Mathematics
The National Curriculum for Mathematics in Year 6
Number  number and place value
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 0
 solve number and practical problems that involve all of the above
Number  addition, subtraction, multiplication and division
Pupils should be taught to:
 multiply multidigit numbers up to 4 digits by a twodigit whole number using the formal written method of long multiplication
 divide numbers up to 4 digits by a twodigit 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 twodigit 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 4 operations
 solve addition and subtraction multistep 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
Number  fractions (including decimals and percentages)
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, 1/4 × 1/2 = 1/8 ]
 divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6 ]
 associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8]
 identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places
 multiply onedigit numbers with up to 2 decimal places by whole numbers
 use written division methods in cases where the answer has up to 2 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
Ratio and proportion
Pupils should be taught to:
 solve problems involving the relative sizes of 2 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
Algebra
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 2 unknowns
 enumerate possibilities of combinations of 2 variables
Measurement
Pupils should be taught to:

 solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 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 3 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  properties of shape
Pupils should be taught to:
 draw 2D shapes using given dimensions and angles
 recognise, describe and build simple 3D 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
Geometry  position and direction
Pupils should be taught to:
 describe positions on the full coordinate grid (all 4 quadrants)
 draw and translate simple shapes on the coordinate plane, and reflect them in the axes
Statistics
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