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Choosing Maths Tools
Mathematical Thinking
Select and use tools and representations strategically: choose between mental methods, formal written methods, algebraic approaches, coordinate grids, and technology based on the demands of the problem
Classifying shapes by properties
Geometry
Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties
Comparing fractions (age 10+)
Fractions
Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
Constructing mathematical arguments
Mathematical Thinking
Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches
Coordinates (age 10+)
Geometry
Describe positions on the full coordinate grid (all four quadrants); use coordinates with negative values
Counting Unit Cubes
Measurement
Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units
Decimal place value
Measurement
Convert among different-sized standard measurement units within a given system (e.g. 5 cm to 0.05 m) using decimal notation to up to three decimal places; convert between smaller and larger units of length, mass, volume, and time
Decimal place value
Multiplication & Division
Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)
Decimal place value
Number Representation & Place Value
Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
Decimals and fractions (age 10+)
Fractions
Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
Dividing by Fractions
Fractions
Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend
Dividing by two-digit numbers
Multiplication & Division
Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context
Dividing fractions (unit fractions)
Fractions
Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result
Dividing unit fractions and whole numbers
Fractions
Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations
Division with Decimals
Multiplication & Division
Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers
Division with remainders (age 10+)
Multiplication & Division
Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate
Equations with Two Unknowns
Algebra
Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15)
Estimating answers (age 10+)
Measurement
Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)
Estimation to check answers to calculations
Multiplication & Division
Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Experimental vs Theoretical
Probability
Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results
Fraction Word Problems
Fractions
Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness
Fractions of a whole (age 10+)
Fractions
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
Generalising with repeated reasoning
Mathematical Thinking
Recognise and use repeated reasoning to generalise: describe algebraic rules for nth terms, use properties of operations to simplify, and verify generalisations with specific cases
Line graphs (age 10+)
Data & Statistics
Interpret and construct pie charts and line graphs; use these to solve problems