Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. They should also apply their mathematical knowledge to science and other subjects. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas.

can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.

become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

The national curriculum for mathematics aims to ensure that all pupils: A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems.

3 multiplication table up to 100