Year 6 Mathematics

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

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

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

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

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]

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

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

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

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 

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]

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

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

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