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The Road Less Travelled

Explore the concept of independent thinking and problem-solving skills through mathematics. Develop critical understanding and creative thinking abilities. Enhance teamwork and self-management skills. Communicate and reflect on findings. Use NRICH resources and problem-solving strategies. Embed PLTS skills in the learning process.

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The Road Less Travelled

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  1. The Road Less Travelled Jennifer Piggott jsp38@cam.ac.uk

  2. TWO roads diverged in a yellow wood, And sorry I could not travel both And be one traveller, long I stood And looked down one as far as I could To where it bent in the undergrowth; Then took the other, as just as fair, And having perhaps the better claim, Because it was grassy and wanted wear; Though as for that the passing there Had worn them really about the same, And both that morning equally lay In leaves no step had trodden black. Oh, I kept the first for another day! Yet knowing how way leads on to way, I doubted if I should ever come back. I shall be telling this with a sigh Somewhere ages and ages hence: Two roads diverged in a wood, and I— I took the one less travelled by, And that has made all the difference. By Robert Frost

  3. Mathematics and Personal learning and Thinking Skills • Independent Enquirers • Creative Thinkers • Team Workers • Self-managers • Effective participators • Reflective learners

  4. NC - Key Concepts Competence Creativity Applications and implications of mathematics Critical understanding

  5. NC - Key Processes 2.1 Representing 2.2 Analysing Use mathematical reasoning Use appropriate mathematical procedures 2.3 Interpreting and evaluating 2.4 Communicating and reflecting

  6. Problem solving • Understanding the Problem • What is known? • What is given? • What do I need to find? • Devising the Plan • Have I seen something like this before? • What mathematical approaches might be helpful? • Carrying out the Plan • Check each step • Estimate and assess – does this look right? • Look Back • Check the result • Could I use this idea somewhere else? • Communicate • Share your findings and consider what others have done • Could I have got there another way? • Would I do something like this differently next time?

  7. NRICH Website • Mapping documents http://nrich.maths.org/public/viewer.php?obj_id=5665 Content and process mapping documents • Teachers’ menu http://nrich.maths.org/public/viewer.php?obj_id=6318 • Problems with teachers’ notes • Student solutions • Case studies Teachers using NRICH, for example: http://nrich.maths.org/public/viewer.php?obj_id=6388 • CPD http://nrich.maths.org/public/viewer.php?obj_id=2695

  8. Embedding PLTS • Identify questions to answer and problems to solver, planning and carrying out research • Generating ideas and constructing mathematical models, exploring and varying values • Discussing and writing up findings • Reflecting and communicating using appropriate representations • Organising time and resources and prioritising • Comparing other people’s methods and approaches with their own • Planning and preparing ways forward, breaking problems down

  9. Some problems • Seven squares http://nrich.maths.org/public/viewer.php?obj_id=2290 • Stringy quads http://nrich.maths.org/public/viewer.php?obj_id=2913 • Hundred square http://nrich.maths.org/public/viewer.php?obj_id=2397

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