## Year 6

· 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.

· 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.

· 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.

· 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, ¼ x ½ = ⅛].

· 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, ⅜].

· 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.

· 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.

· 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.

· 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].

· 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.

· 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.

· Interpret and construct pie charts and line graphs and use these to solve problems.

· Calculate and interpret the mean as an average.

· 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.

· 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.

· 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.

· 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, ¼ x ½ = ⅛].

· 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, ⅜].

· 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.

· 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.

· 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.

· 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].

· 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.

· 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.

· Interpret and construct pie charts and line graphs and use these to solve problems.

· Calculate and interpret the mean as an average.

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