Mathematics – United Kingdom – National Curriculum
Year 4 programme of study
KS2.Y4.N.NPV – Number  number and place value
Pupils should be taught to:
KS2.Y4.N.NPV.1 – Count in multiples of 6, 7, 9, 25 and 1,000

3 learning outcomes – click to view
Samples: Groups of 6. Groups of 7. Groups of 9. Rows of 6. Rows of 7. Rows of 9.

Groups and rows of 6
 Activities: 2 course, 0 extra

Groups and rows of 7
 Activities: 2 course, 0 extra

Groups and rows of 9
 Activities: 2 course, 0 extra


3 learning outcomes – click to view
KS2.Y4.N.NPV.2 – Find 1,000 more or less than a given number
KS2.Y4.N.NPV.3 – Count backwards through 0 to include negative numbers

1 learning outcomes – click to view
Samples: Negative numbers. Negative numbers.

Negative numbers  an introduction
 Activities: 1 course, 1 extra


1 learning outcomes – click to view
KS2.Y4.N.NPV.4 – Recognise the place value of each digit in a fourdigit number (1,000s, 100s, 10s, and 1s)

2 learning outcomes – click to view
Samples: Writing large numbers  four digits. Expanded Notation. Expanded notation: Activity 1. Expanded notation.

Writing large numbers  four digits
 Activities: 1 course, 0 extra

Expanded notation
 Activities: 2 course, 4 extra


2 learning outcomes – click to view
KS2.Y4.N.NPV.5 – Order and compare numbers beyond 1,000

2 learning outcomes – click to view
Samples: Place Value to 1000. Great than or Less than. Identifying place value to 10000.

Place Value to 10000
 Activities: 2 course, 12 extra

Comparing numbers to 10,000 (<,=,>)
 Activities: 2 course, 1 extra


2 learning outcomes – click to view
KS2.Y4.N.NPV.6 – Identify, represent and estimate numbers using different representations

4 learning outcomes – click to view
Samples: Expanded Notation Part 1. Placing Decimals On A Number Line. Compare and order decimals: Activity 1.

Identifying the place value of digits  numbers to 10000
 Activities: 3 course, 1 extra

Decimals on a number line.
 Activities: 2 course, 2 extra

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

Paying for goods and services
 Activities: 1 course, 3 extra


4 learning outcomes – click to view
KS2.Y4.N.NPV.7 – Round any number to the nearest 10, 100 or 1,000

2 learning outcomes – click to view
Samples: Rounding numbers to the nearest 10. Round to the nearest 100  round up or down?. Rounding numbers to ten.

Rounding numbers to the nearest multiple of 10.
 Activities: 6 course, 3 extra

Round to the nearest 100
 Activities: 2 course, 0 extra


2 learning outcomes – click to view
KS2.Y4.N.NPV.8 – Solve number and practical problems that involve all of the above and with increasingly large positive numbers

4 learning outcomes – click to view
Samples: Challenge puzzle. Ordering large numbers. Large numbers presented in tables. Paying for goods.

Challenge puzzle  Odd and Even Numbers
 Activities: 1 course, 0 extra

Ordering large numbers
 Activities: 1 course, 6 extra

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

Paying for goods and calculating totals
 Activities: 1 course, 6 extra


4 learning outcomes – click to view
KS2.Y4.N.NPV.9 – Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value
KS2.Y4.N.AS – Number  addition and subtraction
Pupils should be taught to:
KS2.Y4.N.AS.1 – Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

14 learning outcomes – click to view
Samples: Place value  'Adding On' single digit numbers. Place value  Two digit addition without trading.

