Mathematics: Ages Nine to Twelve
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Mathematics Overview
The Montessori mathematics curriculum for children aged 9 to 12 is grounded in the belief that all children have the capacity to develop a ‘mathematical mind’—a mind that not only calculates, but also reasons, imagines, models, and solves problems with creativity and logic.
Mathematical learning begins in the Children’s House, where children are first presented and then actively explore fundamental concepts through concrete materials. These materials embody mathematical concepts in physical form, allowing young learners to engage the hand and the mind together to internalise abstract concepts, sometimes without the need for words, which unhooks language processing from mathematical learning.
Each Montessori mathematics lesson, in both the Children’s House and in environments prepared for children over six, has both a direct aim (the concept or skill being presented) and an indirect aim (a more abstract aim which the child will achieve without being aware of it). The indirect aim prepares children for more advanced concepts they will meet later in the curriculum. Dr Montessori observed that, when children move through the 6- 9 curriculum at their own pace working first with materials through to exploring increasingly complex ideas and abstraction, the learning is deeper and more lasting.
Beyond the age of six, children continue to learn mathematical principles through the manipulation of concrete materials however they begin to seek freedom from the materials and strive to solve problems mentally and abstractly. The materials become stepping-stones only, keys that open the door to abstraction whenever a child is ready. Children at this stage, generalise from their experience with the concrete experience, often creating their own formulae and problem-solving strategies.
The Montessori curriculum, in many areas, extends children in the 9-12yr olds classroom beyond conventional standards and expectations. Children continue their deep work with the decimal system, ready to explore, through both a mathematical and historical perspective, alternative number systems. These extensions challenge students to think flexibly and reinforce and develop deep conceptual understanding.
The mathematics curriculum considers the social constructions of mathematics and a need to acknowledge the personal connections that students may have to their own culture or in other cultures where they live. This inclusive vision embraces the traditional Western views of mathematics alongside the mathematics that sits outside the realms of academia, informed by multiple standpoints and contexts. This ethnomathematical approach values the existing culturally connected knowledge of First Nations peoples’ learning of mathematics (Rioux, 2024; Ewing, Cooper, Baturo, Matthews & Sun, 2010).
Students also learn to connect concepts across strands. They may apply compound multiplication to fractions and decimals, extend their understanding of geometric patterns to algebraic thinking, or explore the relationship between square roots and area. These rich connections ensure that students don’t just do mathematics—they truly understand it.
Montessori educators carefully observe and guide, offering help only when the children have had a chance to work with a problem and determined a few solutions for themselves. This scaffolds and allows embedding of the mathematical process to ensure that mathematics doesn’t isolate computation from understanding. Instead, it integrates mathematical processes—including problem-solving, reasoning, modelling, statistical investigation, and computational thinking—throughout the curriculum.
Montessori environments invite children to explore mathematics in a wide range of real-world contexts—measuring spaces, time and schedules, sharing food, creating and measurement, shopping, money and budgeting or games and probability. Command cards and self-directed and/or group projects offer meaningful opportunities for independent exploration and opportunities for real-world applications. Through these, children apply core mathematical operations (addition, subtraction, multiplication, and division) across whole numbers, decimals, fractions, and negative numbers, often extending into squaring, cubing, and extracting roots. These tasks mirror the process of mathematical modelling, where students use mathematics to understand and make decisions about real phenomena. In doing so, they learn to plan and make assumptions, recognise and consider patterns, and formulate, analyse, reflect upon and communicate solutions.
This process of learning encourages Montessori learners to naturally develop computational thinking: they decompose problems, identify patterns, make generalisations, and even create their own algorithms (step-by-step procedures). The skills of computational thinking are cultivated through hands-on logic work, geometric constructions, and dynamic exploration with materials that mirror model-building and simulation, laying a strong foundation for future engagement with digital technologies and AI systems.
