Year 4 programme of study (statutory requirements)

Notes and guidance (non-statutory)

Number, place value and rounding

Pupils should be taught to

• count in multiples of 6, 7, 9, 25 and 1000
• find 1000 more or less than a given number
• count backwards through zero to include negative numbers
• recognise the place value of each digit in a four-digit number

(thousands, hundreds, tens, and ones)

• order and compare numbers beyond 1000
• identify, represent and estimate numbers using different representations
• round any number to the nearest 10, 100 or 1000
• 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 understand how, over time, the numeral system changed to include the concept of zero and place value.

Number, place value and rounding

Using a variety of representations, including measures, pupils should become fluent in the order and place value of numbers

beyond 1000, including counting in tens and hundreds, and

maintaining fluency in other multiples through varied and frequent

They begin to extend their knowledge of the number system to

include the decimal numbers and fractions that they have met so

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 zero and place value

were introduced over a period of time.

Addition and subtraction Pupils should be taught to:

• add and subtract numbers with up to 4 digits using the efficient 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.

Addition and subtraction

Pupils should continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency.

Multiplication and division

Pupils should 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 by1; multiplying together three 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 and harder multiplication problems such as which n objects are connected to m objects.

Multiplication and division

Pupils should continue to practise recalling and using multiplication tables and related division facts to aid fluency.

Pupils should practise mental methods and extend this to three- digit numbers to derive facts, for example 200 × 3 = 600 into 600 ÷ 3 = 200, to become fluent.

Pupils should practise to become fluent in the efficient written method of short multiplication for multiplying using multi-digit numbers, and short division with exact answers when dividing by a one-digit number.

Pupils should write statements about the equality of expressions

(e.g. use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)).

Pupils should solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers.

This should include correspondence questions such as three cakes shared equally between 10 children.

Fractions

Pupils should be taught to:

• count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten

• 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

• identify, name and write equivalent fractions of a given fraction, including tenths and hundredths

• add and subtract fractions with the same denominator.

Fractions

Pupils should connect hundredths to tenths and place value and decimal measure.  They should extend the use of the number line to connect fractions, numbers and measures.

Pupils should understand the relation between non-unit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths.

Pupils should associate fractions of a length, of a shape and as a representation of one whole or set of quantities. Pupils should use factors and multiples to recognise equivalent fractions and simplify where appropriate (e.g. ⁶/₉ = ²/₃ or ¹/₄ = ²/₈).

Pupils should continue practice in adding and subtracting fractions with the same denominator, to become fluent through a variety of increasingly complex problems beyond one whole.

They should practise counting using simple fractions and decimal fractions, both forwards and backwards.

Decimals and fractions

Pupils should be taught to:

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

• recognise and write decimal equivalents to ¹/₄; ¹/₂; 3/4

• 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

  units, tenths and hundredths

• round decimals with one decimal place to the nearest whole

  number

• compare numbers with the same number of decimal places

  up to two decimal places

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

Decimals and fractions

Pupils should be taught throughout that decimals and fractions are different ways of expressing numbers.

Pupils’ understanding of the number system and decimal place value is extended at this stage to tenths and then hundredths. This includes relating the decimal notation to division of whole numbers by 10 and later 100.

Pupils should learn decimal notation and the language associated with it, including in the context of measurements. They make comparisons and order decimal amounts and quantities that are expressed to the same number of decimal places. They should be able to represent numbers with one or two decimal places in multiple ways, such as on number lines.

Measures

Pupils should be taught to:

• convert between different units of measure (e.g. 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

• 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.

 Measures

Pupils should use multiplication and their knowledge of place value to convert from larger to smaller units.

They should relate area to arrays and multiplication.

Pupils should build on their understanding of decimal notation to record measures.

Geometry: properties of shapes

Pupils should 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 two 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.

Geometry: properties of shapes

Pupils should continue to classify shapes using geometrical properties, extending to classifying different triangles (e.g. isosceles, equilateral, scalene) and quadrilaterals (e.g. parallelogram, rhombus, trapezium).

Pupils should 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 should 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.

 Geometry: position, direction, motion Pupils should 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.

Geometry: position, direction, motion

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

Data

Pupils should be taught to:

• interpret and present discrete data using bar charts and continuous data using line graphs

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

Data

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