Place value  'Adding On' single digit numbers
 Activities: 1 course, 0 extra

Place value  Adding two digit numbers (no regrouping)
 Activities: 1 course, 0 extra

Adding multiples of 10
 Activities: 2 course, 4 extra

Place value  Adding three digit numbers (no regrouping)
 Activities: 1 course, 0 extra

Make 100
 Activities: 2 course, 2 extra

Adding three numbers
 Activities: 5 course, 10 extra

Subtracting 10  Blocks as visual cues
 Activities: 1 course, 0 extra

Subtracting multiples of 10  Blocks as visual cues
 Activities: 1 course, 0 extra

Place value  Subtract three digit numbers
 Activities: 1 course, 0 extra

Subtracting two digit numbers (adding on)
 Activities: 3 course, 0 extra

Subtracting two digit numbers (jump back strategy)
 Activities: 4 course, 16 extra

Subtracting two digit numbers (written strategy)
 Activities: 5 course, 10 extra

Subtracting two digit numbers
 Activities: 1 course, 1 extra

Subtracting large numbers
 Activities: 4 course, 14 extra


14 learning outcomes – click to view
KS2.Y4.N.AS.2 – Estimate and use inverse operations to check answers to a calculation

6 learning outcomes – click to view
Samples: Addition of three digit numbers. Mental strategy for adding 3 numbers. Adding three numbers.

Three digit addition (Skill 48)
 Activities: 5 course, 7 extra

Mental strategies for adding 3 numbers (Skill 60)
 Activities: 5 course, 1 extra

Adding 3 numbers (Skill 61)
 Activities: 4 course, 7 extra

Four digit addition (Skill 62)
 Activities: 5 course, 7 extra

Four digit subtraction (Skill 63)
 Activities: 5 course, 7 extra

Subtracting from 1000 (Skill 64)
 Activities: 5 course, 7 extra


6 learning outcomes – click to view
KS2.Y4.N.AS.3 – Solve addition and subtraction twostep problems in contexts, deciding which operations and methods to use and why

4 learning outcomes – click to view
Samples: Adding large numbers (problem solving). Addition of large numbers (puzzle). Subtraction  missing number.

Adding large numbers (problem solving)
 Activities: 2 course, 9 extra

Addition of large numbers (puzzle)
 Activities: 1 course, 0 extra

Subtraction  missing number
 Activities: 1 course, 2 extra

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


4 learning outcomes – click to view
KS2.Y4.N.MD – Number  multiplication and division
Pupils should be taught to:
KS2.Y4.N.MD.1 – Recall multiplication and division facts for multiplication tables up to 12 × 12

8 learning outcomes – click to view
Samples: 6x tables. 7x tables. 9x tables. 11x tables. 12x tables. Dividing by 6. Dividing by 7. Dividing by 9. 6x tables. 7x tables.

6x tables
 Activities: 3 course, 5 extra

7x tables
 Activities: 3 course, 6 extra

9x tables
 Activities: 3 course, 6 extra

11x tables
 Activities: 2 course, 1 extra

12x tables
 Activities: 2 course, 1 extra

Dividing by 6
 Activities: 2 course, 1 extra

Dividing by 7
 Activities: 2 course, 1 extra

Dividing by 9
 Activities: 2 course, 1 extra


8 learning outcomes – click to view
KS2.Y4.N.MD.2 – Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers

14 learning outcomes – click to view
Samples: 2x10x tables. Division with no remainders. Multiplying by 10. Multiplying by 100. Six times tables (6x).

2x10x tables
 Activities: 2 course, 7 extra

Division facts
 Activities: 3 course, 8 extra

Multiplying by 10
 Activities: 4 course, 7 extra

Multiplying by 100
 Activities: 3 course, 8 extra

6x times tables (Skill 50)
 Activities: 4 course, 7 extra

7x times tables (Skill 51)
 Activities: 4 course, 7 extra

9x times tables (Skill 53)
 Activities: 4 course, 7 extra

Multiplying by 10 (Skill 57)
 Activities: 5 course, 7 extra

Multiplying by 100 (Skill 58)
 Activities: 5 course, 1 extra

Multiplying lots of 10 by a single digit number (Skill 66)
 Activities: 5 course, 7 extra

Mental strategies for short multiplication (Skill 68)
 Activities: 4 course, 1 extra

Short multiplication (Skill 69)
 Activities: 4 course, 7 extra

Dividing multiples of 10 by a single digit number (Skill 70)
 Activities: 4 course, 1 extra

Dividing 3 digits by 1 digit  no remainders (Skill 71)
 Activities: 4 course, 7 extra


14 learning outcomes – click to view
KS2.Y4.N.MD.3 – Recognise and use factor pairs and commutativity in mental calculations

3 learning outcomes – click to view
Samples: Factors. Identifying multiples. Factor trees. Identifying factors: Activity 1. Identifying factors: Activity 1.