Children conduct informal statistical investigations early on—such as conducting surveys of their classmates’ opinions, comparing measurements, graphing temperatures, conducting audits, or tracking plant growth. As they mature, they learn to gather, interpret, and analyse data more rigorously, using these investigations to ask questions, test hypotheses, and evaluate variability. They also begin to explore probability through experimentation within mathematics and across their learning, by using Montessori materials to simulate outcomes and make predictions, linking statistical thinking with real-life uncertainty.
As nine-to-twelve-year-old children develop in mathematical abstraction, advancing into what Piaget called the formal operational stage, they may begin to incorporate digital tools such as spreadsheets, chance simulations, graphing software, chance simulations and dynamic geometry applications. These platforms allow children to simulate variation, analyse large data sets, and test mathematical models dynamically—essential skills in a world shaped by AI, automation, and data science.
Taking part in and creating activities such as mental maths challenges, maths games with patterns, maths story problems and step-based problem-solving which use algorithmic thinking etc also assist children in this stage to develop computational fluency.
Digital tools may also be accessed to help children apply mathematical operations, transformations, and procedures to diverse data types—numbers, shapes, equations, or even symbolic expressions. As children gain confidence, they may experiment with algorithm-based processes, exploring how variables change outcomes or impact graphical models.
In Montessori classrooms, the aim is not merely to produce children who can pass tests or memorise formulas, but to cultivate independent, flexible, and creative thinkers. The mathematical mind is not a talent for the few—it is, in the view of Montessori, the birth-right of every child.
History of Mathematics 3.MA.010
Knowledge, Skills and Understanding
Typically, children will:
.01 Explore stories about the history of numbers and mathematics
.02 Research ancient number systems
First Nations Australians
Babylonian
Egyptian
Mayan
Chinese
Hindu-Arabic
Roman
.03 Explore the history of the number system used in our culture: the decimal system
.04 Explore and research history of mathematical invention and discovery
.05 Study ancient and modern mathematicians
.06 Study ancient and contemporary numeration systems other than the decimal system
＋ Materials and Activity
Activities include:
- great lesson: the Story of Numbers
- independent research
- creating charts, models and timelines
- counting and calculating using earlier number systems eg Roman numerals.
- lessons and demonstrations
- research projects including preparing biographies of mathematicians and accounts of mathematical systems from other times and places.
- experimenting with other number systems to count and perform simple calculations e.g., Roman numerals noting the consequences of having no zero; base two/binary, base 5; base 60
- research projects e.g., use of base 2 in First Nations Australians communities and in computer-based technology; history and use of base 60 to measure angles and calculate time
Resources include:
- charts, card material and artefacts
- research and reference materials (paper-based, digital, web-based, multimedia)
- Story of Numbers charts
- Timeline of Mathematicians
- teacher and student-made concrete material for working with other number systems
Memorisation: review and extension 3.MA.020
Knowledge, Skills and Understanding
Typically, children will:
.01 Review and consolidate knowledge of number facts (addition, subtraction, multiplication, division)
.02 Develop automaticity, speed and accuracy of number fact recall and application to mastery level
.03 Understand the connection between multiplication and division as inverse operations and use this to develop families of number facts
＋ Materials and Activity
Activities include:
- activities to consolidate memorisation of number facts
- activities to increase automaticity, speed and accuracy of number fact recall and application, including quizzes and speed tests, including online websites (e.g., Mental Math)
Resources include:
- concrete materials as needed (e.g., flash cards)
- practice activities and games
- paper-based, digital, web-based and/or multimedia resources (e.g., Mental Math)
＋ Links to Australian Curriculum (ACv9)
AC9M5A01
Multiples of Numbers 3.MA.030
Knowledge, Skills and Understanding
Typically, children will:
.01 Complete, review and consolidate knowledge of multiples
＋ Materials and Activity
Activities include:
- activities to complete, review and consolidate knowledge of multiples
Resources include:
- concrete materials, charts and tables as needed
- paper-based, digital, web-based and/or multimedia resources.
