Developing problem solving and reasoning Parents meeting 28 th January 2016

National Curriculum 2014 Aims The national curriculum for mathematics aims to ensure that all pupils: 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. 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 sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

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 should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Progression Old curriculumNew curriculum

Fluency Rapid recall of number facts – Times tables – Doubling/halving – Number bonds Transfer of number facts into everyday calculations Using known facts to aid calculations Clear understanding of place value

Reasoning Explaining thinking and methods used. – Being able to say why you think an answer is correct or not. How do you know? Understanding and being able to use mathematical language. Verbalising their ideas.

Examples of reasoning activities Convince me (Year 1) In my head I have two odd numbers with a difference of 2. What could they be? Convince me (Year 3) __ __ + __ __ + __ __ The total is 201 Each missing digit is either a 9 or a 1. Write in the missing digits. Is there only one way of doing this or lots of ways? Convince me

Examples of reasoning activities Always, sometimes or never (Year 2) Is it always, sometimes or never true that when you fold a square in half you get a rectangle. (Year 4) Is it always, sometimes or never true that the two diagonals of a rectangle meet at right angles. (Year 6) Is it always, sometimes or never true that, in a polyhedron, the number of vertices plus the number of faces equals the number of edges.

Examples of reasoning activities True or false? (Year 2) Are these number sentences true or false? = – 18 = = – 67 = 35 Give your reasons. (Year 5) Are these number sentences true or false? = – 0.9 = 8.3 Give your reasons.

Problem solving is good for learners and learning. It promotes thinking It promotes understanding It promotes a range of different styles of learning It promotes discussion and debate It creates interest, challenge and fun

Problem Solving

Finding rules and describing patterns

Birthday candles Year 3 Sally is 10 years old today. How many birthday candles has she blown out since she was born?

Three enders Year 5

Finding all possibilities

Sheepdog trials – Year 3/4 A farmer and his dog enter a sheepdog trial. In this event his dog must shepherd 24 sheep into three pens of different sizes. Each pen must have a different even number of sheep. The largest pen must have the most sheep and the smallest pen must have the fewest sheep. How many sheep might the dog try to get in each pen? Find as may different ways as you can.

Logic

Visual problems

Word problems