Maths in Year Six - National Curriculum

Number – number and place value

Statutory requirements

Pupils should be taught to:

  • read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

  • round any whole number to a required degree of accuracy

  • use negative numbers in context, and calculate intervals across zero

  • solve number and practical problems that involve all of the above.

Number – fractions (including decimals and percentages)

Statutory requirements

Pupils should be taught to:

  • use common factors to simplify fractions; use common multiples to express fractions in the same denomination

  • compare and order fractions, including fractions > 1

  • add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

  • multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, × = ]

  • divide proper fractions by whole numbers [for example, ÷ 2 = ]

  • associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ]

  • identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

  • multiply one-digit numbers with up to two decimal places by whole numbers

  • use written division methods in cases where the answer has up to two decimal places

  • solve problems which require answers to be rounded to specified degrees of accuracy

  • recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Algebra

Statutory requirements

Pupils should be taught to:

  • use simple formulae

  • generate and describe linear number sequences

  • express missing number problems algebraically

  • find pairs of numbers that satisfy an equation with two unknowns

  • enumerate possibilities of combinations of two variables.

Geometry – properties of shapes

Statutory requirements

Pupils should be taught to:

  • draw 2-D shapes using given dimensions and angles

  • recognise, describe and build simple 3-D shapes, including making nets

  • compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

  • illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

  • recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

Number – addition, subtraction, multiplication and division

Statutory requirements

Pupils should be taught to:

  • multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

  • 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, or by rounding, as appropriate for the context

  • 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

  • perform mental calculations, including with mixed operations and large numbers

  • identify common factors, common multiples and prime numbers

  • use their knowledge of the order of operations to carry out calculations involving the four operations

  • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

  • solve problems involving addition, subtraction, multiplication and division

  • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Ratio and proportion

Statutory requirements

Pupils should be taught to:

  • solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

  • solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison

  • solve problems involving similar shapes where the scale factor is known or can be found

  • solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Measurement

Statutory requirements

Pupils should be taught to:

  • solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

  • use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places

  • convert between miles and kilometres

  • recognise that shapes with the same areas can have different perimeters and vice versa

  • recognise when it is possible to use formulae for area and volume of shapes

  • calculate the area of parallelograms and triangles

  • calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3].

Geometry – position and direction

Statutory requirements

Statistics

Statutory requirements

Pupils should be taught to:

  • interpret and construct pie charts and line graphs and use these to solve problems

  • calculate and interpret the mean as an average.

Pupils should be taught to:

  • describe positions on the full coordinate grid (all four quadrants)

  • draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

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