LCM and GCF (HCF) 3.MA.040
Knowledge, Skills and Understanding
Typically, children will:
.01 Find lowest common multiple (LCM)
.02 Find greatest (highest) common factor (GCF/HCF)
＋ Materials and Activity
Activities include:
- demonstrations and lessons with pegboard
- finding divisors using the pegboard
- finding LCM and GCF/HCF using pegboard
- finding LCM and GCF/HCF using prime factors
- calculating LCM and GCF/HCF abstractly
- solving word problems
- using knowledge of LCM in operations with fractions.
Resources include:
- pegboard, colour-coded pegs and labels
- card material
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Divisibility 3.MA.050
Knowledge, Skills and Understanding
Typically, children will:
.01 Explore, formulate and recognise rules for establishing divisibility of numbers
＋ Materials and Activity
Activities include: - exploring divisibility using golden bead material - making divisibility charts - applying knowledge of prime factors to study of divisibility - identifying divisibility rules for number groups.
Resources include: - golden bead material - pegboard, colour-coded pegs and labels - divisibility tables and charts - paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
AC9M5N10
All Operations 3.MA.060
Knowledge, Skills and Understanding
Typically, children will:
.01 Review and consolidate knowledge of operations with whole numbers
.02 Master operations with whole numbers
.03 Perform complex operations with whole numbers
＋ Materials and Activity
Activities include: - activities to review and consolidate mastery of the four operations with whole numbers - activities to increase automaticity, speed and accuracy of calculations - using technology to verify answers e.g., calculators - applying knowledge of decimal system, memorisation and operations in a range of practical contexts e.g., money, measurement.
Resources include: - concrete materials as needed - command cards; word problems - paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
AC9M5N08 AC9M5N09
Multiplication 3.MA.070
Knowledge, Skills and Understanding
Typically, children will:
.01 Extend skills in mental multiplication
.02 Develop skill in cross multiplication
.03 Demonstrate proficiency in mental calculation
＋ Materials and Activity
Activities include:
- group activities with the bank game
- mental multiplication with continuous exchanging
- verifying answers.
- demonstrations and lessons
- forming and solving long multiplications using cross multiplication
- making charts and tables
- writing products directly onto paper without concrete material
- using technology to verify answers.
Resources include:
- bank game card material
- paper-based, digital, web-based and/or multimedia resources.
- multiplication checkerboard and extensions
- calculators
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
AC9M5N09
Division 3.MA.080
Knowledge, Skills and Understanding
Typically, children will:
.01 Complete and master concept and process of distributive division with multi-digit divisors
.02 Complete and master concept and process of group division with multi-digit divisors
.03 Develop skill in division with zero in dividend and divisor
＋ Materials and Activity
Activities include:
- demonstrations and lessons
- forming long divisions and solving using distributive division, first with, and later without, concrete material (racks and tubes), recording calculations including intermediate remainders
- forming long divisions and solving using group division, first with, and later without, concrete material (stamp game), recoding calculations
- verifying answers using concrete material and technology.
Resources include:
- racks and tubes material
- stamp game
- calculators
- command cards
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Fractions 3.MA.090
Knowledge, Skills and Understanding
Typically, children will:
.01 Review and consolidate knowledge of fractions
.02 Build mastery in the use of fractions
.03 Review and consolidate knowledge of equivalence
.04 Review and consolidate ability to reduce fractions to lowest terms
.05 Review equivalent fractions and variation in notation for equivalent fractions
.06 Explore the following types of fractions and corresponding notation:
proper and improper fractions
mixed numbers
unlike fractions
.07 Find the lowest common multiple of unlike denominators
.08 Review adding and subtracting fractions with same denominators
.09 Add fractions with unlike denominators
.10 Subtract fractions with unlike denominators
.11 Multiply a whole number by fraction
.12 Multiply a fraction by a fraction
.13 Divide a whole number by a fraction
.14 Divide a fraction by a fraction
.15 Divide fractions using group division
.16 Perform complex operations with fractions
＋ Materials and Activity
Activities include: - activities to consolidate knowledge of fractions and fraction notation - activities to consolidate knowledge of equivalence - activities to consolidate ability to reduce fractions to lowest terms, first with concrete material and later abstractly - exploring variety of ways for representing fractions e.g., shaded squares in a grid or shaded sectors of a pie graph - activities linking knowledge about fractions with the solution of real life problems
- activities with concrete materials and manipulable labels to explore improper fractions, mixed numbers and unlike fractions
- creating charts and booklets
- creating own problems (progressing from concrete representation accompanied by notation to increasingly abstract representation).
