Mathematics – United Kingdom – National Curriculum
Year 6 programme of study
KS2.Y6.N.NPV – Number  number and place value
Pupils should be taught to:
KS2.Y6.N.NPV.1 – Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
KS2.Y6.N.NPV.2 – Round any whole number to a required degree of accuracy
KS2.Y6.N.NPV.3 – Use negative numbers in context, and calculate intervals across 0
KS2.Y6.N.NPV.4 – Solve number and practical problems that involve all of the above

2 learning outcomes – click to view
Samples: Order of Operations. Numbers. Numbers Problem Solving. Number Operations 1 Extension. Number Operations 2 Extension.

Order of operations
 Activities: 1 course, 0 extra

Problem Solving
 Activities: 1 course, 5 extra


2 learning outcomes – click to view
KS2.Y6.N.ASMD – Number  addition, subtraction, multiplication and division
Pupils should be taught to:
KS2.Y6.N.ASMD.1 – Multiply multidigit numbers up to 4 digits by a twodigit whole number using the formal written method of long multiplication
KS2.Y6.N.ASMD.2 – Divide numbers up to 4 digits by a twodigit 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

1 learning outcomes – click to view
Samples: Long division  no remainders. Long division.

Long division
 Activities: 2 course, 0 extra


1 learning outcomes – click to view
KS2.Y6.N.ASMD.3 – Divide numbers up to 4 digits by a twodigit number using the formal written method of short division where appropriate, interpreting remainders according to the context
KS2.Y6.N.ASMD.4 – Perform mental calculations, including with mixed operations and large numbers

7 learning outcomes – click to view
Samples: Short multiplication (missing number). Adding large numbers. Subtraction of large numbers.

Short multiplication  missing number (Skill 75)
 Activities: 4 course, 1 extra

Adding large numbers (Skill 76)
 Activities: 4 course, 1 extra

Subtraction of large numbers (Skill 77)
 Activities: 4 course, 1 extra

Mixed operations e.g. 8 x 5 + 9 (Skill 80)
 Activities: 4 course, 1 extra

Mixed operations e.g. 81 x 9 + 42 (Skill 81)
 Activities: 4 course, 1 extra

Order of operations e.g. 47 x 8 + 24 x 6 (Skill 82)
 Activities: 4 course, 1 extra

Long multiplication  missing number (Skill 83)
 Activities: 4 course, 1 extra


7 learning outcomes – click to view
KS2.Y6.N.ASMD.5 – Identify common factors, common multiples and prime numbers
KS2.Y6.N.ASMD.6 – Use their knowledge of the order of operations to carry out calculations involving the 4 operations

3 learning outcomes – click to view
Samples: Order of operations eg 56 + 7 x 3. Order of operations eg 126  6 x 7. Order of operations: Activity 1.

Order of operations : Multiply before adding
 Activities: 3 course, 0 extra

Order of operations  Multiply before subtracting
 Activities: 2 course, 0 extra

Order of operations  mixed
 Activities: 4 course, 0 extra


3 learning outcomes – click to view
KS2.Y6.N.ASMD.7 – Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why

3 learning outcomes – click to view
Samples: Balancing equations Addition of larger numbers. Two step problem solving (addition and subtraction).

Balancing equations  Equivalent number sentences
 Activities: 5 course, 2 extra

Two step problem solving (addition and subtraction)
 Activities: 1 course, 0 extra

Two step problem solving (money)
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y6.N.ASMD.8 – Solve problems involving addition, subtraction, multiplication and division

5 learning outcomes – click to view
Samples: Two step problem solving. Two step problem solving. Two step problem solving. Two step problem solving. Long division.

