relevant, but tends not to be able to follow this through to solution.
For example, Packing Pots part c, Speedy Snail part a. Can list some of the options in simple Cartesian product situations.
For example, Canteen Capers part a. Orders 2 digit numbers.
For example, partially correct ordering of times in Swimming Sports part a. Some evidence of multiplicative thinking as equal groups or shares are
Sensing
Demonstrates intuitive sense of proportion and partitioning.
For example, Butterfly House part f (partial solution), Missing Numbers part b. Works with ‘useful’ numbers such as 2 and 5, and strategies such as doubling and halving.
For example, Packing Pots part b, Pizza Party part c. May list all options in a simple Cartesian product situation but cannot explain or justify solutions.
For example, Canteen Capers part b. Uses abbreviated methods for counting groups. Uses doubling and doubling again to find 4 groups of, or repeated halving to compare simple fractions.
For example, Pizza Party part c. Beginning to work with larger whole numbers and patterns but tends to rely on count all methods or additive thinking to solve problems.
For example, Stained Glass Windows parts a and b, Tiles, Tiles, Tiles part c.
Strategy Exploring
Solves more familiar multiplication and division problems involving twodigit numbers.
For example: Butterfly House parts c and d • Packing Pots part c • Speedy Snail part a. Tends to rely on additive thinking, drawings and/or informal strategies to tackle problems involving larger numbers and/or decimals and less familiar situations.
For example: • Packing Pots part d • Filling the Buses parts a and b • Tables & Chairs parts g and h • Butterfly House parts h and g • Speedy Snail part c • Computer Game part a • Stained Glass Windows parts a and b. Tends not to explain their thinking or indicate working. Able to partition given number or quantity into equal parts and describe part formally (for example Pizza Party parts a and b). Can locate familiar fractions (for example, Missing Numbers part a). Beginning to work with simple proportion.
For example, can make a start, represent problem, but unable to complete successfully or justify their thinking (for example, How Far part a, School Fair parts a and b).
Strategy Refining
Systematically solves simple proportion and array problems, suggesting Multiplicative Thinking.
For example: • Butterfly House part e • Packing Pots part a • How Far part a. May use additive thinking to solve simple proportion problems involving fractions.
For example: • School Fair part a • Speedy Snail part b. Able to solve simple, twostep problems using a recognised rule or relationship (for example, Fencing the Freeway Part A). However, finds this difficult for larger numbers.
For example: • Tables & Chairs parts k and l • Tiles, Tiles, Tiles part c • Stained Glass Windows part c. Able to order numbers involving tens, ones, tenths and hundredths in supportive context.
For example, Swimming Sports part a. Able to determine all options in Cartesian product situations involving relatively small numbers, but tends to do this additively.
For example: • Canteen Capers part a • Butterfly House parts l and i. Beginning to work with decimal numbers and percent but unable to apply efficiently to solve problems.
For example, Swimming Sports parts a and b, Computer Game part b. Some evidence that multiplicative thinking being used to support partitioning.
For example, Missing Numbers part b. Beginning to approach a broader range of multiplicative situations more systematically.
Strategy Extending
Can work with Cartesian Product idea to systematically list or determine the number of options.
For example: • Canteen Capers part b • Butterfly House parts i and h. Can solve a broader range of multiplication and division problems involving two digit numbers, patterns and/or proportion.
For example: • Tables & Chairs part h • Butterfly House part f • Stained Glass Windows parts b and c Computer Game parts a and b. However, may not be able to explain or justify solution strategy.
For example: • Fencing the Freeway parts b and d • Swimming Sports part b • How Far part b • Speedy Snail part b. Able to rename and compare fractions in the halving family (for example, Pizza Party part c) and use partitioning strategies to locate simple fractions (for example, Missing Numbers part a). Developing sense of proportion (for example, sees relevance of proportion in Adventure Camp part a and Tiles, Tiles, Tiles part b), but unable to explain or justify thinking. Developing a degree of comfort with working mentally with multiplication and division facts.
Connecting
Able to solve and explain onestep problems involving multiplication and division with whole numbers using informal strategies and/or formal recording.
For example: • Filling the Buses part a • Fencing the Freeway part d • Packing Pots part d. Can solve and explain solutions to problems involving simple patterns, percent and proportion.
For example: • Fencing the Freeway part c • Swimming Sports part b • Butterfly House part g • Tables & Chairs parts g and l • Speedy Snail part c • Tiles, Tiles, Tiles parts b and c • School Fair part a • Stained Glass Windows part a • Computer Game part b • How Far part b. May not be able to show working and/or explain strategies for situations involving larger numbers.
For example: • Tables & Chairs parts m and k • Tiles, Tiles, Tiles part c. May not be able to show working and/or explain strategies for less familiar problems.
For example: • Adventure Camp part b • School Fair part b • How Far part c. Locates fractions using efficient partitioning strategies.
For example, Missing Numbers part a. Beginning to make connections between problems and solution strategies and understand how to communicate this mathematically.
Reflective Knowing
Can use appropriate representations, language and symbols to solve and justify a wide range of problems involving unfamiliar multiplicative situations including fractions and decimals.
For example: • Adventure Camp part b • Speedy Snail part b. Can justify partitioning.
For example, Missing Numbers part b.Can use and formally describe patterns in terms of general rules.
For example, Tables and Chairs, parts m and k. Beginning to work more systematically with complex, openended problems.
For example: • School Fair part b • Computer Game part c.
Mapping to the Australian Curriculum: Mathematics
LAF ZONES (Siemon et al., 2006) 
LINKS TO ACARA (2015) 

