Year 6 Maths Expectations

In mathematics by the end of Year 6
most children should be able to:

• solve multi-step problems, including those that involve fractions, decimals and percentages
• develop and refine their strategies to solve increasingly complex problems, recognising that to simplify a problem is a helpful starting point
• work systematically and independently
• organise their work clearly, interpreting results and reflecting on the efficiency of their methods
• recognise that representing a problem may require a diagram, numbers or calculations, and that after solving the problem, the solution needs to be interpreted and checked in the original context
• describe, interpret and use patterns and relationships which they observe
• use words then letters as symbols to construct and use simple expressions or formulae
• make and test predictions and general statements
• make deductions from given statements or information
• explain their reasoning and justify their choices and conclusions
• manipulate a range of types of numbers
• order positive and negative whole numbers and decimal numbers with up to three decimal places and position these on number lines
• find the difference between positive and negative numbers in context
• partition whole and decimal numbers, using place value to compare and order them
• understand how to simplify fractions by cancelling, dividing the numerator and denominator by a common factor
• order a set of fractions by converting them to equivalent fractions with a common denominator,
• express a larger whole number as a fraction of a smaller whole number and convert it to a mixed number
• find fractions and percentages of numbers and quantities
• solve problems involving direct proportion
• scale quantities up or down, such as the ingredients in a recipe
• consolidate their knowledge of number facts involving all four operations and use known facts to derive related facts
• use these facts to add and subtract mentally whole numbers and numbers with one decimal place
• apply their knowledge of multiplication and division facts to multiplication and division of two-digit numbers that include decimals
• use their knowledge of place value to multiply whole numbers by 1000, 100, 10, 0.1 and 0.01 and by multiples of these
• have a secure, reliable method of written calculation for each operation and recognise when one method may be more efficient than another, for both whole numbers and decimals
• recognise when mental methods are more appropriate and use a calculator to solve problems where sequences of addition and subtraction calculations are involved
• continue to approximate first and check their answers
• explain the method they use and the steps involved
• make and draw shapes with increasing accuracy
• recognise, describe and visualise solids with parallel and perpendicular edges or faces
• recognise how the nets of these solids are formed and how a solid can be made from a given net
• use their growing understanding of angles to classify and describe 2-D shapes
• measure the angles in shapes they draw to check estimates and to test statements
• know that a complete turn is four right angles or 360º and use this to calculate the size of angles around a point
• use the coordinate system to identify and plot points in the first quadrant
• draw shapes on grids of different types, determine and describe the positions of the shapes after a transformation, including a reflection, a translation or a rotation through a quarter or half turn about its centre or a vertex
• recognise that the shape remains identical after one of these transformations and use this knowledge to identify congruent shapes in patterns, pictures and diagrams
• read and interpret the scales on measuring instruments where the intervals are large, few or mostly unlabelled
• recognise that taking a measurement involves a comparison to agreed standard units and that the measurement made is approximate
• record their results using an appropriate unit and to a required degree of accuracy
• calculate the perimeter and area of a rectangle and compound shapes that can be split into squares, half squares or rectangles
• develop their understanding of the language of chance and likelihood by describing situations where outcomes are equally likely
• begin to place outcomes from observed events and from experiments onto a numbered probability scale to indicate the chances of occurrence, using 0 to represent 'impossible' and 1 to represent 'certain'
• solve problems by collecting data, processing the data using tables or lists and presenting it to show findings and to draw conclusions
• use the mode, range, median and mean to represent and describe a set of data
• construct frequency tables with single and grouped data items and represent these as bar charts
• extend their use of line graphs to interpret graphs where intermediate points have meaning, for example on a conversion graph
• interpret tables, charts and databases they have generated using ICT or taken from a secondary source such as another subject area
• interpret pie charts and use their knowledge of fractions and percentages to estimate the size of sectors in a pie chart
• recognise that pie charts that look similar can represent different totals and that a small sector in one pie chart can represent more items than a big sector on another