Statutory guidance

National curriculum in England

Mathematics programme of study

Lower "Year 4" key stage 2 - programme of study

### Number - number and place value

Pupils will be taught to:

• count in multiples of 6, 7, 9, 25 and 1,000

• find 1,000 more or less than a given number

• count backwards through 0 to include negative numbers

• recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)

• order and compare numbers beyond 1,000

• identify, represent and estimate numbers using different representations

• round any number to the nearest 10, 100 or 1,000

• solve number and practical problems that involve all of the above and with increasingly large positive numbers

• 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

#### Notes and guidance (non-statutory)

Using a variety of representations, including measures, pupils become fluent in the order and place value of numbers beyond 1,000, including counting in 10s and 100s, and maintaining fluency in other multiples through varied and frequent practice.
They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far.
They connect estimation and rounding numbers to the use of measuring instruments.
Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of 0 and place value were introduced over a period of time.

### Number - addition and subtraction

Pupils will be taught to:

• add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

• estimate and use inverse operations to check answers to a calculation

• solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Notes and guidance (non-statutory)
Pupils continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics appendix 1).

Number - multiplication and division

Pupils will be taught to:

• recall multiplication and division facts for multiplication tables up to 12 × 12

• 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

• recognise and use factor pairs and commutativity in mental calculations

• multiply two-digit and three-digit numbers by a one-digit number using formal written layout

• solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

### Number - fractions (including decimals)

Pupils will be taught to:

• recall multiplication and division facts for multiplication tables up to 12 × 12

• recognise and show, using diagrams, families of common equivalent fractions

• count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10

• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

• add and subtract fractions with the same denominator

• recognise and write decimal equivalents of any number of tenths or hundreds

• recognise and write decimal equivalents to

• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths

• round decimals with 1 decimal place to the nearest whole number

• compare numbers with the same number of decimal places up to 2 decimal places

• solve simple measure and money problems involving fractions and decimals to 2 decimal places

Notes and guidance (non-statutory)

### Measurement

Pupils will be taught to:

• convert between different units of measure [for example, kilometre to metre; hour to minute]

• measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

• find the area of rectilinear shapes by counting squares

• estimate, compare and calculate different measures, including money in pounds and pence

• read, write and convert time between analogue and digital 12- and 24-hour clocks

• solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days

Notes and guidance (non-statutory)

#### Pupils build on their understanding of place value and decimal notation to record metric measures, including money. They use multiplication to convert from larger to smaller units. Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit. They relate area to arrays and multiplication.

Geometry - properties of shapes

Pupils will be taught to:

• compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

• identify acute and obtuse angles and compare and order angles up to 2 right angles by size

• identify lines of symmetry in 2-D shapes presented in different orientations

• complete a simple symmetric figure with respect to a specific line of symmetry

Notes and guidance (non-statutory)

Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (for example, isosceles, equilateral, scalene) and quadrilaterals (for example, parallelogram, rhombus, trapezium).
Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.
Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the line of symmetry does not dissect the original shape.

### Pupils will be taught to:

• describe positions on a 2-D grid as coordinates in the first quadrant

• describe movements between positions as translations of a given unit to the left/right and up/down

• plot specified points and draw sides to complete a given polygon

Notes and guidance (non-statutory)

Pupils draw a pair of axes in one quadrant, with equal scales and integer labels. They read, write and use pairs of co-ordinates, for example (2, 5), including using co-ordinate-plotting ICT tools.

Statistics

### Pupils will be taught to:

• interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

• solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

Notes and guidance (non-statutory)

Pupils understand and use a greater range of scales in their representations.
Pupils begin to relate the graphical representation of data to recording change over time.

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