Two step problem solving
 Activities: 1 course, 0 extra

Two step problem solving
 Activities: 1 course, 0 extra

Two step problem solving
 Activities: 1 course, 0 extra

Two step problem solving
 Activities: 1 course, 0 extra

Long division  problem solving
 Activities: 1 course, 5 extra


5 learning outcomes – click to view
KS2.Y6.N.ASMD.9 – Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
KS2.Y6.N.F – Number  Fractions (including decimals and percentages)
Pupils should be taught to:
KS2.Y6.N.F.1 – Use common factors to simplify fractions; use common multiples to

2 learning outcomes – click to view
Samples: Simplifying answers to their lowest form. Converting improper fractions to mixed fractions (in equations).

Simplifying answers to their lowest form
 Activities: 1 course, 0 extra

Converting improper fractions to mixed fractions (in equations)
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.N.F.2 – Express fractions in the same denomination
KS2.Y6.N.F.3 – Compare and order fractions, including fractions >1

4 learning outcomes – click to view
Samples: Compare fractions to a half. Comparing fractions  identify the smallest.

Compare fractions to a half
 Activities: 1 course, 0 extra

Comparing fractions  identify the smallest
 Activities: 1 course, 0 extra

Comparing fractions  identify the largest
 Activities: 1 course, 0 extra

Comparing fractions (< = >)
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
KS2.Y6.N.F.4 – Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

4 learning outcomes – click to view
Samples: Addition of fractions with unlike denominators (with clues). Addition of fractions with unlike denominators.

Addition of fractions with unlike denominators (with clues)
 Activities: 1 course, 0 extra

Addition of fractions with unlike denominators
 Activities: 1 course, 0 extra

Subtraction of fractions (unlike denominators)
 Activities: 1 course, 0 extra

Adding mixed fractions
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
KS2.Y6.N.F.5 – Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ × ½ = â…› ]

1 learning outcomes – click to view
Samples: Multiplying Fractions  Fraction by Fraction. Fractions Problem Solving. Fractions Problem Solving.

Multiplying Fractions
 Activities: 1 course, 2 extra


1 learning outcomes – click to view
KS2.Y6.N.F.6 – Divide proper fractions by whole numbers [for example, â…“ ÷ 2 = â…™ ]

6 learning outcomes – click to view
Samples: Multiplying fractions by a whole number  visual. Division  Answers as fractions.

Multiplying fractions by a whole number  visual
 Activities: 1 course, 0 extra

Division Answers as fractions
 Activities: 1 course, 0 extra

Division  Answers as fractions
 Activities: 1 course, 0 extra

Solving (by division) improper fractions
 Activities: 1 course, 0 extra

Divide whole numbers by fractions
 Activities: 1 course, 0 extra

Multiplying and Dividing Fractions
 Activities: 1 course, 0 extra


6 learning outcomes – click to view
KS2.Y6.N.F.7 – Associate a fraction with division and calculate decimal fraction
KS2.Y6.N.F.8 – Equivalents [for example, 0.375] for a simple fraction [for example, â…œ ]
KS2.Y6.N.F.9 – 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

4 learning outcomes – click to view
Samples: thousandths  identifying the value of digits. Dividing Whole Numbers by 10. Multiplying Decimals By 10.

Thousandths  identifying the value of digits
 Activities: 1 course, 0 extra

Dividing whole numbers by 10
 Activities: 4 course, 0 extra

Multiplying decimals by 10
 Activities: 2 course, 0 extra

Multiplying decimals by 1000
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
KS2.Y6.N.F.10 – Multiply onedigit numbers with up to 2 decimal places by whole numbers

1 learning outcomes – click to view
Samples: Multiplying Decimals By A Single Digit Number. Multiplying decimals by a whole number.

Multiplying decimals by a whole number
 Activities: 3 course, 4 extra


1 learning outcomes – click to view
KS2.Y6.N.F.11 – Use written division methods in cases where the answer has up to 2 decimal places
KS2.Y6.N.F.12 – Solve problems which require answers to be rounded to specified degrees of accuracy

2 learning outcomes – click to view
Samples: Rounding Decimals to Whole Numbers. Division (estimation)  1. Division (estimation)  2.

