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Equally Likely Outcomes
Probability
Understand that 'equally likely' means every outcome has exactly the same chance of occurring; identify whether a given situation has equally likely outcomes (a fair coin, a fair die, a spinner with equal sections) or unequally likely outcomes (a bag with more of one colour, a spinner with unequal sections)
Equivalent fractions (age 9+)
Fractions
Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths
Estimating Angles
Geometry
Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size
Estimating answers (age 9+)
Measurement
Apply the area formula (l × w) and perimeter formula (2l + 2w) for rectangles including squares in real-world and mathematical problems; calculate and compare areas using standard units (cm², m²) and estimate areas of irregular shapes
Estimating volume
Measurement
Estimate volume of cuboids using 1 cm³ blocks; estimate capacity of containers using water
Factors, multiples, and primes
Multiplication & Division
Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems
Factors, multiples, and primes (age 9+)
Multiplication & Division
Solve problems involving multiplication and division using knowledge of factors, multiples, squares, and cubes
Fluent addition and subtraction (age 9+)
Addition & Subtraction
Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm
Fraction Addition Concepts
Fractions
Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
Fractions of a whole (age 9+)
Fractions
Solve word problems involving multiplication of a fraction by a whole number using visual models and equations
Fractions on a number line
Measurement
Solve word problems involving distances, time intervals, liquid volumes, masses, and money using the four operations with fractions or decimals; represent with diagrams including number lines
Fractions on a number line (age 9+)
Mathematical Thinking
Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions, decimals, and percentages, explaining connections between representations
Fractions, Decimals & Percentages
Mathematical Thinking
Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically
Likelihood Language
Probability
Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible
Lines, Rays & Angles
Geometry
Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures
Long multiplication
Multiplication & Division
Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models
Measurement Line Plots
Measurement
Make a line plot to display measurement data in fractions of a unit (1/2, 1/4, 1/8); solve problems involving addition and subtraction of fractions using line plot data
Measuring angles
Geometry
Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure
Measuring angles (age 9+)
Geometry
Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown
Mental addition and subtraction (age 9+)
Addition & Subtraction
Add and subtract numbers mentally with increasingly large numbers, using place-value knowledge and derived facts
Mental multiplication and division (age 9+)
Multiplication & Division
Multiply and divide numbers mentally drawing upon known facts, including related facts and place-value adjustments
Metric & Imperial Conversion
Measurement
Understand and use approximate equivalences between metric units and common imperial units (inches, pounds, pints)
Mixed numbers and improper fractions
Fractions
Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)
Multiplicative Comparison
Multiplication & Division
Solve word problems involving multiplicative comparison using drawings and equations with a symbol for the unknown number