Mathematics – United Kingdom – National Curriculum
Year 5 programme of study
KS2.Y5.N.NPV – Number  number and place value
Pupils should be taught to:
KS2.Y5.N.NPV.1 – Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit

2 learning outcomes – click to view
Samples: Write numbers – to 100,000. Ordering large numbers. Ordering large numbers No:1. Ordering large numbers No:2.

Write numbers – to 100,000
 Activities: 1 course, 0 extra

Ordering large numbers
 Activities: 1 course, 2 extra


2 learning outcomes – click to view
KS2.Y5.N.NPV.2 – Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
KS2.Y5.N.NPV.3 – Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0

1 learning outcomes – click to view
Samples: Integers on a number line.

Integers on a Number Line
 Activities: 1 course, 0 extra


1 learning outcomes – click to view
KS2.Y5.N.NPV.4 – Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
KS2.Y5.N.NPV.5 – Solve number problems and practical problems that involve all of the above

2 learning outcomes – click to view
Samples: Large numbers presented in tables. Numbers.

Large numbers presented in tables
 Activities: 1 course, 0 extra

Numbers
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.N.NPV.6 – Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals
KS2.Y5.N.AS – Number  addition and subtraction
Pupils should be taught to:
KS2.Y5.N.AS.1 – Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

4 learning outcomes – click to view
Samples: Addition Of Five Digit Numbers. Adding on to Multiples of 10. Addition of large numbers.

Addition of large numbers
 Activities: 4 course, 10 extra

Adding on to multiples of 10
 Activities: 2 course, 0 extra

Addition and Subtraction Revision
 Activities: 2 course, 2 extra

Subtract from 1000
 Activities: 3 course, 0 extra


4 learning outcomes – click to view
KS2.Y5.N.AS.2 – Add and subtract numbers mentally with increasingly large numbers

4 learning outcomes – click to view
Samples: Addition of four digit numbers. Subtraction of four digit numbers. Subtracting from lots of 1000.

Four digit addition (Skill 62)
 Activities: 5 course, 1 extra

Four digit subtraction (Skill 63)
 Activities: 5 course, 1 extra

Subtracting from 1000 (Skill 64)
 Activities: 5 course, 1 extra

Subtracting from 10000 (Skill 65)
 Activities: 5 course, 1 extra


4 learning outcomes – click to view
KS2.Y5.N.AS.3 – Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

2 learning outcomes – click to view
Samples: Adding on to multiples of 10  1. Subtracting large numbers. Adding on to multiples of 10  2.

Adding on to multiples of 10  problem solving
 Activities: 2 course, 4 extra

Subtracting large numbers  problem solving
 Activities: 2 course, 4 extra


2 learning outcomes – click to view
KS2.Y5.N.AS.4 – Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why
KS2.Y5.N.MD – Number  multiplication and division
Pupils should be taught to:
KS2.Y5.N.MD.1 – Identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers

3 learning outcomes – click to view
Samples: Identifying multiples. Common factors. How many factors?.

Identifying multiples
 Activities: 1 course, 0 extra

Common factors
 Activities: 1 course, 0 extra

How many factors?
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y5.N.MD.2 – Know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers

2 learning outcomes – click to view
Samples: Prime and Composite Numbers. Identifying prime numbers.

Prime and Composite Numbers
 Activities: 1 course, 0 extra

Identifying prime numbers
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.N.MD.3 – Establish whether a number up to 100 is prime and recall prime numbers up to 19

1 learning outcomes – click to view
Samples: Identifying prime numbers < 100 (puzzle).

Identifying prime numbers < 100 (puzzle)
 Activities: 1 course, 0 extra


1 learning outcomes – click to view
KS2.Y5.N.MD.4 – Multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit numbers

4 learning outcomes – click to view
Samples: 11x Multiplication facts (times tables). 12x Multiplication facts (times tables). Long Multiplications.

11x tables  skills
 Activities: 2 course, 0 extra

12x tables  skills
 Activities: 2 course, 0 extra

Long Multiplication
 Activities: 4 course, 2 extra

Revision
 Activities: 5 course, 3 extra


4 learning outcomes – click to view
KS2.Y5.N.MD.5 – Multiply and divide numbers mentally, drawing upon known facts

5 learning outcomes – click to view
Samples: Multiply a two digit number by a multiple of ten. Long Multiplication. Three digit division (with remainders).

