References & where to explore further

Official curriculum sources — Year 4 patterns & balance

• ACARA — Australian Curriculum: Mathematics Version 9.0, Year 4 Mathematics: the official curriculum page for Year 4; the content description codes quoted below come from it.
  australiancurriculum.edu.au — Mathematics, Year 4
• The Mathematics Hub — Year 4 algebra planning tool: the Australian Government's official planning tool for Year 4 algebra, delivered by Education Services Australia; it lists the teaching sequences for the algebra strand with their steps.
  mathematicshub.edu.au/planning-tool/4/algebra
• The Mathematics Hub — Year 4 algebra, "Find unknown values" sequence: the sequence that focuses on finding unknown values in numerical equations — the balance-and-unknown territory pupils meet in this site's Balance Scales and Case Files games.
  mathematicshub.edu.au/planning-tool/4/algebra/find-unknown-values

Pattern Detective — The Balance Files supports the Australian Curriculum: Mathematics Version 9.0, Year 4 — AC9M4N09 (Number): 'follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns'; AC9M4A01 (Algebra): 'find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations'; with the pattern and skip-counting work building toward AC9M4A02 (Algebra): 'recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts'.

The Year 4 Explorer Pathway — whole-year claim block

The Year 4 Explorer Pathway supports the Australian Curriculum: Mathematics Version 9.0, Year 4 — across Number, Algebra, Measurement, Space, Statistics and Probability. Unit by unit:

• Unit 8 — Number Basecamp supports AC9M4N01 (Number): 'Recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals'; AC9M4N05 (Number): 'Solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits'; AC9M4N02 (Number): 'Explain and use the properties of odd and even numbers'; and AC9M4N06 (Number): 'Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder'.
• Unit 10 — Fraction Forest supports AC9M4N03 (Number): 'Find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation'; and AC9M4N04 (Number): 'Count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines'.
• Unit 11 — Market Day supports AC9M4N08 (Number): 'Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate'; AC9M4N07 (Number): 'Choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions'; and builds toward AC9M4A02 (Algebra): 'Recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator'.
• Unit 12 — The Time Machine supports AC9M4M01 (Measurement): 'Interpret unmarked and partial units when measuring and comparing attributes of length, mass, capacity, duration and temperature, using scaled and digital instruments and appropriate units'; and AC9M4M03 (Measurement): 'Solve problems involving the duration of time including situations involving "am" and "pm" and conversions between units of time'.
• Unit 7 — Angle Hunters supports AC9M4M04 (Measurement): 'Estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle'.
• Unit 9 — Grids, Maps & Mazes supports AC9M4SP02 (Space): 'Create and interpret grid reference systems using grid references and directions to locate and describe positions and pathways'.
• Unit 13 — Data Detectives supports AC9M4ST01 (Statistics): 'Acquire data for categorical and discrete numerical variables to address a question of interest or purpose, using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information'; AC9M4ST02 (Statistics): 'Analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data'; AC9M4ST03 (Statistics): 'Conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results'; AC9M4P01 (Probability): 'Describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events'; and AC9M4P02 (Probability): 'Conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results'.
• Unit 14 — The Pathway Gala reviews the whole-year set above; it introduces no new content descriptions.
• Units 1–6 and the website games (Shapes, Perimeter, Circle, Pi, Circumference, Pattern Detective) support AC9M4SP01 (Space): 'Represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects'; AC9M4SP03 (Space): 'Recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures, using dynamic geometric software where appropriate'; AC9M4M02 (Measurement): 'Recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units'; AC9M4N09 (Number): 'follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns'; and AC9M4A01 (Algebra): 'find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations'.

Descriptor wording quoted from the IXL mirror of the official page at authoring time; final print-time condition: re-verify each quote against the official ACARA Year 4 page above.

Free official tools that model patterns and rules

• MakeCode for micro:bit — Flashing Heart tutorial: the official step-by-step project that beats a heart on the micro:bit's display; a repeating-pattern model, because the loop repeats one unit — a heartbeat — over and over, exactly like the unit of repeat in Bead Rule.
  makecode.microbit.org/projects/flashing-heart
• MakeCode for micro:bit — Repeat block reference: the official guide to the repeat block — a rule in block form: it tells the micro:bit how many times to run the same unit of steps, just as a pattern rule tells you how a pattern continues.
  makecode.microbit.org/blocks/loops/repeat
• MakeCode for micro:bit — Math reference: the official guide to the maths blocks (arithmetic, comparison, random) in Microsoft's free block editor for the micro:bit — the blocks pupils can use to generate and check their own number patterns and balance sentences.
  makecode.microbit.org/reference/math

About our text

All definitions, explanations, examples, games, and exercises on this site and in the Maths Explorers Club series were written by our authors from standard mathematical knowledge. Nothing was copied from the pages listed above or from any other source; the links are provided so readers can explore the official material themselves.