Mathematisation Theme
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Addition and Subtraction
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Multiplication and
Division
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Fractions, Decimals and
Percentages
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Structuring number
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Understanding the
underlying connections between numbers (e.g. 16=10+6,8+8, etc.)
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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
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Linking and applying knowledge
of Multiplication and Division to Fractions, Decimals and Percentages
Understand composite and unitary aspects of a
quantity
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Extending the range of numbers
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Progressively introducing
a wider range of numbers to calculate with
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Introducing multiples and sequences in steps to
ensure secure understanding
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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.
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Decimalising towards Base-ten thinking
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Developing base ten thinking
that exploits using ten as a unit (e.g. conceptual place value and counting
in tens)
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Applying conceptual place value to multiplication
and division
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Applying conceptual place value to Fractions,
Decimals and Percentages
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Unitising and not counting by ones
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Regarding a number larger
than one as a unit and use this unit to solve a task.
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Adopting appropriate settings to explore the
composite and unitary aspects of a
quantity
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Unitising, Partitioning, Disembedding and Iterating
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Distancing the setting of materials
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Progressively reducing
the role of materials
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Distancing the Setting (Manipulate it àSee itàFlash itàScreen ItàCheck ItàExpress It and Explain It)
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Distancing the Setting (Manipulate it àSee ità Flash ità Screen Ità Check Ità Express It and Explain It)
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Notating
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Progressively formalising
mathematical thought in a structured way
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Notation (Informal JottingsàSemi-Formal Written StrategiesàFormal Written Algorithms)
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Notation (Informal Jottingsà Semi-Formal Written Strategiesà Formal Written Algorithms)
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Formalising and generalising
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Developing arithmetic to
involve more formal notation and more formal procedures.
Reasoning that involves
proceeding from a few cases to many cases
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Increasing the range of tasks to which children apply
their strategies
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Increasing the range of tasks to which children
apply their strategies
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