Multiply a 2 digit number by a multiple of 10 (Skill 72)
 Activities: 4 course, 1 extra

Long Multiplication (Skill 73)
 Activities: 4 course, 1 extra

Three digit division  with remainders (Skill 74)
 Activities: 4 course, 1 extra

Long multiplication  3 digits by 2 digits (Skill 78)
 Activities: 4 course, 1 extra

Long division (Skill 79)
 Activities: 4 course, 1 extra


5 learning outcomes – click to view
KS2.Y5.N.MD.6 – Divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context

3 learning outcomes – click to view
Samples: Division with no remainders. Division (estimation)  1. Division  large numbers (no remainders).

Dividing three digits by one digit  no remainders
 Activities: 3 course, 2 extra

Division (estimation)
 Activities: 2 course, 0 extra

Division  large numbers
 Activities: 2 course, 1 extra


3 learning outcomes – click to view
KS2.Y5.N.MD.7 – Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000

4 learning outcomes – click to view
Samples: Multiplying By 10. Multiplying by 10, 100 or 1000. Multiplying By Multiples Of 10. Dividing Whole Numbers by 100.

Multiplying by 10
 Activities: 5 course, 3 extra

Multiplying by 100
 Activities: 5 course, 3 extra

Multiplying by multiples of 10
 Activities: 2 course, 3 extra

Dividing whole numbers by 100 and 1000
 Activities: 3 course, 0 extra


4 learning outcomes – click to view
KS2.Y5.N.MD.8 – Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)

3 learning outcomes – click to view
Samples: Squaring numbers. Square root. Square root. Index notation: Activity 1. Square roots: Activity 1.

Index notation.
 Activities: 3 course, 3 extra

Square roots
 Activities: 3 course, 0 extra

Square root
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y5.N.MD.9 – Solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes

4 learning outcomes – click to view
Samples: Identifying factors. Challenge puzzle  identifying prime numbers. Index notation (puzzle).

Identifying factors
 Activities: 1 course, 0 extra

Identifying prime numbers
 Activities: 1 course, 0 extra

Index notation
 Activities: 1 course, 0 extra

Square roots
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
KS2.Y5.N.MD.10 – Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

6 learning outcomes – click to view
Samples: Challenge puzzle  flow diagram. Equivalent number sentences (written form). Identifying expressions.

Challenge puzzle  flow diagram
 Activities: 1 course, 0 extra

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

Identifying expressions
 Activities: 1 course, 1 extra

Brackets in number operations
 Activities: 1 course, 0 extra

Brackets in number operations  Two Step
 Activities: 1 course, 0 extra

Balancing equations  Equivalent number sentences
 Activities: 4 course, 0 extra


6 learning outcomes – click to view
KS2.Y5.N.MD.11 – Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

8 learning outcomes – click to view
Samples: Multiplying Multiples of 10 with a missing number. Problem Solving: Multiplication.

Multiplying multiples of 10  Missing Numbers
 Activities: 3 course, 4 extra

Long Multiplication  problem solving
 Activities: 2 course, 5 extra

Dividing multiples of 10 by a single digit number  problem solving
 Activities: 1 course, 2 extra

Dividing three digits by one digit  no remainders  problem solving
 Activities: 0 course, 4 extra

Division  large numbers  problem solving
 Activities: 2 course, 4 extra

Division puzzle
 Activities: 1 course, 0 extra

Division Answers as fractions
 Activities: 1 course, 0 extra

Division  Answers as fractions
 Activities: 1 course, 0 extra


8 learning outcomes – click to view
KS2.Y5.N.F – Number  fractions (including decimals and percentages)
Pupils should be taught to:
KS2.Y5.N.F.1 – Compare and order fractions whose denominators are all multiples of the same number

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

Compare and order fractions.
 Activities: 2 course, 1 extra

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


5 learning outcomes – click to view
KS2.Y5.N.F.2 – Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

6 learning outcomes – click to view
Samples: Equivalence. Matching equivalent fractions. Hundredths In Their Lowest Form.

Modelling equivalent fractions.
 Activities: 2 course, 2 extra

Matching equivalent fractions
 Activities: 1 course, 0 extra

Hundredths in their lowest forms
 Activities: 2 course, 0 extra

Equivalence to a half  identifying the numerator
 Activities: 1 course, 0 extra

Calculating equivalent fractions
 Activities: 4 course, 6 extra

Reducing fractions to their simplest form.
 Activities: 2 course, 2 extra


6 learning outcomes – click to view
KS2.Y5.N.F.3 – Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, â…– + â…˜ = 6/5 = 1 â…• ]

5 learning outcomes – click to view
Samples: Converting Mixed Numbers To Improper Fractions. Converting improper fractions to mixed numbers.

