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NCTM 2013

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This is the presentation made at the conference in Denver.

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NCTM 2013

  1. 1. 1Exploring Reasoning & Communicationwith Problems fromSingapore ClassroomsSt Gabriel’s Primary School, SingaporeYeap Ban HarMarshall Cavendish InstituteSingaporewww.facebook.com/MCISingapore
  2. 2. 2Outline What is Reasoning & Communication? How to Develop Reasoning & Communication? Measurement & Geometry Problems Re-looking at Reasoning & Communication
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  6. 6. 6  We can find area by counting squares.We can find area bytransforming the figure into asimple figure (without changing itsarea) such as a rectangle.We can use fraction to find area.
  7. 7. 7We found squares of area 1 square unit, 2 square unit, 4 square unit, 9 square unitsand 16 square units.5 square units.10 square units.Someone found a square of area 13square units. Can you find it?
  8. 8. 8
  9. 9. 9Is it possible to draw the square we have found on a grid such as this one (4 by 4 grid)?All the square we found have area less than 16 square units.It seems like they should be able to fit onto this grid.But is that true?
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  13. 13. 13Answer: 68 cm
  14. 14. 14
  15. 15. 15abcabc19 cm x 5 = 95 cm150 cm – 95 cm = 55 cm55 cm of the wire were left.Answer: 55 cm
  16. 16. 16
  17. 17. 17It is not given that theangles indicated by are equal. So they can beor not. What if they are.
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  20. 20. 20
  21. 21. 2131o71o31o19o19o???180o – 2 x 19o – 2 x 31o = …Answer: The required angle is 80o.Why is this a right angle?Why is this also 31o?Why is this found bysubtracting from180o?
  22. 22. 22During class discussion,some students had adifferent interpretationof the problem fromthe others.How should the problem bephrased such that theshaded region andunshaded region refer tothose that are as seen onthe figure?Or is this version alreadynot ambiguous?Let’s solve this version ofthe problem.
  23. 23. 23Let’s clarify.The figure is created by a circle overlapping asemicircle, as shown. The region on the semicirclenot covered by the circle is shaded.
  24. 24. 24544R2r2=94½ R2½ r2=94If we are comparing the semicircles…If we arecomparing thesemicircles …Answer: The ratio is 2 : 3 .
  25. 25. 25Exploring Reasoning & Communicationwith Problems fromSingapore ClassroomsSt Gabriel’s Primary School, SingaporeCommunication- through actions- through pictures and diagrams- through words and symbols
  26. 26. 26Exploring Reasoning & Communicationwith Problems fromSingapore ClassroomsSt Gabriel’s Primary School, SingaporeDescribing what they sawExplaining what they sawRelational explanationCausal explanation
  27. 27. 27Presentation of theProblem – A square sheetis folded twice to form aright triangle. When apart is removed, it formsa particular figure.Lesson Study on Reasoning and CommunicationMarymount Convent School, Singapore
  28. 28. 28Marymount Convent School, Singapore
  29. 29. 29These are the figures formed when thesquare sheet is folded twice, three timesand four times. Students describe what theysee, what they think and what they wander…Marymount Convent School, Singapore
  30. 30. 30Marymount Convent School, Singapore
  31. 31. 31Students present what they thinkthe next figure looks like andtheir reasons.Students check if their predictionis correct or otherwise.Marymount Convent School, Singapore
  32. 32. 323 folds2 folds4 folds 6 folds5 folds 7 foldsEast Coast Primary School, Singapore
  33. 33. 33Exploring Reasoning & Communicationwith Problems fromSingapore ClassroomsSt Gabriel’s Primary School, SingaporeYeap Ban HarMarshall Cavendish InstituteSingaporewww.facebook.com/MCISingapore

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