Strands with level identifiers
When planning, ensure that age expected objectives are linked in a progressive manner – eg To know place value to of a two-digit number (Year Two) has the progression objective To recognise value of each digit in a three-digit number (Year Three). The Year 3 objective would be the challenge objective to follow the Year Two objective.Objectives in blue are mental objectives.
Number
Year Five / Year Six / Year SevenTo read, write, order and compare numbers to at least 1000000 and determine the value of each digit
To count forwards or backwards in steps of powers of 10 for any given number up to 1000000
To interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
To solve sequences involving negative numbers
To round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000
To solve number problems and practical problems that involve all of the above
To read Roman numerals to 1000 (M) and recognise years written in Roman numerals.
To identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
To multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 / To read, write, order and compare numbers up to 10000000 and determine the value of each digit
To round any whole number to a required degree of accuracy
To use negative numbers in context, and calculate intervals across zero
To solve number and practical problems that involves all of the above.
To solve problems involving inverse operation and brackets / To understand and use place value for decimals, measures and integers of any size
To order positive and negative integers, decimals and fractions; use the number line as a
model for ordering of the real numbers; use the symbols =, ≠, <, >, =, =
To use the concepts and vocabulary of prime numbers, factors (or divisors), multiples,
common factors, common multiples, highest common factor, lowest common multiple,
prime factorisation, including using product notation and the unique factorisation
property
To use the four operations, including formal written methods, applied to integers, decimals,
proper and improper fractions, and mixed numbers, all both positive and negative
To use conventional notation for the priority of operations, including brackets, powers,
roots and reciprocals
To recognise and use relationships between operations including inverse operations
To use integer powers and associated real roots (square, cube and higher), recognise
powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their
decimal approximations
To interpret and compare numbers in standard form A x 10n1=A<10, where n is a positive
or negative integer or zero
To work interchangeably with terminating decimals and their corresponding fractions
To define percentage as ‘number of parts per hundred’, interpret percentages and
percentage changes as a fraction or a decimal, interpret these multiplicatively, express
one quantity as a percentage of another, compare two quantities using percentages,
and work with percentages greater than 100%
To interpret fractions and percentages as operators
To use standard units of mass, length, time, money and other measures, including with decimal quantities
To round numbers and measures to an appropriate degree of accuracy [for example,to a
number of decimal places or significant figures]
To use approximation through rounding to estimate answers and calculate possible
resulting errors expressed using inequality notation ax=b
To use a calculator and other technologies to calculate results accurately and then
interpret them appropriately
To appreciate the infinite nature of the sets of integers, real and rational numbers.
Calculating
YearFive / Year Six / Year SevenTo add and subtract whole numbers with more than 4 digits, using formal written methods (columnar addition and subtraction)
To add and subtract numbers mentally with increasingly large numbers
To use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
To solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
To know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
To establish whether a number up to 100 is prime and recall prime numbers up to 19
To multiply numbers up to 4 digits by a one- or two- or 3-digit number using a formal written method, including long multiplication for two-digit numbers
To multiply and divide numbers mentally drawing upon known facts
To divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
To solve two step problems involving multiplication
and division / To multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of multiplication
To divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, decimals or by rounding, as appropriate for the context
To divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context including decimal remainders
To perform mental calculations, including with mixed operations and large numbers
To identify common factors, common multiples and prime numbers
To use knowledge of the order of operations (bodmas) to carry out calculations involving the four operations
To solve multi-step problems involving all four contexts, deciding which operations and methods to use and why
To use simple formulae
To generate and describe linear number sequences
To express missing number problems algebraically
To find pairs of numbers that satisfy an equation with two unknowns
To enumerate possibilities of combinations of two variables. / To use and interpret algebraic notation, including:
ab in place of a × b
3y in place of y + y + y and 3 × y
coefficients written as fractions rather than as decimals
b in place of a × a × b
brackets
To substitute numerical values into formulae and expressions, including scientific formulae
To understand and use the concepts and vocabulary of expressions, equations,
inequalities, terms and factors
To simplify and manipulate algebraic expressions to maintain equivalence by:
collecting like terms
multiplying a single term over a bracket
taking out common factors
expanding products of two or more binomials
To understand and use standard mathematical formulae; rearrange formulae to change the subject
To model situations or procedures by translating them into algebraic expressions or
formulae and by using graphs
To use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
To work with coordinates in all four quadrants
To recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
To interpret mathematical relationships both algebraically and graphically
To reduce a given linear equation in two variables to the standard form y = mx + c;
calculate and interpret gradients and intercepts of graphs of such linear equations
numerically, graphically and algebraically
To use linear and quadratic graphs to estimate values of y for given values of x and viceversa and to find approximate solutions of simultaneous linear equations
To find approximate solutions to contextual problems from given graphs of a variety offunctions, including piece-wise linear, exponential and reciprocal graphs
To generate terms of a sequence from either a term-to-term or a position-to-term rule
To recognise arithmetic sequences and find the nth term
To recognise geometric sequences and appreciate other sequences that arise.
