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Listening to you, working for you www.bexley.gov.uk
Helping your child with
mathematical reasoning at
home
Orchard School
...
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Orchard Handout Parent Workshop Reasoning

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Orchard Handout Parent Workshop Reasoning

  1. 1. Listening to you, working for you www.bexley.gov.uk Helping your child with mathematical reasoning at home Orchard School February 2016 Emma Blackman
  2. 2. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk National Curriculum  The national curriculum for mathematics aims to ensure that all pupils:  become fluent in the fundamentals of mathematics,  reason mathematically  can solve problems
  3. 3. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Development Matters EYFS  Overlap in many aspects of the ‘Good Levels of Development’  Thinking and reasoning skills are crucial to the characteristics of effective learning:  creating and thinking critically  to communication and language, understanding and speaking  Developed alongside the mathematics.
  4. 4. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk What is reasoning in mathematics?  Reason mathematically in mathematics is:  following a line of enquiry,  conjecturing relationships and generalisations,   developing an argument,  justification or proof using mathematical language.
  5. 5. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Why should you help your child to reason?  Research by Nunes (2009) says that ‘ability to reason mathematically is the most important factor in a pupil’s success in mathematics…Such skills support deep and sustainable learning and enable pupils to make connections in mathematics’.
  6. 6. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Creating and thinking critically at home  Model being a thinker, showing that you don’t always know, are curious and sometimes puzzled, and can think and find out  Encourage divergent thinking: what else is possible  Value questions, and many responses, without rushing towards answers too quickly.  Support your child’s interests over time, remind them of previous approaches and encourage them to make connections between their experiences
  7. 7. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk continued  Model the creative process, showing your thinking in as many possible ways forward  Give reasons rather than directive ‘rules’ for any limits on your child’s activities  Be a sensitive conversational partner and co-thinker  Show and talk about strategies - how to do things – include problem solving, thinking and learning.
  8. 8. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Challenge your child to think and talk about their own learning process with questions such as: How did you do that? How else could you have done that? What could you do when you are stuck on that? Convince me you are correct.
  9. 9. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Reasoning in stories
  10. 10. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Toys
  11. 11. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk What do we have in common?  What do we have in common?  Sort into group – no more than two to start with  Tell you why they have sorted them that way (Identify characteristics of each set)
  12. 12. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Animals
  13. 13. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Family photos
  14. 14. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Food
  15. 15. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Puzzles and problems Suduku
  16. 16. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Games
  17. 17. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Walking to school  How shall we travel to school today? Why?  Which route do you want to take? Why?  Which will be the quickest? Which will be the slowest?  Which car do you like? Why not this one? How are these cars similar? How are these cars different?
  18. 18. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk In the kitchen  Which is more, 1.7kg of apples or 1007g of apples?  Which is more, 1.25kg of apples or 1025g of apples?  Decisions, decisions: which is the best container to store a drink in?  Which spoon would you eat soup with? Why?  Which piece of crockery would you eat a piece of cake from? Why?
  19. 19. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Getting dressed  Get three items of clothing out that are appropriate for different seasons.  Which top would be best worn on a sunny day? Which top would be best worn on a winter’s day? Why?  Decisions, decisions Compare using size, colour Use, material, parts and shape
  20. 20. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk What’s the time  True or False? There are more hours in a day than minutes in an hour.  True or false? There are more days in February than there is in March.
  21. 21. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk In the bath  Explore:  The taller the container, the more water it holds.  Is it always true, sometimes true or never true.
  22. 22. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk What is the same? What is different?  Number line and a clock
  23. 23. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Money problems  How to Live Forever’ costs £5.50 plus VAT in Waterstones or £6.60 minus a 10% discount in WHS. Which shop is it the cheapest in?  The smaller the coin the lesser the value?
  24. 24. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk True or False  Odd + odd + odd = odd  When adding 4 numbers, it doesn’t matter which order I add them up in.  If I start at the number 2 and count in 4’s I will say the number 32
  25. 25. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Sometimes, always or never  Multiplication makes things bigger
  26. 26. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Always true, sometimes true or never true? The sum of the digits of multiples of nine add up to nine or a multiple of nine Further investigation – True or false – a multiple of nine is also a multiple of three
  27. 27. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Times tables  Are the multiples of 3 odd or even?  Can you describe the pattern the ringed numbers make?  How will it continue?
  28. 28. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Spot the mistake George says that, “13 + 23 + 33 is equal to 18”. Where has he gone wrong? What should the answer be?
  29. 29. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk What reasoning could we do here? 12 + ____ = 14 12 + ____ = 16 12 + ____ = 18 12 + ____ = 20 12 + ____ = 22 12 + ____ = 24 146 = 140 + 6 146 = 130 + 16 146 = 120 + 26
  30. 30. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk How would you calculate this? ____ + 20 = 25 + 45
  31. 31. www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.ukListening to you, working for you www.bexley.gov.uk Any questions?

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