The National Curriculum for Mathematics aims to ensure that all pupils reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing arguments, justification or proof using mathematical language so that they 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.
At Westfield, Reasoning and Problem solving are key elements which are interwoven into maths lessons throughout the year groups and stages of calculation. Children are given a variety of rich problems to increase their fluency and understanding at a particular stage. The language of Maths is a key aspect to children’s fluency and understanding. Therefore, the key vocabulary is explicitly taught and revised regularly. Children are given regular opportunities to explain their processes and understanding.
The fundamental idea in maths is explained: the principle that we can only add two or more items (or “nouns”) when they are both the same.
An illustration of the progression of learning number bonds from first exploring with concrete materials to representing the amounts using symbols (digits) and an exploration of the systematic approach to discovering the many possibilities of number bonds to 10.
A demonstration of breaking a number into its component parts to assist in building understanding of abstract subtraction methods.
Strategies for learning calculation by starting with concrete materials (base 10 blocks).
Using visual methods and reasoning to figure out more demanding calculations from what we already know in our tables’ knowledge.
Exploring strategies to partition numbers and investigating their number bonds to simplify long division. A strategy can involve finding easier number bonds within a larger number in order to divide the larger number more conveniently.
Bar Model 1
An illustration of how to use diagrams with rectangles to find unknown quantities.
Bar Model 2
A further illustration using a word problem to find unknown quantities.