Converting mixed numbers to improper frac.
 Activities: 2 course, 0 extra

Convert improper fractions to mixed numbers
 Activities: 2 course, 0 extra

Adding mixed fractions
 Activities: 1 course, 0 extra

Adding and subtracting fractions
 Activities: 1 course, 0 extra

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


5 learning outcomes – click to view
KS2.Y5.N.F.4 – Add and subtract fractions with the same denominator, and denominators that are multiples of the same number

3 learning outcomes – click to view
Samples: Add Subtract Related Fractions USA. Adding fractions  Tenths and Hundredths.

Addition and subtraction of fractions with the same denominators.
 Activities: 3 course, 0 extra

Adding fractions  Tenths and Hundredths
 Activities: 1 course, 0 extra

Addition and subtraction of related fractions.
 Activities: 4 course, 0 extra


3 learning outcomes – click to view
KS2.Y5.N.F.5 – Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

2 learning outcomes – click to view
Samples: Multiplying fractions by a whole number  visual. Multiplying Mixed Fractions.

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

Multiplying Mixed Fractions
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.N.F.6 – Read and write decimal numbers as fractions [for example, 0.71 = 71/100 ]

1 learning outcomes – click to view
Samples: Changing mixed fractions to decimals.

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


1 learning outcomes – click to view
KS2.Y5.N.F.7 – Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

3 learning outcomes – click to view
Samples: Read and write decimals in the thousandths. thousandths  identifying the value of digits.

Read and write decimals in the thousandths
 Activities: 1 course, 0 extra

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

Place value  thousandths
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y5.N.F.8 – Round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
KS2.Y5.N.F.9 – Read, write, order and compare numbers with up to 3 decimal places

2 learning outcomes – click to view
Samples: Compare and order decimals: Activity 1. Comparing decimals in the thousandths.

Compare and order decimals.
 Activities: 2 course, 1 extra

Comparing decimals in the thousandths
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.N.F.10 – Solve problems involving number up to 3 decimal places

4 learning outcomes – click to view
Samples: Adding Decimals. Subtracting Decimals. Multiplying Decimals By A Single Digit Number. Calculations involving money.

Adding decimals
 Activities: 5 course, 1 extra

Subtracting decimals
 Activities: 5 course, 0 extra

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

Calculations involving money
 Activities: 1 course, 2 extra


4 learning outcomes – click to view
KS2.Y5.N.F.11 – Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction

2 learning outcomes – click to view
Samples: Representing Fractions As Percentage. Percentages as Decimals.

Matching fractions, decimals and percentages.
 Activities: 3 course, 1 extra

Percentages as Decimals
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.N.F.12 – Solve problems which require knowing percentage and decimal equivalents of ½ , ¼ , â…• , â…– , â…˜ and those fractions with a denominator of a multiple of 10 or 25

2 learning outcomes – click to view
Samples: Calculating Percentages. Fractions of numbers  1. Percentages of numbers (answers whole numbers).

Calculating percentages
 Activities: 3 course, 1 extra

Simple fractions of quantities  problem solving
 Activities: 2 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.M – Measurement
Pupils should be taught to:
KS2.Y5.M.1 – Convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]

4 learning outcomes – click to view
Samples: Units of measure. Converting between Kilometres and Metres tutorial. Converting between grams and kilograms.

Converting between kilometers and meters
 Activities: 1 course, 0 extra

Converting between metric units of length.
 Activities: 2 course, 7 extra

Converting between grams and kilograms
 Activities: 1 course, 0 extra

Convert units of mass  between kilograms and grams
 Activities: 5 course, 3 extra


4 learning outcomes – click to view
KS2.Y5.M.2 – Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints

1 learning outcomes – click to view
Samples: Measuring capacity using different units.

Customary units
 Activities: 0 course, 1 extra


1 learning outcomes – click to view
KS2.Y5.M.3 – Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

1 learning outcomes – click to view
Samples: Calculating the Area of Irregular Shapes. Area of irregular shapes. Area of irregular shapes.

Area of irregular shapes
 Activities: 3 course, 1 extra


1 learning outcomes – click to view
KS2.Y5.M.4 – Calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes

1 learning outcomes – click to view
Samples: Area in daily use. Area Problem Solving. Area Problem Solving. Area Problem Solving. Area Problem Solving.

Area
 Activities: 1 course, 4 extra


1 learning outcomes – click to view
KS2.Y5.M.5 – Estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]

1 learning outcomes – click to view
Samples: Comparing the volume of liquids tutorial. Comparing the volume of liquids no.2 tutorial. Volume and Capacity.