Zone 1:
Multiplicative thinking (MT) not really apparent as no indication that groups are perceived as composite units, dealt with systematically, or that the number of groups can be manipulated to support more efficient calculation. 
Foundation Year:
Problem Solving: use familiar counting sequences to solve unfamiliar problems. Year 1:
Problem Solving: use familiar counting sequences to solve unfamiliar problems. Year 2:

Zone 2:
Some evidence of MT as equal groups/shares seen as entities that can be counted. 
Year 2:
Understanding: connecting number calculations with counting sequences and partitioning and combining numbers flexibly. Fluency: counting numbers in sequences readily. Year 3:
Understanding: partitioning and combining numbers flexibly and representing unit fractions Fluency: recalling multiplication facts 
Zone 3:
Beginning to work with larger whole numbers and patterns but tends to rely on count all methods or additive thinking (AT). 
Year 4:
Problem Solving: using properties of numbers to continue patterns Reasoning: using generalising from number properties and results of calculations and deriving strategies for unfamiliar multiplication and division tasks 
Zone 4:

Year 4:
Understanding: partitioning and combining numbers flexibly Year 5:
Understanding: comparing and ordering fractions and decimals and representing them in various ways Problem Solving: formulating and solving authentic problems using whole numbers 
Zone 5:

Year 5:
Reasoning: investigating strategies to perform calculations efficiently and continuing patterns involving fractions and decimals Year 6:
Fluency: calculating simple percentages, converting between fractions and decimals, and using operations with fractions, decimals and percentages Problem Solving: formulating and solving authentic problems using fractions, decimals and percentages 
Zone 6:
Developing capacity to work mentally with multiplication and division facts 
Year 6:
Understanding: representing fractions and decimals in various ways and describing connections between them Reasoning: explaining mental strategies for performing calculations Year 7:
Fluency: calculating accurately with integers and representing fractions and decimals in various ways Problem Solving: formulating and solving authentic problems using numbers 
Zone 7:

Year 7:
Understanding: describing patterns in uses of indices with whole numbers, and connecting the laws and properties of numbers to algebraic terms and expressions Fluency: calculating accurately with integers and representing fractions and decimals in various ways Problem Solving: formulating and solving authentic problems using numbers Reasoning: applying the number laws to calculations and applying an understanding of ratio Year 8:
Understanding: identifying commonalities between operations with algebra and arithmetic. 
Zone 8:

Year 8:
Understanding: describe patterns involving indices, connecting rules for linear relations and their graphs. Fluency: includes formulating, and modelling practical situations involving ratios, profit and loss, and areas and perimeters of common shapes. Year 9:
Understanding: describe the relationship between graphs and equations. Fluency: applying the index laws to expressions with integer indices. 
Mapping to the National Numeracy Learning Progression
LAF ZONES (Siemon et al., 2006) 
LINKS TO ACARA (2015) 

Zone 1:
Multiplicative thinking (MT) not really apparent as no indication that groups are perceived as composite units, dealt with systematically, or that the number of groups can be manipulated to support more efficient calculation. 
Foundation Year:
Problem Solving: use familiar counting sequences to solve unfamiliar problems. Year 1:
Problem Solving: use familiar counting sequences to solve unfamiliar problems. Year 2:

Zone 2:
Some evidence of MT as equal groups/shares seen as entities that can be counted. 
Year 2:
Understanding: connecting number calculations with counting sequences and partitioning and combining numbers flexibly. Fluency: counting numbers in sequences readily. Year 3:
Understanding: partitioning and combining numbers flexibly and representing unit fractions Fluency: recalling multiplication facts 
Zone 3:
Beginning to work with larger whole numbers and patterns but tends to rely on count all methods or additive thinking (AT). 
Year 4:
Problem Solving: using properties of numbers to continue patterns Reasoning: using generalising from number properties and results of calculations and deriving strategies for unfamiliar multiplication and division tasks 
Zone 4:

Year 4:
Understanding: partitioning and combining numbers flexibly Year 5:
Understanding: comparing and ordering fractions and decimals and representing them in various ways Problem Solving: formulating and solving authentic problems using whole numbers 
Zone 5:

Year 5:
Reasoning: investigating strategies to perform calculations efficiently and continuing patterns involving fractions and decimals Year 6:
Fluency: calculating simple percentages, converting between fractions and decimals, and using operations with fractions, decimals and percentages Problem Solving: formulating and solving authentic problems using fractions, decimals and percentages 
Zone 6:
Developing capacity to work mentally with multiplication and division facts 
Year 6:
Understanding: representing fractions and decimals in various ways and describing connections between them Reasoning: explaining mental strategies for performing calculations Year 7:
Fluency: calculating accurately with integers and representing fractions and decimals in various ways Problem Solving: formulating and solving authentic problems using numbers 
Zone 7:

Year 7:
Understanding: describing patterns in uses of indices with whole numbers, and connecting the laws and properties of numbers to algebraic terms and expressions Fluency: calculating accurately with integers and representing fractions and decimals in various ways Problem Solving: formulating and solving authentic problems using numbers Reasoning: applying the number laws to calculations and applying an understanding of ratio Year 8:
Understanding: identifying commonalities between operations with algebra and arithmetic. 
Zone 8:

Year 8:
Understanding: describe patterns involving indices, connecting rules for linear relations and their graphs. Fluency: includes formulating, and modelling practical situations involving ratios, profit and loss, and areas and perimeters of common shapes. Year 9:
Understanding: describe the relationship between graphs and equations. Fluency: applying the index laws to expressions with integer indices. 