Identifying factors
 Activities: 2 course, 1 extra

Identifying multiples
 Activities: 1 course, 0 extra

Factor trees
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y4.N.MD.4 – Multiply twodigit and threedigit numbers by a onedigit number using formal written layout

3 learning outcomes – click to view
Samples: Multiplying 2 by 1 digit (mental strategy). Multiplying 2 by 1 digit (written strategy). Multiplying 2 by 1 digit.

Multiplying 2 by 1 digit (mental strategy)
 Activities: 1 course, 2 extra

Multiplying 2 by 1 digit (written strategy)
 Activities: 3 course, 11 extra

Multiplying 2 by 1 digit
 Activities: 1 course, 10 extra


3 learning outcomes – click to view
KS2.Y4.N.MD.5 – Solve problems involving multiplying and adding, including using the distributive law to multiply twodigit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

13 learning outcomes – click to view
Samples: 6x Multiplication facts (times tables)  1. 7x tables (problem solving). 9x tables (problem solving).

6x tables  problem solving
 Activities: 2 course, 3 extra

7x tables (problem solving)
 Activities: 2 course, 3 extra

9x tables (problem solving)
 Activities: 3 course, 5 extra

2x10x tables (problem solving)
 Activities: 4 course, 4 extra

2x10x tables  puzzle
 Activities: 1 course, 0 extra

Multiplying by 10 or 100 (problem solving)
 Activities: 3 course, 6 extra

Multiples of 10 by 1 digit  problem solving
 Activities: 0 course, 1 extra

Multiplying multiples of 10  puzzle
 Activities: 1 course, 0 extra

Multiplying 2 digits by a 1 digit number  Puzzle
 Activities: 1 course, 0 extra

Multiplying 2 by 1 digit (missing number)
 Activities: 2 course, 7 extra

Dividing by 6 (problem solving)
 Activities: 3 course, 2 extra

Dividing by 7 (problem solving)
 Activities: 3 course, 2 extra

Division facts (problem solving)
 Activities: 2 course, 7 extra


13 learning outcomes – click to view
KS2.Y4.N.F – Number  fractions (including decimals)
Pupils should be taught to:
KS2.Y4.N.F.1 – Recognise and show, using diagrams, families of common equivalent fractions

2 learning outcomes – click to view
Samples: Matching equivalent fractions. Equivalence. Modelling equivalent fractions.

Matching equivalent fractions
 Activities: 1 course, 0 extra

Modelling equivalent fractions.
 Activities: 2 course, 3 extra


2 learning outcomes – click to view
KS2.Y4.N.F.2 – Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10

3 learning outcomes – click to view
Samples: Recognizing Naming Hundredths. Introduction to decimals: Activity 1. Converting tenths and hundredths to decimals.

Tenths and hundredths.
 Activities: 3 course, 4 extra

Introduction to decimals.
 Activities: 2 course, 0 extra

Converting tenths and hundredths to decimals
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
KS2.Y4.N.F.3 – Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including nonunit fractions where the answer is a whole number

2 learning outcomes – click to view
Samples: Adding fractions  Tenths and Hundredths. Multiplying fractions by a whole number  visual.

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

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


2 learning outcomes – click to view
KS2.Y4.N.F.4 – Add and subtract fractions with the same denominator

1 learning outcomes – click to view
Samples: Add Subtract Related Fractions USA. Adding and subtracting fractions with same denominators.

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


1 learning outcomes – click to view
KS2.Y4.N.F.5 – Recognise and write decimal equivalents of any number of tenths or hundredths

1 learning outcomes – click to view
Samples: Comparing fractions and decimals  tenths and hundredths.