Resources include: - metal fraction insets (to tenths) - fraction circles box of manipulable cut-out fractions - fractions activity sets
- decimal fraction exercise activity sets
- labels (words and symbols)
- geometry charts
- command cards; word problems
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Decimals 3.MA.100
Knowledge, Skills and Understanding
Typically, children will:
.01 Build knowledge of decimals to millionths (0.000001)
.02 Use notation for decimals to millionths (0.000001)
03 Add and subtract decimals using concrete materials
.04 Add and subtract decimals abstractly, using estimation, rounding and digital tools to check
.05 Multiply and divide decimals, using concrete materials to solve
.06 Multiply and divide decimals by powers of 10 without materials, using estimation, rounding and digital tools to check
.07 Multiply and divide decimals abstractly, using estimation, rounding and digital tools to check
.08 Explore repeating and non-repeating decimal numbers
＋ Materials and Activity
Activities include:
- activities with concrete materials that reveal relationship between fractions and decimals
- identifying and reading aloud decimal numerals to millionths
- forming decimals to millionths in quantities and symbols
- matching quantities and symbols
- counting activities forwards and back
- reading and notation activities: comparing decimal quantities and notation; placing the decimal point; comparing whole numbers and decimal numbers; forming complex numbers
- making charts; pinwheel, candelabra
- representing decimal fractions graphically in a variety of ways
- demonstrations and lessons in adding and subtracting decimals, with exchanging, using concrete materials and corresponding notation
- activities multiplying decimal numbers by 10, 100 and 1000 using concrete material
- demonstrations and lessons in multiplying decimal numbers by whole numbers, whole numbers by decimal numbers and decimal numbers by decimal numbers, using concrete material
- demonstrations and lessons in dividing decimal numbers by whole numbers, whole numbers by decimal numbers and decimal numbers by decimal numbers, using concrete material
- forming and solving own problems with decimal numbers
- recording and verifying answers
- formulating rules and notation for abstract calculation i.e. without concrete material
- verifying answers using concrete material and technology.
- recognising and identifying a repeating decimal
- using technology to explore repeating and non-repeating numbers.
Resources include:
- fraction insets
- yellow board of decimal hierarchies, colour-coded beads, charts and colour-coded cards
- command cards
- lined and grid paper
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Percentage 3.MA.110
Knowledge, Skills and Understanding
Typically, children will:
.01 Explore the concept of percentage and compare to fractions and decimals
.02 Apply knowledge of percentages to solve practical problems s
＋ Materials and Activity
Activities include:
- demonstrations and exercises with concrete materials to explore the relation between fractions, decimals and percentages
- converting fractions such as thirds and sixths to decimals and percentages
- calculating 1% and10%
- exploring fractions of percentages
- formulating rules and notation for calculating percentage problems
- solving percentage problems e.g., research projects, discounting, profit and loss, simple interest, compound interest
- applying knowledge of percentage to practical problems.
