By the end of Year 6 most children should be able to:
Number and Place Value

read, write, order numbers up to 10 000 000 and know the value of each digit

round any whole number

use negative numbers in context

solve number and practical problems that involve all of the above.
Addition, Subtraction, Multiplication and Division

multiply multidigit numbers up to 4 digits by a twodigit whole number

divide numbers up to 4 digits by a twodigit whole number and interpret remainders as whole number remainders or fractions

perform mental calculations

identify common factors, common multiples and prime numbers

solve addition and subtraction multistep problems in contexts

solve problems involving addition, subtraction, multiplication and division

use estimation to check answers to calculations
Ratio and Proportion

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 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.
Fractions, Decimals and Percentages

use common factors to simplify fractions

use common multiples to express fractions in the same denomination

compare and order fractions, including fractions greater than 1

add and subtract fractions with different denominators and mixed numbers

multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ × ½ = 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 three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

multiply onedigit 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
Ratio and Proportion

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 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

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
Measurement

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

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].
Properties of Shapes

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

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
Position and Direction

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

draw and translate simple shapes and reflect them in the axes.
Statistics

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

calculate and interpret the mean as an average.
Year 6