The programmes of study for mathematics are set out year-by-year for key stages 1 and 2. These are the statutory requirements of the new National curriculum in England.
More detailed information can be found at the following government website:
The national curriculum for mathematics aims to ensure that all pupils:
Become fluent in the fundamentals of mathematics, through frequent practice of increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
Can solve problems by applying their mathematics to a variety of routine and non -routine problems with increasing difficulty, including breaking down problems into a series of simpler steps.
The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress are always based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly will be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material will need to consolidate their understanding through additional practice, before moving on.