Year 2 programme of study (statutory requirements)

Notes and Guidance (non-statutory)

Number and place value

Pupils should be taught to:

• count in steps of 2, 3, and 5 from 0, and count in tens from any number, forward or backward
• recognise the place value of each digit in a two-digit number (tens, ones)
• 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.

Number and place value

Using materials and a range of representations, pupils should practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They should count in multiples of three to support their later understanding of a third.

As they become more confident with numbers up to 100, pupils should be 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 (e.g. 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 two-digit numbers. They begin to understand zero as a place holder.

Addition and subtraction

Pupils should be taught to:

• solve simple one-step 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 two-digit number and ones, a two-digit number and tens, two two-digit numbers, adding three one-digit numbers

• show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems.

Addition and subtraction

Pupils should extend their understanding of the language of addition and subtraction to include sum and difference.

Pupils should 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 should check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (e.g. 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5).

Recording addition and subtraction in columns supports place value and prepares for efficient written methods with larger numbers.

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

• recognise and use the inverse relationship between multiplication and division in calculations

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

• solve one-step problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

Multiplication and division

Pupils should use a variety of language to describe multiplication and division. They are taught multiplication and division with larger numbers through equal grouping and sharing out quantities, relating multiplication tables to arrays and repeated addition and finding more complex fractions of objects, numbers and quantities.

Pupils should be introduced to the multiplication tables. They should 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 should work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, relating these to fractions and measures (e.g. 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (e.g. 4 × 5 = 20 and 20 ÷ 5 = 4).

Fractions

Pupils should be taught to:

• recognise, find, name and write fractions ¹/₃, ¹/₄, ²/₄ and ³/₄ of a length, shape, set of objects or quantity

• write simple fractions e.g. ¹/₂ of 6 = 3 and recognise the equivalence of two quarters and one half.

Fractions

Pupils should use additional fractions as operators on 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, quantity, a set of objects or shapes. They meet ³/₄ as the first example of a non-unit fraction.

Pupils should count in fractions up to 10, starting from any number and using the ¹/₂ and ²/₄ equivalence on the number line (e.g. 1¹/₄, 1²/₄ , (or 1¹/₂), 1³/₄, 2). This reinforces the concept of fractions as numbers and that they can add up to more than one.

Measures

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 =

• read relevant scales to the nearest numbered unit

• recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value and match different combinations of coins to equal the same amounts of money; add and subtract money of the same unit, including giving change

• solve simple problems in a practical context involving addition and subtraction of money

• 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.

 Measures

Pupils should use standard units of measurement with increasing accuracy, using their knowledge of the number system. They should use the appropriate language and record using standard

They should become fluent in telling the time on analogue clocks and recording it.

Pupils should also become fluent in counting and recognising coins. They should use the symbols £ and p accurately and say the amounts of money confidently.

Geometry: properties of shapes

Pupils should be taught to:

• identify and describe the properties of 2-D shapes, including

  the number of sides and symmetry in a vertical line

• identify and describe the properties of 3-D shapes, including

  the number of edges, vertices and faces

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

• compare and sort common 2-D and 3-D shapes and everyday objects.

Geometry: properties of shapes

Pupils should handle and name a wider variety of common 2-D and 3-D shapes including: quadrilaterals and cuboids, prisms, cones and polygons, and identify the properties of each shape (e.g. 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 should read and write names for shapes that are appropriate for their word reading and spelling.

Pupils should draw lines and shapes using a straight edge.

Geometry: position, direction, motion

Pupils should be taught to:

• order and arrange combinations of mathematical objects in patterns

• use mathematical vocabulary to describe position, direction and movement, including distinguishing between rotation as a turn and in terms of right angles for quarter, half and three- quarter turns (clockwise and anti-clockwise), and movement in a straight line.

 Geometry: position, direction, motion

Pupils should work with patterns of shapes, including those in different orientations.

Pupils should use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts (e.g. pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles).

Data

Pupils should be taught to:

• interpret and construct simple pictograms, tally charts, block

  diagrams and simple tables

• ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity ask and answer questions about totalling and compare categorical data.

Data

At this stage, pupils’ recording and interpretation become more sophisticated as they collate, organise and compare information (e.g. using many-to-one correspondence in pictograms and using simple ratios 2, 5, 10).