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.

• multiply multi-digit numbers up to 4 digits by a two-digit whole number

• divide numbers up to 4 digits by a two-digit 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 multi-step 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 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

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 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

• 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

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