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Explore various problem-solving types, develop reasoning abilities, and support National Curriculum aims with rich mathematical tasks. Enhance fluency, reasoning, and understanding of mathematical concepts for young learners.
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Lynne McClure, Jennie Pennant, Bernard Bagnall and Liz WoodhamNRICH Project Taking the Fear Factor Out of Rich Tasks: Supporting the Three Aims of the National Curriculum
* Reasoned Roundinghttp://nrich.maths.org/10945
* Spiralling Decimals http://nrich.maths.org/10326 0.5 0.25 0.75 0.3 0.35 0.9 0.99 0.999 0.1 0.01 0.05 1.79 0.64 0.32 0.54 0.865
* It’s a Scrabble http://nrich.maths.org/7953
I think this because… • If this is true then…… • I know that the next one is …..because…. • This can't work because …. • When I tried xxx I noticed that ….. • The pattern looks like…… • All the numbers begin with….. • Because xxxx then I think xxxxx • It will never work because…..
Understanding How Others WorkLots of Lollies http://nrich.maths.org/2360 Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. Just as they had finished sharing them their friends Kishan, Hayley and Paul came along. They wanted some lollies too so the children shared them out again between all of them. This time they had two lollies left over. How many lollies could there have been in the bag?
Types of Task • Finding all possibilities • Visual problems • Logic problems • Rules and patterns • Word problems
Problem-solving skills • Getting started try a simpler case draw a diagram represent with model act it out 2. Working on the problem visualise work backwards reason logically conjecture work systematically look for a pattern trial and improvement 3. Going further generalise verify prove 4. Concluding communicate findings evaluate
Structured Development of Problem Solving • Types of problems • Problem-solving skills • Objectives for a lesson or series of lessons
NRICH Support Developing Excellence in Problem Solving with Young Learners by Jennie Pennant http://nrich.maths.org/10865 Problem Solving and the New National Curriculum by Lynne McClure http://nrich.maths.org/10334 Improving Reasoning: Analysing Alternative Approaches by Malcolm Swan http://nrich.maths.org/7812
Lynne McClure, Jennie Pennant, Bernard Bagnall and Liz WoodhamNRICH Project Embedding Problem Solving in Our Classrooms: Engaging All Learners