Comparing fractions and decimals  tenths and hundredths
 Activities: 1 course, 0 extra


1 learning outcomes – click to view
KS2.Y4.N.F.6 – Recognise and write decimal equivalents to ¼ ,½ , ¾

1 learning outcomes – click to view
Samples: Equivalence between fractions and decimals: Activity 1. Equivalence between fractions and decimals: Activity 2.

Equivalence between fractions and decimals.
 Activities: 2 course, 2 extra


1 learning outcomes – click to view
KS2.Y4.N.F.7 – Find the effect of dividing a one or twodigit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths

1 learning outcomes – click to view
Samples: Dividing Whole Numbers by 10. Dividing a whole number by 10. Divide by 10. Dividing a whole number by 100.

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


1 learning outcomes – click to view
KS2.Y4.N.F.8 – Round decimals with 1 decimal place to the nearest whole number

1 learning outcomes – click to view
Samples: Rounding Decimals to Whole Numbers.

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


1 learning outcomes – click to view
KS2.Y4.N.F.9 – Compare numbers with the same number of decimal places up to 2 decimal places

2 learning outcomes – click to view
Samples: Placing Decimals On A Number Line. Compare and order decimals: Activity 1. Decimals on the number line.

Decimals on a number line.
 Activities: 2 course, 2 extra

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


2 learning outcomes – click to view
KS2.Y4.N.F.10 – Solve simple measure and money problems involving fractions and decimals to 2 decimal places

3 learning outcomes – click to view
Samples: Divide whole numbers by fractions. Multiplying Decimals By A Single Digit Number. Fractions of numbers  1.

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

Multiplying decimals by a whole number
 Activities: 3 course, 6 extra

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


3 learning outcomes – click to view
KS2.Y4.M – Measurement
Pupils should be taught to:
KS2.Y4.M.1 – Convert between different units of measure [for example, kilometre to metre; hour to minute]

4 learning outcomes – click to view
Samples: Converting between kilometres and metres. Converting between grams and kilograms.

Converting between kilometres and metres
 Activities: 1 course, 0 extra

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

Converting between litres and millilitres
 Activities: 1 course, 0 extra

Convert between units of time
 Activities: 2 course, 1 extra


4 learning outcomes – click to view
KS2.Y4.M.2 – Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

1 learning outcomes – click to view
Samples: Calculating Perimeter Regular Shapes. Perimeter of squares and rectangles. Calculating perimeter tutorial.

Perimeter of squares and rectangles.
 Activities: 2 course, 4 extra


1 learning outcomes – click to view
KS2.Y4.M.3 – Find the area of rectilinear shapes by counting squares

2 learning outcomes – click to view
Samples: Area using square tiles. Measure using square centimetres. Measure area using a grid tutorial.

Area using square tiles
 Activities: 1 course, 0 extra

Comparing and measuring area using a grid.
 Activities: 3 course, 10 extra


2 learning outcomes – click to view
KS2.Y4.M.4 – Estimate, compare and calculate different measures, including money in pounds and pence

7 learning outcomes – click to view
Samples: Budgeting and Expenses. Paying with currencies from around the world. Different payment options. Units of measure.

Budgeting
 Activities: 1 course, 0 extra

Currencies around the world
 Activities: 2 course, 0 extra

Different payment options
 Activities: 1 course, 0 extra

Choose appropriate units when measuring length.
 Activities: 2 course, 3 extra

Measure volume using centicubes
 Activities: 2 course, 6 extra

Customary units
 Activities: 0 course, 1 extra

Choosing appropriate units for measuring volume (mL or L)
 Activities: 1 course, 0 extra


7 learning outcomes – click to view
KS2.Y4.M.5 – Read, write and convert time between analogue and digital 12 and 24hour clocks

1 learning outcomes – click to view
Samples: 24 hour time  am or pm. 24hour time: Activity 2. 24hour time: Activity 1. Twentyfour hour time.

24 hour time  am or pm
 Activities: 2 course, 7 extra


1 learning outcomes – click to view
KS2.Y4.M.6 – Solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days

4 learning outcomes – click to view
Samples: Time  'a.m.' and 'p.m.'. Challenge puzzle perimeter. Two step problem solving. Two step problem solving.