Resources include:
- fraction insets
- yellow board of decimal hierarchies, charts and card material
- hundredth circle
- commercial resources
- command cards; word problems
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Powers of Numbers 3.MA.120
Knowledge, Skills and Understanding
Typically, children will:
.01 Understand the concept of powers of numbers
.02 Express any number as a power of 10
.03 Sequence powers geometrically
.04 Use exponential notation
.05 Use powers in operations
＋ Materials and Activity
Activities include:
- reviewing knowledge of multiples applied making squares and cubes
- story: the kingdom of powers to introduce 0 power, 1st power, 2nd power, 3rd power
- activities to identify a unit and increase its power and to label each power
- demonstrations and lessons on the Kingdoms of 10 and of 1
- drawing and labelling activities
- demonstrations to build knowledge of vocabulary for talking about the notation of powers of numbers: base, index
- using power notation to label bead squares and bead cubes
- labelling and sequencing powers represented geometrically
- comparing size and shape of powers in a geometric sequence
- using power notation to write very large and very small numbers
- adding and subtracting; multiplying and dividing powers of numbers (same base/different base)
- building the algebraic formula for expanding powers, and operations with powers
Resources include:
- wooden hierarchical material
- cabinet of colour-coded bead chains, bead squares and bead cubes
- power of 2 material
- command cards
- calculators
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Squaring 3.MA.130
Knowledge, Skills and Understanding
Typically, children will:
01. Review and consolidate knowledge of squaring
02. Extend knowledge and application of squaring
03. Perform operations with squares (addition, subtraction, multiplication, division, combined operations)
＋ Materials and Activity
Activities include: - constructing squares of numbers 1-10 using concrete material - calculating the passage from one square to another square using concrete materials i.e. calculating the difference between the squares and recording calculation - notating squares of single numbers - completing and reviewing the decanomial (bead array and numerical card layout) - building the algebraic formula for squaring - building the algebraic decanomial (card layout and notation) - solving problems with squares of numbers (four operations), first with concrete material, and later without - applying knowledge of squaring to decimal numbers using concrete material - verifying squares of numbers using concrete material and technology.
Resources include: - golden bead materials - box of bead bars - numerical and algebraic decanomial card material - pegboard, colour-coded pegs and labels - colour-coded decimal beads - colour-coded guide squares - command cards - calculators - paper-based, digital and web-based resources.
＋ Links to Australian Curriculum (ACv9)
AC9M5A02
Squares of Binomials and Trinomials 3.MA.140
Knowledge, Skills and Understanding
Typically, children will:
.01 Review and extend squaring of binomials (a+b)2 and trinomials (a+b+c)2
.02 Use binomial and trinomial representation and notation to expand squares of 2- and 3-digit numbers
.03 Find products of binomial and trinomial squares:
units only
tens and units
.04 Consolidate and extend notation of the squares of 2- and 3-digit numbers represented as binomials and trinomials
.05 Identify and manipulate the terms of expanded binomial (a+b)2 and trinomial (a+b+c)2 expressions
.06 Write and solve equations that include squares of numbers and sums of binomials and trinomials squared
＋ Materials and Activity
Activities include:
- analysing 100-bead square into a binomial or trinomial
- building binomial and trinomial squares with coloured-coded bead bars and golden bead material
- reviewing representation of binomial and trinomial squares using concrete materials and notation
- manipulating and constructing concrete representations of binomial and trinomial squares and labelling the terms
- using concrete material and manipulable labels to build and balance equations, and isolate unknowns
- using colour-coded pegs on a pegboard to represent products and squares of 2- and 3-digit numbers
- representing products and squares of 2- and 3-digit numbers symbolically using binomial and trinomial notation
- calculating products and squares of binomials and trinomials using concrete and symbolic representation
- forming squares of decimal numbers using colour-coded pegs on a pegboard
- using guide squares to calculate squares of 2- and 3-digit numbers represented as binomials and trinomials
- building the algebraic formula for calculating the square of a binomial and trinomial
- substituting numerical terms with algebraic terms in equations
- forming equations and solving for unknown terms using algebraic notation, and recording answers
- verifying answers using concrete material and technology.
Resources include:
- pegboard, colour-coded pegs and labels
- colour-coded guide squares
- golden bead material
- box of bead bars
- bead squares
- pegboard and pegs
- grid paper and coloured pencils
- binomial and trinomial cubes
- wooden cubing material
- command cards
- calculators
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
AC9M5A02 AC9M6A01
Square Roots 3.MA.150
Knowledge, Skills and Understanding
Typically, children will:
.01 Understand and work with the concept of square root of a number
.02 Determine the square root of a 2- and 3-digit number represented as a binomial or trinomial
.03 Find square roots abstractly
＋ Materials and Activity
Activities include: - naming simple squares and identifying their roots using concrete material - drawing and labelling squares and labelling their roots - finding square roots of 2- and 3-digit numbers represented as binomial and trinomial squares using colour-coded pegs, and recording answers - estimating square roots using concrete materials and records of square root calculations - building the algebraic formula for calculating square root - guided abstract calculation of square roots and recording - verifying answers using concrete material and technology.