Fractions, decimals, % and ratio
Year Five / Year Six / Year SevenTo recognise common equivalent fractions
To count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
To solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities
To recognise mixed numbers and improper fractions and convert from one form to the other
To add and subtract fractions with the same denominator
To recognise and write decimal equivalents of any number of tenths or hundredths
To recognise and write decimal equivalents to , ,
To find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
To round decimals with one decimal place to the nearest whole number
To order and comparedecimals with the same number of decimal places up to two decimal places
To solve simple measure and money problems involving fractions and decimals to two decimal places / To compare and order fractions where denominators are multiples of the same number
To find equivalent fractions of a given fraction
To recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number [for example,+ = = 1]
To cancel fractions to simplest form
To add and subtract fractions with the same denominator and denominators that are multiples of the same number
To multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
To read and write decimal numbers as fractions [for example, 0.71 = ]
To recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
To round decimals with two decimal places to the nearest whole number and to one decimal place
To read, write, order and compare decimals with a mix of decimal places (up to three decimal places)
To solve problems involving number up to three decimal places
To recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
To solve problems which require knowing percentage and decimal equivalents of , , , , and those fractions with a denominator of a multiple of 10 or 25.
To find proportion as a % of a number / To change freely between related standard units [for example time, length, area,
volume/capacity, mass]
To use scale factors, scale diagrams and maps
To express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
To use ratio notation, including reduction to simplest form
To divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
To understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
To relate the language of ratios and the associated calculations to the arithmetic of
fractions and to linear functions
To solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
To solve problems involving direct and inverse proportion, including graphical and
algebraic representations
To use compound units such as speed, unit pricing and density to solve problems.
Measures
Year Five / Year Six / Year SevenTo convert between different units of measure [for example, kilometre to metre; hour to minute]
To measure and calculate the perimeter of a rectangle (including squares) in centimetres and metres
To find the area of rectangles by counting squares and then by using a formula
To estimate, compare and calculate different measures, including money in pounds and pence
To read, write and convert time between analogue and digital 12- and 24-hour clocks
To solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.
To read and solve problems involving timetables
To measure to the nearest mm
To read scales involving a range of divisions / To convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre) including decimal notation
To understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
To measure and calculate the perimeter of shapes in centimetres and metres
To calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes
To find the area and perimeter of compound shapes
To read scales involving a range of divisions
To estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]
To solve problems involving converting between units of time
To use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling. / To derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) andother prisms (including cylinders)
To calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
To draw and measure line segments and angles in geometric figures, including
interpreting scale drawings
To derive and use the standard ruler and compass constructions (perpendicular bisector ofa line segment, constructing a perpendicular to a given line from/at a given point,bisecting a given angle); recognise and use the perpendicular distance from a point toa line as the shortest distance to the line
Shape
Year Five / Year Six / Year SevenTo compare and classify 2D and 3D shapes, including a range of quadrilaterals and triangles, based on their properties and sizes
To identify nets of 3D shape
To recognise sides that are perpendicular, parallel and adjacent.
To identify acute and obtuse angles and compare and order angles up to two right angles by size
To measure and draw acute/obtuse angles to the
nearest 5 degrees.
To identify lines of symmetry in 2-D shapes presented in different orientations
To complete a simple symmetric figure with respect to a specific line of symmetry.
To reflect shape across a vertical/horizontal/oblique line
To describe positions on a 2-D grid as coordinates in the first quadrant
To describe movements between positions as translations of a given unit to the left/right and up/down
To rotate shape
To plot specified points and draw sides to complete a given polygon on a co-ordinate grid / To identify 3-D shapes, including cubes and other cuboids, from 2-D representations
To know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
To draw given angles, and measure them in degrees (o)
To identify:
angles at a point and one whole turn (total 360o)
angles at a point on a straight line and a turn (total 180o)
other multiples of 90o
To use the properties of rectangles to deduce related facts and find missing lengths and angles
To use the properties of triangles to find missing angles
To distinguish between regular and irregular polygons based on reasoning about equal sides and angles.
To identify, describe and represent the position of a shape following a reflection or translation, or rotation using the appropriate language, and know that the shape has not changed (congruent)
To plot and read co-ordinates across four quadrants / To describe, sketch and draw using conventional terms and notations: points, lines,
parallel lines, perpendicular lines, right angles, regular polygons, and other polygons
that are reflectively and rotationally symmetric
To use the standard conventions for labelling the sides and angles of triangle ABC, andknow and use the criteria for congruence of triangles
To derive and illustrate properties of triangles, quadrilaterals, circles, and other plane
figures [for example,equal lengths and angles]using appropriate language and
technologies
To identify properties of, and describe the results of, translations, rotations and reflectionsapplied to given figures
To identify and construct congruent triangles, and construct similar shapes by
enlargement, with and without coordinate grids
To apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
To understand and use the relationship between parallel lines and alternate and
corresponding angles
To derive and use the sum of angles in a triangle and use it to deduce the angle sum inany polygon, and to derive properties of regular polygons
To apply angle facts, triangle congruence, similarity and properties of quadrilaterals toderive results about angles and sides, including Pythagoras’ Theorem, and use knownresults to obtain simple proofs
To use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problemsinvolving right-angled triangles
To use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms,cylinders, pyramids, cones and spheres to solve problems in 3-D
To interpret mathematical relationships both algebraically and geometrically.
Handling & Interpreting Data
Year Five / Year Six / Year SevenTo interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.
To solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.
To use the language of probability to discuss events and outcomes (certain/impossible)
To calculate mode of a set of data
TO calculate range of a set of data / To interpret and present discrete, grouped and continuous data using appropriate graphical methods, including bar charts and time graphs.
To solve comparison, sum and difference problems using information presented in a line graph
To complete, read and interpret information in tables, including timetables.
To interpret simple pie charts
To use an increasing language of probability to discuss events and outcomes