Links to NC:
· Understand how to use squares, cubes and roots
· Write powers in index form
· Recognise and generate square numbers
· Appreciate the infinite nature of the sets of integers, real and rational numbers
· Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
· Use the four operations, including formal written methods, applied to integers, both positive and negative
· Understand the definition of prime factors
· Find HCF and LCM using Venn Diagrams or Factor Trees
· Round numbers to decimal places and to the nearest 10, 100, 1000
· Round very large and very small numbers to 1, 2 and 3 significant figures
· Multiply and divide positive proper and improper fractions and mixed numbers
· Efficiently use a calculator to solve multistep calculations involving brackets, powers, decimals, fractions and negative numbers
· Convert hours and minutes into decimal time
· Understand how to raise a negative number to a given power on a calculator
· Understand and avoid rounding errors

Links to NC:
· Simplify and manipulate algebraic expressions to maintain equivalence by:
· collecting like terms
· multiplying a single term over a bracket
· taking out common factors
· Use and write 2 stage formulae
· Rearrange formulae requiring factorisation
· Rearrange formulae with up to 4 steps
· Solve simple linear equations using the balancing method, including those with fractional solutions in the form ax+b=c and a(x+b)=c
· Solve linear equations with an unknown on both sides
· Construct simple linear equations from contextual problems
· Substitute numerical values into formulae and expressions, including scientific formulae
· Interpret mathematical relationships both algebraically and geometrically
· Use the formula for the area of a trapezium to work out the area or a missing length
· Use the formula for the area of a circle to work out the area or radius
· Use Pythagoras’ theorem

Links to NC:
· Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
· Use a pair of compasses to construct triangles and polygons
· Enlarge a shape by a given scale factor
· Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
· Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
· Recall and use basic metricimperial conversions
· Change freely between related standard units [for example time, length, area, volume/ capacity, mass]
· Convert between metric units of length, capacity and mass
· Convert between seconds and minutes & seconds
· Express minutes in hours & minutes (e.g. 70mins = 1hr10m) and as a decimal
· Convert between area units
· Find unknown angles involving parallel lines
· Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
· Calculate the area of abstract composite shapes requiring Pythagoras and πr² and leave answers to a specified degree of accuracy including in terms of π
· Identify names of solids, including prisms and pyramids
· Calculate the surface area of solids from nets

Links to NC:
· Understand the difference between additive and multiplicative ways of thinking
· Apply knowledge of how to keep things in proportion to solve problems relating to:
· Side lengths of similar shapes and scale drawings
· Recipes
· Price comparison
· Compare simple proportions
· Increase and decrease amounts by simple percentages (ones that do not require a calculator)
· Convert fractions and percentages (using a calculator) into decimal multipliers to solve increase and decrease problems
· Use ratio notation, including reduction to simplest form
· Divide a quantity into a given ratio
· Solve simple problems involving ratio
· Understand the difference between ratio and proportion
· Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
· Recall and use the formulae for speed, pressure and density

Links to NC:
· Name parts of a circle (chord, tangent, diameter, radius, arc, sector, segment)
· Calculate circumference of a circle giving answer to required degree of accuracy or to π
· Visualise and identify 3D shapes and their nets
· Draw plans and elevations of simple 3D shapes
· Plot 3D coordinates
· Calculate the volume of cuboids, prisms, cylinders, pyramids, cones, spheres and composite solids
· Solve volumedensity problems
· Convert between volume units

Links to NC:
· Solve questions involving twoway tables including:
· Completing parts of the table
· Extracting proportions and ratios from the table
· Draw bar charts, line graphs and pie charts to represent data
· Interpret bar charts, frequency tables, line graphs and pie charts
· Interpret grouped and ungrouped data
· Find the median, mode and range of discrete, ungrouped data
· Understand the concept of ‘central tendency’
· Draw conclusions about data based on average and range (including outliers)
· Use sensible averages to examine data