Rounding Decimals to Whole Numbers
 Activities: 1 course, 0 extra

Division (estimation)
 Activities: 2 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.N.F.13 – Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

5 learning outcomes – click to view
Samples: Increasing by a Percentage. Simple Interest. Decreasing by a Percentage. Percentages as Decimals.

Increasing by a Percentage
 Activities: 1 course, 0 extra

Simple Interest
 Activities: 1 course, 0 extra

Decreasing by a Percentage
 Activities: 1 course, 0 extra

Percentages as Decimals
 Activities: 1 course, 0 extra

Changing mixed fractions to decimals
 Activities: 0 course, 1 extra


5 learning outcomes – click to view
KS2.Y6.RP – Ratio and proportion
Pupils should be taught to:
KS2.Y6.RP.1 – Solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts

2 learning outcomes – click to view
Samples: Simplifying Ratios. Calculating Equivalent Ratios.

Simplifying Ratios
 Activities: 1 course, 0 extra

Calculating Equivalent Ratios
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.RP.2 – Solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison

2 learning outcomes – click to view
Samples: Simple Quantities (fractions of whole numbers). Fractions of numbers  1. Simple fractions of quantities.

Simple fractions of quantities
 Activities: 6 course, 0 extra

Simple fractions of quantities  problem solving
 Activities: 2 course, 2 extra


2 learning outcomes – click to view
KS2.Y6.RP.3 – Solve problems involving similar shapes where the scale factor is known or can be found
KS2.Y6.RP.4 – Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

2 learning outcomes – click to view
Samples: Simplifying Ratios Involving Units. Problem Solving  Unitary Method.

Simplifying Ratios involving Units
 Activities: 1 course, 0 extra

Problem Solving  Unitary Method
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.A – Algebra
Pupils should be taught to:
KS2.Y6.A.1 – Use simple formulae

2 learning outcomes – click to view
Samples: Equivalent number sentences (written form). Identifying expressions. Identifying Expressions.

Solve equivalent number sentences presented in written form
 Activities: 1 course, 0 extra

Identifying expressions
 Activities: 1 course, 1 extra


2 learning outcomes – click to view
KS2.Y6.A.2 – Generate and describe linear number sequences

2 learning outcomes – click to view
Samples: Continue number patterns (multiplication). Rules defining number patterns.

Describe and continue number patterns resulting from multiplication
 Activities: 1 course, 0 extra

Rules defining number patterns
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.A.3 – Express missing number problems algebraically

2 learning outcomes – click to view
Samples: Applying rules to number tables. Continuing number sequences including fractions and decimals.

Applying rules to number tables
 Activities: 1 course, 0 extra

Continuing number sequences
 Activities: 1 course, 6 extra


2 learning outcomes – click to view
KS2.Y6.A.4 – Find pairs of numbers that satisfy an equation with 2 unknowns

2 learning outcomes – click to view
Samples: Substituting numbers for letters. Subtraction of Like Terms. Input  Output. Input  Output. Number Pattern Tables.

Introducing variables
 Activities: 5 course, 0 extra

Subtraction of Like Terms
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.A.5 – Enumerate possibilities of combinations of 2 variables

2 learning outcomes – click to view
Samples: Represent problems using algebraic equation. Substituting Numerals 1. Algebraic Techniques.

Represent problems using algebraic equation
 Activities: 1 course, 0 extra

Substituting values for variables
 Activities: 5 course, 1 extra


2 learning outcomes – click to view
KS2.Y6.M – Measurement
Pupils should be taught to:
KS2.Y6.M.1 – Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate
KS2.Y6.M.2 – 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
KS2.Y6.M.3 – Convert between miles and kilometres
KS2.Y6.M.4 – Recognise that shapes with the same areas can have different perimeters and vice versa
KS2.Y6.M.5 – Recognise when it is possible to use formulae for area and volume of shapes

3 learning outcomes – click to view
Samples: Cubic Cm Rectangular Prism. Volume Extension. Circumference of a Circle. Volume Of Rectangular Prism.

