Year 6

Children will learn to:

• read, write, order and compare numbers up to 1,000,000,000 and determine the value of each digit

• round any whole number to a required degree of accuracy including powers of 10

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

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

Children will learn to:

• perform mental calculations, including with mixed operations and large 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

• identify common factors, common multiples and prime numbers

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

• 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 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

• solve problems involving addition, subtraction, multiplication and division

• use their knowledge of the order of operations (BIDMAS) to carry out calculations involving four operations.

Children will learn to:

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

• 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

• divide proper fractions by whole numbers

• identify the value of each digit in numbers given to three decimal places

• 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

• associate a fraction with division and calculate decimal fraction equivalents

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

Children will learn 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 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.

Children will learn to:

• use simple formulae

• generate and describe linear number sequences

• find the nth term of a linear sequence

• express missing number problems algebraically

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

• substitute values into expressions

• collect like terms

• enumerate possibilities of combinations of two variables.

Children will learn 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 and cubic metres, and extending to other units.

Children will learn to:

• draw 2-D shapes using given dimensions and angles

• compare and classify geometric shapes based on their properties and sizes

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

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

• find unknown angles in any triangles, quadrilaterals, and regular polygons

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

• describe positions on the full coordinate grid

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

Children will learn to:

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

• calculate and interpret averages