Use a.m. and p.m.
 Activities: 1 course, 1 extra

Challenge puzzle perimeter
 Activities: 1 course, 0 extra

Two step problem solving
 Activities: 1 course, 0 extra

Two step problem solving
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
KS2.Y4.G.PS – Geometry  properties of shapes
Pupils should be taught to:
KS1.Y4.G.PS.1 – Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

6 learning outcomes – click to view
Samples: Shapes. Splitting shapes. Attributes of two dimensional shapes. Grouping shapes based on attributes.

Describe two dimensional shapes
 Activities: 0 course, 1 extra

Splitting shapes
 Activities: 2 course, 0 extra

Attributes of two dimensional shapes
 Activities: 1 course, 0 extra

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

Naming triangles
 Activities: 1 course, 1 extra

Identifying properties and naming prisms and pyramids
 Activities: 2 course, 11 extra


6 learning outcomes – click to view
KS1.Y4.G.PS.2 – Identify acute and obtuse angles and compare and order angles up to 2 right angles by size

4 learning outcomes – click to view
Samples: Measuring obtuse angles using a protractor. Estimating the size of angles.

Measuring obtuse angles using a protractor
 Activities: 1 course, 3 extra

Estimate the size of angles.
 Activities: 1 course, 0 extra

Naming angles
 Activities: 4 course, 3 extra

Naming angles within shapes
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
KS1.Y4.G.PS.3 – Identify lines of symmetry in 2D shapes presented in different orientations

2 learning outcomes – click to view
Samples: Symmetry: Manmade structures. Identify line of symmetry. Symmetry in the environment. Line of symmetry.

Symmetry: Manmade structures
 Activities: 1 course, 1 extra

Identify line of symmetry
 Activities: 1 course, 1 extra


2 learning outcomes – click to view
KS1.Y4.G.PS.4 – Complete a simple symmetric figure with respect to a specific line of symmetry

1 learning outcomes – click to view
Samples: Drawing symmetrical pictures. Create symmetrical patterns. Creating Symmetrical Drawings and Patterns.

Drawing symmetrical pictures
 Activities: 0 course, 6 extra


1 learning outcomes – click to view
KS2.Y4.G.PD – Geometry  position and direction
Pupils should be taught to:
KS2.Y4.G.PD.1 – Describe positions on a 2D grid as coordinates in the first quadrant

2 learning outcomes – click to view
Samples: Interpret simple maps  the zoo. Using grid references. Interpret simple maps: Activity 1. Position Problem Solving.

Interpret simple maps  the zoo
 Activities: 1 course, 2 extra

Using grid references
 Activities: 1 course, 10 extra


2 learning outcomes – click to view
KS2.Y4.G.PD.2 – Describe movements between positions as translations of a given unit to the left/right and up/down

1 learning outcomes – click to view
Samples: Identify transformations  pictures. Translations, reflections or rotations: Activity 1.

Identify transformations  pictures
 Activities: 1 course, 2 extra


1 learning outcomes – click to view
KS2.Y4.G.PD.3 – Plot specified points and draw sides to complete a given polygon
KS2.Y4.S – Statistics
Pupils should be taught to:
KS2.Y4.S.1 – Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

2 learning outcomes – click to view
Samples: Interpreting Dot Plots. Interpret a spreadsheet. Display data using dot plots. Adding information to a spreadsheet.

Interpret dot plots
 Activities: 1 course, 1 extra

Interpret data presented in a spreadsheet
 Activities: 1 course, 3 extra


2 learning outcomes – click to view
KS2.Y4.S.2 – Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

3 learning outcomes – click to view
Samples: Interpreting column graphs  5. Picture graphs  one symbol represents many. Two way tables.

Interpret data presented in column graphs
 Activities: 1 course, 0 extra

Interpret data presented using picture graphs where one symbol represents many
 Activities: 1 course, 1 extra

Interpret data presented in two way tables.
 Activities: 1 course, 3 extra


3 learning outcomes – click to view