Volume of rectangular prisms
 Activities: 3 course, 2 extra

Volume
 Activities: 1 course, 1 extra

Circumference of a Circle
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y6.M.6 – Calculate the area of parallelograms and triangles

2 learning outcomes – click to view
Samples: Area of Triangles. Area of Parallelograms.

Area of Triangles
 Activities: 1 course, 0 extra

Area of a Parallelogram
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.M.7 – 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]

1 learning outcomes – click to view
Samples: Volume of a Cylinder.

Volume of a Cylinder
 Activities: 1 course, 0 extra


1 learning outcomes – click to view
KS2.Y6.G.PS – Geometry  properties of shapes
Pupils should be taught to:
KS2.Y6.G.PS.1 – Draw 2D shapes using given dimensions and angles
KS2.Y6.G.PS.2 – Recognise, describe and build simple 3D shapes, including making nets

1 learning outcomes – click to view
Samples: Matching  threedimensional objects with their nets. Identifying the nets of threedimensional shapes.

Nets of three dimensional objects
 Activities: 4 course, 2 extra


1 learning outcomes – click to view
KS2.Y6.G.PS.3 – Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

4 learning outcomes – click to view
Samples: Naming prisms and pyramids. Angles on a Triangle. Angles in Quadrilaterals. Angles of Polygons. Prisms and pyramids.

Identifying properties and naming prisms and pyramids
 Activities: 2 course, 8 extra

Angles on a Triangle
 Activities: 0 course, 1 extra

Angles in Quadrilaterals
 Activities: 0 course, 1 extra

Angles of Polygons
 Activities: 0 course, 1 extra


4 learning outcomes – click to view
KS2.Y6.G.PS.4 – Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

2 learning outcomes – click to view
Samples: Angles within a circle. Parts of a circle. Learn the parts of a circle. Parts of a circle.

Angles within a circle
 Activities: 1 course, 0 extra

Parts of a Circle
 Activities: 4 course, 0 extra


2 learning outcomes – click to view
KS2.Y6.G.PS.5 – Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

3 learning outcomes – click to view
Samples: Angles on a Straight Line. Challenge puzzle  angles. Exterior Angles. Angles Problem Solving. Angles Problem Solving.

Angle sum of straight lines, triangles and quadrilaterals.
 Activities: 1 course, 4 extra

Challenge puzzle  angles
 Activities: 1 course, 0 extra

Exterior Angles
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y6.G.PD – Geometry  position and direction
Pupils should be taught to:
KS2.Y6.G.PD.1 – Describe positions on the full coordinate grid (all 4 quadrants)

1 learning outcomes – click to view
Samples: Cartesian coordinate system: Activity 1. Cartesian coordinate system: Activity 2.

Use the cartesian coordinate system to identify location.
 Activities: 2 course, 2 extra


1 learning outcomes – click to view
KS2.Y6.G.PD.2 – Draw and translate simple shapes on the coordinate plane, and reflect them in the axes
KS2.Y6.G.S – Statistics
Pupils should be taught to:
KS2.Y6.G.S.1 – Interpret and construct pie charts and line graphs and use these to solve problems

3 learning outcomes – click to view
Samples: Interpreting column graphs  6. Line graphs. Interpret a pie graph. Data Problem Solving.

Interpret and compare data presented using a column graph
 Activities: 1 course, 2 extra

Interpret line graphs
 Activities: 1 course, 0 extra

Interpret data presented using a pie graph
 Activities: 1 course, 7 extra


3 learning outcomes – click to view
KS2.Y6.G.S.2 – Calculate and interpret the mean as an average

3 learning outcomes – click to view
Samples: Median, Range and Mean. Chance Fraction. Chance from 0 to 1. Chance Problem Solving. Chance Problem Solving.

Calculate mean, median, mode and range.
 Activities: 1 course, 0 extra

Represent chance using fractions.
 Activities: 1 course, 4 extra

Recognise that probabilities range from 0 to 1.
 Activities: 1 course, 0 extra


3 learning outcomes – click to view