Resources include: - golden bead materials - bead squares - pegboard and colour-coded pegs - guide squares and handmade charts - graph paper - command cards - calculators - paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
AC9M5A02
Cubing 3.MA.160
Knowledge, Skills and Understanding
Typically, children will:
.01 Build knowledge of the concept of the cube of a number
.02 Cube successive numbers using concrete material
.03 Perform cubing calculations
＋ Materials and Activity
Activities include: - demonstrations and lessons - using colour-coded concrete material to recognise and name simple cubes, and identify their roots - using concrete material to construct cubes - cubing binomials and trinomials using concrete materials and labelling the parts - building the algebraic formula for cubing - constructing cubes with decimal numbers using concrete material.
Resources include: - bead cubes - wooden cubing material - command cards - calculators
- Paper-based, digital, web-based and/or multimedia resources
＋ Links to Australian Curriculum (ACv9)
AC9M5A02 AC9M6A01
Cube Root 3.MA.170
Knowledge, Skills and Understanding
Typically, children will:
.01 Understand and work with the concept of cube root of a number
.02 Determine the cube root of 2- and 3-digit numbers represented as a binomial or trinomial
.03 Find cube roots abstractly
＋ Materials and Activity
Activities include: - finding cube roots of 2- and 3-digit numbers represented as binomial and trinomial cubes using wooden cubing material, and recording calculations and answers - building the algebraic formula for calculating cube root - guided abstract calculation of cube roots and recording - verifying answers using concrete material, ‘backtracking’ and technology.
Resources include: - bead cubes - wooden cubing material - binomial cube - trinomial cube - hierarchical trinomial cube - box of unit cubes - handmade charts - command cards - calculators - paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
AC9M5A02
Algebra 3.MA.180
Knowledge, Skills and Understanding
Typically, children will:
.01 Find unknown values in numerical equations involving addition and subtraction
.02 Identify, explain and create addition and multiplication patterns using algorithms
.03 Create and use algorithms to experiment with factors, multiples and divisibility
.04 Find unknown values in numerical equations involving multiplication and division
.05 Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
.06 create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns
＋ Materials and Activity
Activities include:
- using concrete material to find unknown terms in simple linear equations, notating calculations using algebraic conventions and recording answers
- forming equations and solving for unknown terms using algebraic notation and recording answers.
Resources include:
- colour-coded concrete materials
- manipulable signs and symbols
- command cards
- calculators
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Positive and Negative Numbers 3.MA.190
Knowledge, Skills and Understanding
Typically, children will:
.01 Understand the concept of integers
.02 Explore positive and negative numbers in different contexts (temperature, elevation, financial)
.03 Use positive and negative numbers in operations
.04 Locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane
＋ Materials and Activity
Activities include:
- demonstrations and lessons
- using concrete material, form and compare positive and negative numbers
- locate integers on number lines and coordinates on Cartesian planes
- forming and solving problems with positive and negative numbers.
Resources include:
- negative snake game
- number lines
- box of bead bars
- division skittles
- command cards; word problems
- paper-based, digital, web-based and/or multimedia resources.
＋ Links to Australian Curriculum (ACv9)
Rational and Irrational Numbers 3.MA.200
Knowledge, Skills and Understanding
Typically, children will:
.01 Explore the concept of rational and irrational numbers
.02 Recognise and use notation for rational and irrational numbers
.03 Perform calculations with rational and irrational numbers
.04 Use mathematical modelling to solve practical problems involving natural and rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made
＋ Materials and Activity
Activities include:
- Activities with concrete materials, recording answers
- Using concrete materials to form rational and irrational numbers
- Making charts and booklets
- Activities to explore rational and irrational numbers using technology
- Calculation activities with rational and irrational numbers.
