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Mathematics // Mathematical Thinking
Justifying mathematical reasoningConstruct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work
Ages 7 to 8Thinking skillMathematics // Mathematical Thinking
Working with moneyModel real-world problems involving measurement, money, and time by choosing appropriate representations and interpreting results in context
Ages 7 to 8Thinking skillMathematics // Mathematical Thinking
Understanding fractionsMove fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents
Ages 7 to 8Thinking skillMathematics // Mathematical Thinking
Choosing the right strategySelect and use appropriate tools and representations strategically, including choosing between mental methods, jottings, formal algorithms, and calculators for…
Ages 7 to 8Thinking skillMathematics // Mathematical Thinking
Shape patterns (age 7+)Look for and use mathematical structure: apply place-value patterns to three-digit operations, use multiplication/division relationships, and exploit shape…
Ages 7 to 8Thinking skillMathematics // Mathematical Thinking
Extending Table PatternsRecognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences
Ages 7 to 8Thinking skillMathematics // Mathematical Thinking
Mathematical PrecisionCommunicate with mathematical precision: use correct fraction/decimal vocabulary, name angle types accurately, specify units in measurement and money, and use…
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Multi-Step Problem SolvingMake sense of multi-step problems involving four operations, fractions, and area/volume by identifying sub-steps, choosing a strategy, and monitoring progress
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Justifying mathematical reasoning (age 8+)Construct and present multi-step mathematical arguments; critique the reasoning of others and explain clearly why a method works or fails
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Choosing mathematical toolsSelect and use appropriate tools and representations strategically: choose between mental, written, and diagrammatic methods; use calculators for checking…
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Modelling with multiplication and fractionsModel real-world problems involving multiplication, area, fractions, and unit conversion by choosing appropriate representations and interpreting mathematical…
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Times tables (age 8+)Recognise and use repeated reasoning to generalise: extend patterns in times tables and equivalent fractions, derive unknown facts from known facts efficiently…
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Fractions on a number lineMove fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what…
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Using Mathematical StructureLook for and use mathematical structure: exploit place-value patterns for ×10/×100, use the distributive property to break apart multiplications, apply fraction…
Ages 8 to 9Thinking skillMathematics // Mathematical Thinking
Complex Multi-Step ProblemsMake sense of complex multi-step problems involving large numbers, fractions, decimals, and percentages by analysing what is known and unknown, planning…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Precise Maths VocabularyCommunicate with mathematical precision: use correct vocabulary for primes, factors, multiples, angle types, and polygon regularity; specify units including…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Understanding fractions (age 9+)Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Real-World Maths ModellingModel real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Choosing representations strategicallySelect and use tools and representations strategically: choose between mental methods, formal written methods, protractors, fraction strips, and diagrams based…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Fractions on a number line (age 9+)Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Reasoning with EquivalencesRecognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Fractions, Decimals & PercentagesLook for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication…
Ages 9 to 10Thinking skillMathematics // Mathematical Thinking
Understanding fractions (age 10+)Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and…
Ages 10 to 11Thinking skillMathematics // Mathematical Thinking
Advanced Multi-Step ProblemsMake sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by…
Ages 10 to 11Thinking skill