# Year 6 Mathematics

The long term plan below shows the order in which units are taught and approximately how many weeks are spent on each unit.

These are broken down further into the small stepsfor each unit of work. All small steps involve an element of reasoning and problem solving and link to the National Curriculum. ## Place Value

Step 1 Numbers to 1,000,000

Step 2 Numbers to 10,000,000

Step 3 Read and write numbers to 10,000,000

Step 4 Powers of 10

Step 5 Number line to 10,000,000

Step 6 Compare and order any integers

Step 7 Round any integer

Step 8 Negative numbers

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 0

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

## Addition, Subtraction, Multiplication and Division

Step 1 Add and subtract integers

Step 2 Common factors

Step 3 Common multiples

Step 4 Rules of divisibility

Step 5 Primes to 100

Step 6 Square and cube numbers

Step 7 Multiply up to a 4-digit number by a 2-digit number

Step 8 Solve problems with multiplication

Step 9 Short division

Step 10 Division using factors

Step 11 Introduction to long division

Step 12 Long division with remainders

Step 13 Solve problems with division

Step 14 Solve multi-step problems

Step 15 Order of operations

Step 16 Mental calculations and estimation

Step 17 Reason from known facts

Pupils should be taught to:

• 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 4 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

## Fractions A

Step 1 Equivalent fractions and simplifying

Step 2 Equivalent fractions on a number line

Step 3 Compare and order (denominator)

Step 4 Compare and order (numerator)

Step 5 Add and subtract simple fractions

Step 6 Add and subtract any two fractions

Step 7 Add mixed numbers

Step 8 Subtract mixed numbers

Step 9 Multi-step problems

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

• 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, 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 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places

• multiply one-digit numbers with up to 2 decimal places by whole numbers

• use written division methods in cases where the answer has up to 2 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

## Fractions B

Step 1 Multiply fractions by integers

Step 2 Multiply fractions by fractions

Step 3 Divide a fraction by an integer

Step 4 Divide any fraction by an integer

Step 5 Mixed questions with fractions

Step 6 Fraction of an amount

Step 7 Fraction of an amount – find the whole

Pupils should be taught to:

• 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 ]

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

## Converting Units

Step 1 Metric measures

Step 2 Convert metric measures

Step 3 Calculate with metric measures

Step 4 Miles and kilometres

Step 5 Imperial measures

Pupils should be taught to:

• solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 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 3 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]

## Ratio

Pupils should be taught to:

• solve problems involving the relative sizes of 2 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

## Algebra

Pupils should be taught to:

• use simple formulae

• generate and describe linear number sequences

• express missing number problems algebraically

• find pairs of numbers that satisfy an equation with 2 unknowns

• enumerate possibilities of combinations of 2 variables

## Decimals

Pupils should be taught to:

• 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 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places

• multiply one-digit numbers with up to 2 decimal places by whole numbers

• use written division methods in cases where the answer has up to 2 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

coming soon

## Area, perimeter and volume

Pupils should be taught to:

• solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 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 3 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]

## Statistics

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

## Shape

Pupils should be taught to:

• 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