Volume and Capacity
 Activities: 3 course, 4 extra


1 learning outcomes – click to view
KS2.Y5.M.6 – Solve problems involving converting between units of time

1 learning outcomes – click to view
Samples: Interpret timetables. Time Problem Solving.

Interpret timetables
 Activities: 1 course, 1 extra


1 learning outcomes – click to view
KS2.Y5.M.7 – Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

7 learning outcomes – click to view
Samples: Length  using decimals and matching equivalence.

Using decimals and matching equivalence.
 Activities: 1 course, 0 extra

Distances on maps.
 Activities: 2 course, 0 extra

How to calculate the area of squares and rectangles.
 Activities: 3 course, 0 extra

Challenge Puzzle  area of irregular shapes
 Activities: 1 course, 0 extra

Choosing appropriate units for measuring mass
 Activities: 2 course, 0 extra

Mass
 Activities: 1 course, 0 extra

Saving money and budgeting
 Activities: 1 course, 0 extra


7 learning outcomes – click to view
KS2.Y5.G.PS – Geometry  properties of shapes
Pupils should be taught to:
KS2.Y5.G.PS.1 – Identify 3D shapes, including cubes and other cuboids, from 2D representations

4 learning outcomes – click to view
Samples: Grouping two dimensional shapes based on their attributes. Identifying corners on 3D objects. Naming 3D Objects.

Grouping two dimensional shapes based on their attributes
 Activities: 1 course, 0 extra

Describe the features of threedimensional objects
 Activities: 4 course, 5 extra

Naming threedimensional objects
 Activities: 2 course, 3 extra

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


4 learning outcomes – click to view
KS2.Y5.G.PS.2 – Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

2 learning outcomes – click to view
Samples: Identifying angles at intersecting lines. Naming angles within shapes. Naming angles: Activity 1.

Classify angles by naming them.
 Activities: 4 course, 1 extra

Naming angles within shapes
 Activities: 1 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.G.PS.3 – Draw given angles, and measure them in degrees (°)

2 learning outcomes – click to view
Samples: Measure and name angles. Estimate, measure and compare angles: Activity 1. Using a protractor to measure angles.

Measure and classify angles.
 Activities: 1 course, 2 extra

Estimating, measuring and comparing angles
 Activities: 2 course, 0 extra


2 learning outcomes – click to view
KS2.Y5.G.PS.4 – Identify:
KS2.Y5.G.PS.4.a: angles at a point and 1 whole turn (total 360°)

1 learning outcomes – click to view
Samples: Angles within a circle.

Angles within a circle
 Activities: 1 course, 0 extra


1 learning outcomes – click to view
KS2.Y5.G.PS.4.b: angles at a point on a straight line and half a turn (total 180°)

1 learning outcomes – click to view
Samples: Angles on a Straight Line. Angles Problem Solving. Angles Problem Solving.

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


1 learning outcomes – click to view
KS2.Y5.G.PS.4.c: other multiples of 90°
KS2.Y5.G.PS.4.d: use the properties of rectangles to deduce related facts and find missing lengths and angles
KS2.Y5.G.PS.4.e:distinguish between regular and irregular polygons based on reasoning about equal sides and angles

1 learning outcomes – click to view
Samples: Angles of Polygons.

Angles of Polygons
 Activities: 0 course, 1 extra


1 learning outcomes – click to view
KS2.Y5.G.PD – Geometry  position and direction
Pupils should be taught to:
KS2.Y5.G.PD.1 – Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed

4 learning outcomes – click to view
Samples: Translations, reflections or rotations: Activity 1. Line of symmetry. Rotational symmetry.

Identify translations, reflections and rotations.
 Activities: 2 course, 0 extra

Identify line of symmetry.
 Activities: 1 course, 0 extra

Identify rotational symmetry.
 Activities: 0 course, 1 extra

Identify combinations of translations, reflections and rotations.
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
KS2.Y5.S – Statistics
Pupils should be taught to:
KS2.Y5.S.1 – Solve comparison, sum and difference problems using information presented in a line graph

1 learning outcomes – click to view
Samples: Line graphs.

Interpret line graphs
 Activities: 1 course, 0 extra


1 learning outcomes – click to view
KS2.Y5.S.2 – Complete, read and interpret information in tables, including timetables

1 learning outcomes – click to view
Samples: Interpret timetables. Time Problem Solving.

Interpret timetables
 Activities: 1 course, 1 extra


1 learning outcomes – click to view