Place value and Number sense
Addition and Subtraction
Multiplication and Division
Estimation and rounding

Perimeter
Factors and Multiples
Area of Rectangles and Triangles
Mean

Angles
Polygons
Area of a parallelogram
Symmetry and reflection

Fractions as part of a whole
Fractions as a value
Fractions as an operation

Order of operations
Basic rules of algebra
Expand and factorise
Rearrange formula
Substitution

Percentages as parts of a whole
Percentages as a value
Percentages as an operation

Links to NC:
 Read and write large numbers up to 1 billion and small numbers down to 0.001
 Understand and use place value for decimals, measures and integers of any size
 Understand definitions of odd and even
 Order positive integers and decimals
 Use the symbols =, ≠, <, >, ≤, ≥ for positive integers and decimals
 Perform simple calculations using mental methods: partitioning, compensation, bridging
 Understand language of addition & subtraction including added, subtrahend and minuend
 Add and subtract large integers
 Add and subtract decimals
 Perform simple calculations using mental methods
 Understand and apply the relationships between times table facts
 Understand language of multiplication and division including factor, product, dividend, divisor and quotient
 Use column multiplication
 Solve problems using short and/or long division (not chunking), giving answers as decimals or fractions (not remainders) where necessary
 Give appropriate answers to division word problems
 Round numbers and measures to an appropriate degree of accuracy [nearest 1, 10, 100 or 1000 or nearest 0.1, 0.01 or 0.001]
 Use approximation through rounding to estimate answers

Links to NC:
 Use standard units of length including with decimal quantities
 Derive and apply formulae to calculate and solve problems involving perimeter of triangles, parallelograms, trapezia
 Understand definitions of multiples, factors, squares, composite and primes
 Identify all the factors of a number
 Recall and apply divisibility rules for 2, 3, 4, 5, 6, 9, 10, 25, 50 and 100
 Find the highest common factor and lowest common multiple of a pair of numbers
 Understand and use the formula for the area of any triangle
 Calculate the area of triangles and compound shapes (not circles).
 Understand the purpose of finding a measure of central tendency and that as well as the mean, the other ones typically used are mode and median
 Calculate the mean of a set of numbers
 Calculate a missing number given the mean and the rest of the set

Links to NC:
 Understand and use angle facts involving straight lines, points, triangles and quadrilaterals (including opposite angles)
 Measure, draw, estimate and name angles
 Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons
 Name, identify and list the properties of isosceles, equilateral, scalene and rightangle triangles including their combinations, e.g. rightangle isosceles
 Name, identify and list the properties of a square, rectangle, parallelogram, rhombus, kite, arrowhead, trapezium and isosceles trapezium
 Name a polygon with up to 10 sides
 Understand the meaning of parallel and perpendicular
 Derive and apply formulae to calculate and solve problems involving area of parallelograms
 Recognise and visualise simple reflections
 Recognise line symmetry
 Find the order of rotational symmetry for any shape

Links to NC:
 Find an equivalent fraction for another fraction given either the desired numerator or denominator
 Simplify fractions to their lowest terms
 Convert between improper fractions and mixed numbers
 Use approximation to divide rectangles into halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths
 Use approximation to divide circles into halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths and twelfths
 Add and subtract fractions by making the denominators equal
 Add and subtract mixed numbers and improper fractions by making the denominators equal
 Approximate where fractions lie on a number line
 Order fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
 Solve division questions represented as fraction
 Recognise special cases, e.g. fractions over 0, over 1 or where the numerator and denominator are equal
 Calculate simple fractions of amounts
 Draw pie charts involving simple fractions of 360

Links to NC:
 Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
 Recognise and use relationships between operations including inverse operations
 Use and interpret algebraic notation, including:
 o ab in place of a × b
 o 3y in place of y + y + y and 3 × y
 o a² in place of a × a, aᶾ in place of a × a × a; a²b in place of a × a × b
 o a/b in place of a ÷ b
 o coefficients written as fractions rather than as decimals
 o brackets
 Simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms
 Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
 Multiply out a single term and a bracket
 Factorise an expression into a single bracket
 Understand and use standard mathematical formulae
 Rearrange formulae to change the subject
 · Generate terms of a sequence from either a termtoterm or a positiontoterm rule
 Find the next number in a variety of sequences. Uses nth term rule to generate a sequence

Links to NC:
 Define percentage as ‘number of parts per hundred’
 Work with percentages greater than 100%
 Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
 Interpret percentages as a fraction or a decimal, interpret these multiplicatively
 Express one quantity as a percentage of another
 Recognise common FractionsDecimalsPercentages (FDP) conversions
 Order fractions, decimals and percentages
 Calculate simple percentages of amounts (using mental methods)
 Compare two quantities using percentages
