# Year 6

The pupils are working on a broad curriculum in mathematics including: place value; addition and subtraction; multiplication and division; fractions; ratio and proportion; algebra, measurement, geometry and statistics. Their Homework Booklets support all the areas below. They are expected to know all multiplication and division facts up to and including 12 x12.

**Number - number and place value**

In Year 6, pupils read, write, order and compare numbers up to 10,000,000 and determine the value of each digit. They round any whole number to a required degree of accuracy and use negative numbers in context, and calculate intervals across 0. Pupils solve number and practical problems that involve all of the above.

**Number - addition, subtraction, multiplication and division**

Pupils multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication. They 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. Pupils 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. They perform mental calculations, including with mixed operations and large numbers; identify common factors, common multiples/prime numbers and use their knowledge of the order of operations to carry out calculations involving the 4 operations. Pupils solve addition, subtraction, multiplication and division multi-step problems in contexts, deciding which operations and methods to use and why. They 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)**

In fractions, pupils use common factors to simplify fractions; use common multiples to express fractions in the same denomination. They compare and order fractions, including fractions >1 and add/subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions. Pupils multiply simple pairs of proper fractions, writing the answer in its simplest form. They divide proper fractions by whole numbers and associate a fraction with division and calculate decimal fraction equivalents for a simple fraction. They 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. Pupils multiply one-digit numbers with up to 2 decimal places by whole numbers. They use written division methods in cases where the answer has up to 2 decimal places. Pupils solve problems which require answers to be rounded to specified degrees of accuracy and recall/use equivalences between simple fractions, decimals and percentages, including in different contexts.

**Ratio and proportion**

In Year 6, pupils solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts. They solve problems involving the calculation of percentages and the use of percentages for comparison. Pupils solve problems involving similar shapes where the scale factor is known or can be found and problems involving unequal sharing and grouping using knowledge of fractions and multiples.

**Algebra**

In algebra, they use simple formulae; generate and describe linear number sequences and express missing number problems algebraically. They find pairs of numbers that satisfy an equation with 2 unknowns and enumerate possibilities of combinations of 2 variables.

**Measurement**

Pupils solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate. They 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. They convert between miles and kilometres. Pupils recognise that shapes with the same areas can have different perimeters and vice versa. They recognise when it is possible to use formulae for area and volume of shapes. In area they also calculate the area of parallelograms and triangles. Pupils 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 shapes**

Pupils draw 2-D shapes using given dimensions and angles. They recognise, describe and build simple 3-D shapes, including making nets. Pupils compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons. They illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius. Pupils 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 describe positions on the full coordinate grid (all 4 quadrants). They draw and translate simple shapes on the coordinate plane, and reflect them in the axes

**Statistics**

In statistics, pupils interpret and construct pie charts and line graphs and use these to solve problems. They calculate and interpret the mean as an average.