# 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.

## Autumn

## 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

National Curriculum Links:

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

National Curriculum Link:

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

National Curriculum Links:

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

National Curriculum Links:

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

National Curriculum Links:

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]

## Spring

## Ratio

Step 1 Add or multiply?

Step 2 Use ratio language

Step 3 Introduction to the ratio symbol

Step 4 Ratio and fractions

Step 5 Scale drawing

Step 6 Use scale factors

Step 7 Similar shapes

Step 8 Ratio problems

Step 9 Proportion problems

Step 10 Recipes

National Curriculum Links:

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

Step 1 1-step function machines

Step 2 2-step function machines

Step 3 Form expressions

Step 4 Substitution

Step 5 Formulae

Step 6 Form equations

Step 7 Solve 1-step equations

Step 8 Solve 2-step equations

Step 9 Find pairs of values

Step 10 Solve problems with two unknowns

National Curriculum Links:

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

Step 1 Place value within 1

Step 2 Place value – integers and decimals

Step 3 Round decimals

Step 4 Add and subtract decimals

Step 5 Multiply by 10, 100 and 1,000

Step 6 Divide by 10, 100 and 1,000

Step 7 Multiply decimals by integers

Step 8 Divide decimals by integers

Step 9 Multiply and divide decimals in context

National Curriculum Links:

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

## Fractions, decimals and percentages

Step 1 Decimal and fraction equivalents

Step 2 Fractions as division

Step 3 Understand percentages

Step 4 Fractions to percentages

Step 5 Equivalent fractions, decimals and percentages

Step 6 Order fractions, decimals and percentages

Step 7 Percentage of an amount – one step

Step 8 Percentage of an amount – multi-step

Step 9 Percentages – missing values

National Curriculum Links:

Pupils should be taught to:

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

Associate a fraction with division and calculate decimal fraction equivalents for a simple fraction

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

Compare and order fractions, including fractions >1

Solve problems involving the calculation of percentages and the use of percentages for comparison

## Area, perimeter and volume

Step 1 Shapes – same area

Step 2 Area and perimeter

Step 3 Area of a triangle – counting squares

Step 4 Area of a right-angled triangle

Step 5 Area of any triangle

Step 6 Area of a parallelogram

Step 7 Volume – counting cubes

Step 8 Volume of a cuboid

National Curriculum Links:

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

Step 1 Line graphs

Step 2 Dual bar charts

Step 3 Read and interpret pie charts

Step 4 Pie charts with percentages

Step 5 Draw pie charts

Step 6 The mean

National Curriculum Links:

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

## Summer

## Shape

Step 1 Measure and classify angles

Step 2 Calculate angles

Step 3 Vertically opposite angles

Step 4 Angles in a triangle

Step 5 Angles in a triangle – special cases

Step 6 Angles in a triangle – missing angles

Step 7 Angles in a quadrilateral

Step 8 Angles in polygons

Step 9 Circles

Step 10 Draw shapes accurately

Step 11 Nets of 3-D shapes

National Curriculum Links:

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

## Position and Direction

Step 1 The first quadrant

Step 2 Read and plot points in four quadrants

Step 3 Solve problems with coordinates

Step 4 Translations

Step 5 Reflections

National Curriculum Links:

Pupils should be taught to:

describe positions on the full coordinate grid (all 4 quadrants)

draw and translate simple shapes on the coordinate plane, and reflect them in the axes