Here are the National Curriculum Expectations for Maths for pupils in Year 6:

Number & Place Value:

• 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 - Addition, Subtraction, Multiplication & Division:

•  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.

Number - Fractions, Decimals & Percentages:

• 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 [ f o r e x a m p l e , 41 × 21 = 81 ]

• divide proper fractions by whole numbers [for example, 31 ÷ 2 = 61 ]

•  associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 38 ]

• 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. 

Ratio & Proportions:

•  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. 

 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  enumerate possibilities of combinations of two variables. 

Measurement:

• 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 & Properties of Shape:

• 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. 

Geometry Position & Direction:

• 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. 

Statistics:

• interpret and construct pie charts and line graphs and use these to solve problems
• calculate and interpret the mean as an average