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Maths Year 6

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.

Addition, Subtraction, Multiplication and Division

  • 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, 1⁄4 × 1⁄2 = 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.