Here are the National Curriculum Expectations for children in Year 2. 

Number and place value

• count in steps of 2, 3, and 5 from 0, and 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

Addition and subtraction

• 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 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

Multiplication and division

• 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 two numbers can be done in any order (commutative) and division of one 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

Fractions

•  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 for example, ¹/₂ of 6 = 3 and recognise the equivalence of ²/₄ and ¹/₂.

Measurement

• 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

Geometry: properties of shapes

•  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: position and direction

• 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 three-quarter turns (clockwise and anti-clockwise)

Statistics

•  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 comparing categorical data