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Assessing without levels
Mastery indicators: Minimum expected outcomes by the end of each stage: 13 in every stage, critical in developing conceptual understanding and essential for pupils to make progress.
Essential knowledge: Critical information that pupils need to know.
Mastery Indicators + Essential Knowledge = Fluency in the Fundamentals of Mathematics
Stage 6

•Multiply and divide numbers with up to three decimal places by 10, 100, and 1000
• Use long division to divide numbers up to four digits by a twodigit number
• Use simple formulae expressed in words
• Generate and describe linear number sequences
• Use simple ratio to compare quantities
• Write a fraction in its lowest terms by cancelling common factors
• Add and subtract fractions and mixed numbers with different denominators
• Multiply pairs of fractions in simple cases
• Find percentages of quantities
• Solve missing angle problems involving triangles, quadrilaterals, angles at a point and angles on a straight line
• Calculate the volume of cubes and cuboids
• Use coordinates in all four quadrants
• Calculate and interpret the mean as an average of a set of discrete data

• Know percentage and decimal equivalents for fractions with a denominator of 2, 3, 4, 5, 8 and 10
• Know the rough equivalence between miles and kilometres
• Know that vertically opposite angles are equal
• Know that the area of a triangle = base × height ÷ 2
• Know that the area of a parallelogram = base × height
• Know that volume is measured in cubes
• Know the names of parts of a circle
• Know that the diameter of a circle is twice the radius
• Know the conventions for a 2D coordinate grid
• Know that mean = sum of data ÷ number of pieces of data

Stage 7

•Use positive integer powers and associated real roots
• Apply the four operations with decimal numbers
• Write a quantity as a fraction or percentage of another
• Use multiplicative reasoning to interpret percentage change
• Add, subtract, multiply and divide with fractions and mixed numbers
• Check calculations using approximation, estimation or inverse operations
• Simplify and manipulate expressions by collecting like terms
• Simplify and manipulate expressions by multiplying a single term over a bracket
• Substitute numbers into formulae
• Solve linear equations in one unknown
• Understand and use lines parallel to the axes, y = x and y = x
• Calculate surface area of cubes and cuboids
• Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines

• Know the first 6 cube numbers
• Know the first 12 triangular numbers
• Know the symbols =, ≠, , ≤, ≥
• Know the order of operations including brackets
• Know basic algebraic notation
• Know that area of a rectangle = l × w
• Know that area of a triangle = b × h ÷ 2
• Know that area of a parallelogram = b × h
• Know that area of a trapezium = ((a + b) ÷ 2) × h
• Know that volume of a cuboid = l × w × h
• Know the meaning of faces, edges and vertices
• Know the names of special triangles and quadrilaterals
• Know how to work out measures of central tendency
• Know how to calculate the range

Stage 8

• Apply the four operations with negative numbers
• Convert numbers into standard form and vice versa
• Apply the multiplication, division and power laws of indices
• Convert between terminating decimals and fractions
• Find a relevant multiplier when solving problems involving proportion
• Solve problems involving percentage change, including original value problems
• Factorise an expression by taking out common factors
• Change the subject of a formula when two steps are required • Find and use the nth term for a linear sequence
• Solve linear equations with unknowns on both sides
• Plot and interpret graphs of linear functions
• Apply the formulae for circumference and area of a circle
• Calculate theoretical probabilities for single events

•Know how to write a number as a product of its prime factors
• Know how to round to significant figures
• Know the order of operations including powers
• Know how to enter negative numbers into a calculator
• Know that a0 = 1
• Know percentage and decimal equivalents for fractions with a denominator of 3, 5, 8 and 10
• Know the characteristic shape of a graph of a quadratic function
• Know how to measure and write bearings
• Know how to identify alternate angles
• Know how to identify corresponding angles • Know how to find the angle sum of any polygon
• Know that circumference = 2πr = πd
• Know that area of a circle = πr²
• Know that volume of prism = area of crosssection × length
• Know to use the midpoints of groups to estimate the mean of a set of grouped data
• Know that probability is measured on a 01 scale
• Know that the sum of all probabilities for a single event is 1

Stage 9

•Calculate with roots and integer indices
• Manipulate algebraic expressions by expanding the product of two binomials
• Manipulate algebraic expressions by factorising a quadratic expression of the form x² + bx + c
• Understand and use the gradient of a straight line to solve problems
• Solve two linear simultaneous equations algebraically and graphically
• Plot and interpret graphs of quadratic functions
• Change freely between compound units
• Use ruler and compass methods to construct the perpendicular bisector of a line segment and to bisect an angle
• Solve problems involving similar shapes
• Calculate exactly with multiples of π
• Apply Pythagoras’ Theorem in two dimensions
• Use geometrical reasoning to construct simple proofs
• Use tree diagrams to list outcomes

•Know how to interpret the display on a scientific calculator when working with standard form
• Know the difference between direct and inverse proportion
• Know how to represent an inequality on a number line
• Know that the point of intersection of to lines represents the solution to the corresponding simultaneous equations
• Know how to find the nth term of a quadratic sequence
• Know the characteristic shape of the graph of a cubic function
• Know the characteristic shape of the graph of a reciprocal function
• Know the definition of speed
• Know the definition of density
• Know the definition of pressure
• Know Pythagoras’ Theorem
• Know the definitions of arc, sector, tangent and segment
• Know the conditions for congruent triangles