- Naming simple squares and their roots
- Drawing and labelling squares and their roots
- Finding square roots with concrete materials, recording answers
- Calculating square roots abstractly
- Using technology to calculate square roots
Resources include:
- Number line
- Box of bead bars
- Fraction insets
- Colour-coded decimal number cards
- Pegboard, colour-coded pegs
- Guide squares
- Handmade charts
- Command cards
- Paper-based, digital, web-based and/or multimedia resources
＋ Links to Australian Curriculum (ACv9)
Data and Probability 3.MA.210
Knowledge, Skills and Understanding
Typically, children will:
.01 Review and extend knowledge of data collection, representation and interpretation
.02 Identify and extend patterns in data and number
.03 Use vocabulary for talking about data and data representation: set, average, mean-median-mode; quantity-category, continuous-discrete; cluster-outlier; sample-census, spreadsheet, database, distribution, frequency, range, statistics
.04 Construct simple line graphs to represent continuous change and use vocabulary for talking about the parts of line graphs (axes, horizontal axis, vertical axis, scale, point, plot)
.05 Conduct statistical investigations, collect and interpret data, choose relevant displays and communicate results. Build a repertoire of data collection and representation techniques and tools, including tables and matrices, bar graphs and pie graphs, flowcharts, electronic database and spreadsheet
.06 Interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape
.07 Identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions
.08 Describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring
.09 Conduct repeated chance experiments including those with and without equally likely outcomes
.10 Recognise that probabilities lie on numerical scales (e.g., of 0-1 or 0%-100%) and use estimation to assign probabilities that events occur in a given context, using fractions, percentages and decimals
＋ Materials and Activity
Activities include:
- Designing own research questions (for topics across the curriculum) that involve data collection and interpretation (whole class, small group and individual projects)
- Collecting data using the most effective technique to answer a research question
- Selecting the most effective way of representing the data to answer a research question
- Using computer databases and spreadsheet programs (e.g., apple numbers, google sheets, microsoft excel)
- Interpreting and evaluating data represented in a variety of ways e.g., in the media, textbooks, reference materials
- Displaying data using presentation software (e.g., keynote, powerpoint, google slides, or prezi)
- Solving puzzle problems with patterns to be identified and extended
- Study of codes (e.g., morse code, semaphore flags, etc.)
- Applying interpretation and evaluation of different representations of data across the curriculum e.g., as evidence in persuasive texts - discussions, essays, debates, spoken presentations; to predict probability.
- Discussing and listing all the possible outcomes of an activity
- Estimate the probabilities of an activity (e.g., estimating the probability of pulling a heart from a deck of cards)
- Conducting experiments to test results and recording outcomes
Resources include:
- Textbooks
- Materials for data collection and drawing (paper-based and electronic)
- Command cards; word problems
- Objects and events in the environment
- Tally sheets
- Graph paper and drawing equipment (paper-based and electronic)
- Paper-based, digital, web-based, and/or multimedia resources
- Chance materials, e.g., coins, dice, spinners, playing cards
- Innovation Lab at TME 2025
＋ Links to Australian Curriculum (ACv9)
AC9M4ST01
AC9M5ST01
AC9M4ST02
AC9M5ST02
AC9M4ST03
AC9M5ST03
AC9M6ST03
AC9M6ST01
AC9M6ST02
AC9M4P01
AC9M4P02
AC9M5P01
AC9M5P02
AC9M6P02
AC9M6P01
Digital Systems 3.MA.220
Knowledge, Skills and Understanding
Typically, children will:
.01 Identify and explore a range of digital systems with peripheral devices for different purposes, and transmit different types of data
.02 Collect, access and present different types of data using simple software to create information and solve problems
.03 Define problems with given or co-developed design criteria and by creating user stories
.04 Explore and explain how digital systems use numbers and data can be represented by zeros and ones
.05 Explore the digital instructional language of coding, including algorithms involving sequencing, comparison operators (branching) and iteration
.06 Evaluate existing and student solutions against the design criteria and user stories and their broader community impact
.07 Implement algorithms as visual programs involving control structures, variables and input
.08 Select and use appropriate digital tools effectively to share content online, plan tasks and collaborate on projects, demonstrating agreed behaviours
.09 Explain the creation and permanence of their digital footprint and consider privacy when collecting user data
＋ Materials and Activity
Activities include:
- Disassembling and reassembling non-working computer tower system to identify parts and their function(e.g., cpu, usb and ethernet ports, memory, keyboard, microphone and other input devices, speakers and other output devices, etc.)
