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Reading and writing numbers to 10,000,000
Number Representation & Place Value
Read, write, order, and compare numbers up to 10,000,000 and determine the value of each digit
Reading Decimal Places
Number Representation & Place Value
Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)
Real-world fraction multiplication
Fractions
Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations
Real-World Mathematical Modelling
Mathematical Thinking
Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations
Rounding Answers
Multiplication & Division
Solve problems which require answers to be rounded to specified degrees of accuracy
Scale and similar shapes
Ratio & Proportion
Solve problems involving similar shapes where the scale factor is known or can be found
Simplifying Fractions
Fractions
Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator
Systematic Listing
Algebra
Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)
The 0-to-1 Probability Scale
Probability
Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages
Translating and reflecting shapes
Geometry
Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes
Understanding angles (age 10+)
Geometry
Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties
Understanding fractions
Ratio & Proportion
Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Understanding fractions
Data & Statistics
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); use operations on fractions to solve problems involving data in line plots (e.g. redistribute total equally)
Understanding fractions (age 10+)
Mathematical Thinking
Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations
Using Simple Formulae
Algebra
Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))
Volume as additive
Measurement
Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
Writing Algebraic Equations
Algebra
Express missing number problems algebraically using letters for unknowns; translate word problems into equations
Writing Number Sentences
Multiplication & Division
Write simple numerical expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g. recognise that 3 × (18932 + 921) is three times as large as 18932 + 921)
3-D shapes (age 11+)
Geometry
Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections
Algebraic Notation
Algebra
Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently
Algebraic Transformations
Algebra
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
Angle sums in triangles and polygons
Geometry
Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons
Angles in triangles (age 11+)
Geometry
Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
Collecting Like Terms
Algebra
Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence