Statutory guidance
National curriculum in England:
mathematics programmes of study
"Year 2" key stage 1  programme of study
Number  number and place value
Pupils should be taught to:

count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backward

recognise the place value of each digit in a twodigit number (10s, 1s)

identify, represent and estimate numbers using different representations, including the number line

compare and order numbers from 0 up to 100; use <, > and = signs

read and write numbers to at least 100 in numerals and in words

use place value and number facts to solve problems
Notes and guidance (nonstatutory)
Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They count in multiples of 3 to support their later understanding of a third.
As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations.
Pupils should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in twodigit numbers. They begin to understand 0 as a place holder.
Number  addition and subtraction
Pupils should be taught to:

solve problems with addition and subtraction:

using concrete objects and pictorial representations, including those involving numbers, quantities and measures

applying their increasing knowledge of mental and written methods


recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

add and subtract numbers using concrete objects, pictorial representations, and mentally, including:

a twodigit number and 1s

a twodigit number and 10s

2 twodigit numbers

adding 3 onedigit numbers


show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannot

recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
Notes and guidance (nonstatutory)
Pupils extend their understanding of the language of addition and subtraction to include sum and difference.
Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10; 10 − 7 = 3 and 7 = 10 − 3 to calculate 30 + 70 = 100; 100 − 70 = 30 and 70 = 100 − 30. They check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (for example, 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and associativity of addition.
Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.
Number  multiplication and division
Pupils should be taught to:

recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

show that multiplication of 2 numbers can be done in any order (commutative) and division of 1 number by another cannot

solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts
Notes and guidance (nonstatutory)
Pupils use a variety of language to describe multiplication and division.
Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations.
Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, to arrays and to repeated addition. They begin to relate these to fractions and measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 = 4).
Number  fractions
Pupils should be taught to:

recognise, find, name and write fractions , , and of a length, shape, set of objects or quantity

write simple fractions, for example of 6 = 3 and recognise the equivalence of and
Notes and guidance (nonstatutory)
Pupils use fractions as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet as the first example of a nonunit fraction.
Pupils should count in fractions up to 10, starting from any number and using the and equivalence on the number line (for example, 1 , 1 (or 1 ), 1 , 2). This reinforces the concept of fractions as numbers and that they can add up to more than 1.
Measurement
Pupils should be taught to:

choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

compare and order lengths, mass, volume/capacity and record the results using >, < and =

recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

find different combinations of coins that equal the same amounts of money

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

compare and sequence intervals of time

tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times

know the number of minutes in an hour and the number of hours in a day
Notes and guidance (nonstatutory)
Pupils use standard units of measurement with increasing accuracy, using their knowledge of the number system. They use the appropriate language and record using standard abbreviations.
Comparing measures includes simple multiples such as ‘half as high’; ‘twice as wide’.
Pupils become fluent in telling the time on analogue clocks and recording it.
They become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.
Geometry  properties of shapes
Pupils should be taught to:

identify and describe the properties of 2D shapes, including the number of sides, and line symmetry in a vertical line

identify and describe the properties of 3D shapes, including the number of edges, vertices and faces

identify 2D shapes on the surface of 3D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]

compare and sort common 2D and 3D shapes and everyday objects
Notes and guidance (nonstatutory)
Pupils handle and name a wide variety of common 2D and 3D shapes including: quadrilaterals and polygons and cuboids, prisms and cones, and identify the properties of each shape (for example, number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces.
Pupils read and write names for shapes that are appropriate for their word reading and spelling.
Pupils draw lines and shapes using a straight edge.
Geometry  position and direction
Pupils should be taught to:

order and arrange combinations of mathematical objects in patterns and sequences

use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and threequarter turns (clockwise and anticlockwise)
Notes and guidance (nonstatutory)
Pupils should work with patterns of shapes, including those in different orientations.
Pupils use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts (for example, pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles).
Statistics
Pupils should be taught to:

interpret and construct simple pictograms, tally charts, block diagrams and tables

ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity

askandanswer questions about totalling and comparing categorical data
Notes and guidance (nonstatutory)
Pupils record, interpret, collate, organise and compare information (for example, using manytoone correspondence in pictograms with simple ratios 2, 5,10).