- Investigating, then mapping or drawing the computer network in the school, including wireless and wired systems
- Monitoring solar energy usage from panels on school measured by online energy usage software
- Using Lego Mindstorms to program Lego robots or Scratch to program a tello drone or similar device with simple commands
- Using online library management software to checkout / return loaned books as class chore; conduct catalogue searches
- Using usb accessories to collect data for science experiments (e.g., to measure soil temperature or water purity, digital microscopes, etc)
- Activities to build understanding of what is meant by “user stories” act(incorporating knowledge of user needs and wants)
- Explore various comparison operators such as “If…then” to determine pathways in games, short narratives etc
- Explore comparison operators by including various alternative inputs
- Apply understandings to real-world scenarios
- Using online library management software to checkout / return loaned books as class chore; conduct catalogue searches
- Using usb accessories Using digital tools to collect data for science experiments (e.g., to measure soil temperature or water purity, analysis through digital microscopes, etc)
- Explore the binary language of digital systems through codes and simple games
- Using online collaborative systems (e.g., google classroom, office teams, hangouts and online calendars) to organise classroom and school events and encourage their use in students’ own lives and to work collaboratively with classmate/s on research and presentations
- Organising files, images or other collected data into folders with a hierarchical structure
- Learning chess and recording all moves on paper
- Solving wooden logic puzzles
- Using coding program such as scratch or python to write simple programs that solve problems on the basis of user choices
- Following and developing multi-stepped algorithms,that respond to variables, to solve both real-world and word problems
- Create or co-create animations, composing digital music or build a personal page on a website using appropriate software
- Discuss how existing and student solutions satisfy the design criteria and user stories
- Deliver respectful peer feedback on design projects
- Design a user interface to meet a specified user need
- Identify what is meant by “personal data” and what this may include
- Access their school account using a memorised password and explain why it should be easy to remember, but hard for others to guess
- Access multiple personal accounts using unique passphrases and explain the risks of password re-use
Resources include:
- Following and developing multi-stepped algorithms to solve both real-world and word problems that respond to variables
- Maths materials
- Problem solving materials
- Procedural texts and instructions
- Manipulative building materials (e.g. Lego)
- Programmable devices including drones, robots, etc.
- Computers and other digital devices
- Strategy games (e.g. Chess)
- Logic puzzles and materials
- Coding apps and programs (e.g. Scratch)
- Age-appropriate digital programs for creating basic graphs and visualisation
- Flowchart templates (teacher-made or sourced)
- Innovation Lab at TME 2025
- Binary code supports e.g ASCII, Unicode
- Guest speakers/School IT support
- Online safety resources e.g:
- Online safety basics | eSafety Commissioner
- Cyber Safety for Kids | ChildSafe Australia -
- ThinkUKnow
＋ Links to Australian Curriculum (ACv9)
AC9TDI4K01
AC9TDI4K02
AC9TDI6K01
AC9TDI6K02
AC9TDI4K03
AC9TDI6K03
AC9TDI4P01
AC9TDI6P01
AC9TDI6K03
AC9TDI6K04
AC9TDI6P02
AC9TDI4P03
AC9TDI6P03
AC9TDI4P05
AC9TDI6P06
AC9TDI4P04
AC9TDI6P04
AC9TDI6P05
AC9TDI4P06
AC9TDI4P07
AC9TDI6P07
AC9TDI6P08
AC9TDI4P09
AC9TDI6P10
AC9TDI4P08
AC9TDI6P09