Mathematisation Theme

Addition and Subtraction

Multiplication and
Division

Fractions, Decimals and
Percentages

Structuring number

Understanding the
underlying connections between numbers (e.g. 16=10+6,8+8, etc.)

Understanding the fairness and
equality of multiplication and division
Linking and applying knowledge
of addition and subtraction to multiplication and division
Understand composite and unitary aspects of a
quantity

Linking and applying knowledge
of Multiplication and Division to Fractions, Decimals and Percentages
Understand composite and unitary aspects of a
quantity

Extending the range of numbers

Progressively introducing
a wider range of numbers to calculate with

Introducing multiples and sequences in steps to
ensure secure understanding

Building on knowledge of fair share and equal parts,
sequentially introduce fractions in steps to ensure secure understanding.
This leads to a depth of understanding within fractions and this knowledge
enables learners to develop a meaningful understanding of decimals and
percentages.

Decimalising towards Baseten thinking

Developing base ten thinking
that exploits using ten as a unit (e.g. conceptual place value and counting
in tens)

Applying conceptual place value to multiplication
and division

Applying conceptual place value to Fractions,
Decimals and Percentages

Unitising and not counting by ones

Regarding a number larger
than one as a unit and use this unit to solve a task.

Adopting appropriate settings to explore the
composite and unitary aspects of a
quantity

Unitising, Partitioning, Disembedding and Iterating

Distancing the setting of materials

Progressively reducing
the role of materials

Distancing the Setting (Manipulate it àSee itàFlash itàScreen ItàCheck ItàExpress It and Explain It)

Distancing the Setting (Manipulate it àSee ità Flash ità Screen Ità Check Ità Express It and Explain It)

Notating

Progressively formalising
mathematical thought in a structured way

Notation (Informal JottingsàSemiFormal Written StrategiesàFormal Written Algorithms)

Notation (Informal Jottingsà SemiFormal Written Strategiesà Formal Written Algorithms)

Formalising and generalising

Developing arithmetic to
involve more formal notation and more formal procedures.
Reasoning that involves
proceeding from a few cases to many cases

Increasing the range of tasks to which children apply
their strategies

Increasing the range of tasks to which children
apply their strategies
