Year 6 programme of study (statutory requirements)

Notes and guidance (non-statutory)

Number, place value and rounding Pupils should be taught to:

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

Number, place value and rounding

Pupils should use the whole number system, including saying, reading and writing numbers accurately.

Addition, subtraction, multiplication and division

Pupils should be taught to:

• multiply multi-digit numbers up to 4 digits by a two-digit whole number using the efficient written method of long multiplication
• divide numbers up to 4 digits by a two-digit whole number using the efficient written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for 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, levels of accuracy.

Addition, subtraction, multiplication and division

Pupils should practise addition, subtraction, multiplication and division for larger numbers, using the efficient written methods of columnar addition and subtraction, short and long multiplication, and short and long division.

They should undertake mental calculations with increasingly large numbers and more complex calculations.

Pupils should continue to use all the multiplication tables to calculate mathematical statements in order to maintain their

Pupils should round answers to a specified degree of accuracy.

Pupils explore the order of operations using brackets; for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9.

Common factors can be related to finding equivalent fractions.

Fractions

Pupils should be taught to:

• use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• compare and order fractions, including fractions >1
• associate a fraction with division to calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. ³/₈)
• 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 (e.g. ¹/₄ × ¹/₂ = ¹/₈)
• divide proper fractions by whole numbers (e.g. ¹/₃ ÷ 2 = ¹/₆ ).

Fractions

Pupils should use their understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (e.g. if ¹/₄ of a length is 36cm, then the whole length is 36 × 4 = 144cm).

They should practise with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators. Denominators of given fractions should not exceed 12, with the exception of 100 and Pupils can explore and make conjectures about converting a

simple fraction to a decimal fraction (e.g. 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils should learn about rounding the decimal to three decimal places.

Pupils should practise, use and understand the addition and subtraction of fractions with different denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the denominator of one fraction is a multiple of the other (e.g. ¹/₂ + ¹/₈ = ⁵/₈) and progress to varied and increasingly complex problems.

Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators, as numbers, and as equal parts of objects, for example as parts of a rectangle.

Decimals and fractions

Pupils should be taught to:

• identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are 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.

Decimals and fractions

Pupils should begin to multiply and divide numbers with up to two decimal places by one-digit and two-digit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money.

Pupils should also be introduced to the division of decimal numbers by one-digit whole numbers and, initially, in practical contexts involving measures and money. They should recognise division

calculations as the inverse of multiplication.

Pupils should also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.

Percentages, decimals and fractions Pupils should be taught to:

• solve problems involving the calculation of percentages of whole numbers or measures such as 15% of 360 and the use of percentages for comparison
• recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Percentages, decimals and fractions

Pupils should understand that calculating a percentage of a quantity is the same as calculating a fraction of a quantity.

Ratio and proportion

Pupils should be taught to:

• solve problems involving the relative sizes of two quantities, including similarity
• solve problems involving unequal sharing and grouping.

Ratio and proportion

Pupils should consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They may use the notation a:b to record their work.

Pupils should recognise proportionality in contexts when the relations between quantities are in the same ratio (e.g. similar shapes, recipes).

Algebra

Pupils should be taught to:

• express missing number problems algebraically
• use simple formulae expressed in words
• generate and describe linear number sequences
• find pairs of numbers that satisfy number sentences involving two unknowns.

Algebra

Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:

• missing numbers, lengths, coordinates and angles
• formulae in mathematics and science
• arithmetical rules (e.g. a + b = b + a)
• generalisations of number patterns
• number puzzles (e.g. what two numbers can add up to).

Measures

Pupils should be taught to:

• solve problems involving the calculation and conversion of units of measure, using decimal notation 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 three decimal places
• convert between miles and kilometres
• recognise that shapes with the same areas can have different perimeters and vice versa
• calculate the area of parallelograms and triangles
• recognise when it is necessary to use the formulae for area and volume of shapes
• calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm³) and cubic metres (m³) and extending to other units, such as mm³ and km³.

Measures

Using the number line, pupils should use, add and subtract positive and negative integers for measures such as temperature.

They should know approximate conversions and be able to tell if an answer is sensible.

They should relate the area of rectangles to parallelograms and triangles, and be able to calculate their areas, understanding and using the formula to do this.

Pupils could be introduced to other compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.

Geometry: properties of shapes

Pupils should be taught to:

• 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
• find unknown angles where they meet at a point, are on a straight line, and are vertically opposite.

Geometry: properties of shapes

Pupils should draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles.

Pupils should describe the properties of shapes and explain how

unknown angles and lengths can be derived from known

Geometry: position, direction, motion Pupils should be taught to:

• 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.

Geometry: position, direction, motion

Pupils should draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to

all four quadrants, including the use of negative numbers.

Pupils should draw and label rectangles (including squares), parallelograms and rhombuses, specified by coordinates in the four quadrants, predicting missing coordinates using the properties of shapes.

Data

Pupils should be taught to:

• interpret and construct pie charts and line graphs and use these to solve problems
• calculate and interpret the mean as an average.

Data

Pupils should connect their work on angles, fractions and percentages to the interpretation of pie charts.

Pupils should both encounter and draw graphs relating two variables, arising from their own enquiry and in other subjects.

They should connect conversion from kilometres to miles in measure to its graphical representation.

Pupils should know when it is appropriate to find the mean of a data set.