Oak Lawn Beyond the Basics 01

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This is the presentation for the first day for the institute held in Oak Lawn.

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Oak Lawn Beyond the Basics 01

  1. 1. Dr. Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com SINGAPORE M AT H Beyond the Basics Day One St Edward’s SchoolSlides are available at Florida, USAwww.banhar.blogspot.com Marshall Cavendish Institute www.facebook.com/MCISingapore www.mcinstitute.com.sg
  2. 2. Dr. Yeap Ban Har CONTACT Marshall Cavendish Institute INFO yeapbanhar@gmail.comSlides are available atwww.banhar.blogspot.com Marshall Cavendish Institute www.mcinstitute.com.sgwww.facebook.com/ MCISingapore
  3. 3. IntroductionWe start the day with an overview ofSingapore Math.
  4. 4. Curriculum document is available at http://www.moe.gov.sg/
  5. 5. THINKING SCHOOLSLEARNING NATION Singapore Ministry of Education 1997
  6. 6. whatis singapore mathematics
  7. 7. key focus of singaporemathematics
  8. 8. problem solving
  9. 9. thinking
  10. 10. anexcellent vehicle for the development &improvement of a person’s intellectual competencies Ministry of Education Singapore 2006
  11. 11. conceptualunderstanding
  12. 12. Fundamentals of Singapore Math – Review & Extend Thinking: It’s the Big Idea! Problem Solving, Visualization, Patterning, and Number Sense The Concrete-Pictorial-Abstract Approach
  13. 13. Lesson 1We do a case study on multiplicationfacts. We will see the use of an anchortask to engage students for anextended period of time.
  14. 14. Strategy 1Get 3 x 4 from 2 x 4Strategy 2DoublingStrategy 3Get 7 x 4 from 2 x 4 and 5 x 4Strategy 4Get 9 x 4 from 10 x 4
  15. 15. Strategy 1Get 3 x 4 from 2 x 4
  16. 16. Strategy 3Get 9 x 4 from 4 x 4 and 5 x 4This is essentially the distributiveproperty. Do we introduce thephrase at this point? Recall thediscussion on Dienes.
  17. 17. Strategy 2 Doubling
  18. 18. Strategy 4Get 9 x 4 from 10 x 4
  19. 19. Unusual ResponseGet 4 x 8 from 4 x 2. Can it be done? Does the numberof cups change? Does the number of counters per cupchange?
  20. 20. Differentiated InstructionThese are examples of how the lesson can bedifferentiated for advanced learners.
  21. 21. Differentiated InstructionThese are examples of how the lesson can bedifferentiated for advanced learners.
  22. 22. ExerciseDiscuss the four ways to represent 1group of 4. Which is used first? Why?Which is used next? Why?
  23. 23. Textbook StudyObserve the various meanings ofmultiplication from Grade 1 to Grade3.
  24. 24. Prior to learning multiplication, studentslearn to make equal groups using concretematerials. Marbles is the suggestedmaterials.
  25. 25. After that they represent these concretesituations using, first, drawings ..
  26. 26. Open Lesson in Chile
  27. 27. … and, later, diagrams. Students alsowrite multiplication sentences inconventional symbols.
  28. 28. First, equal groups –three groups of four. Third, four multiplied three times ….Second, array –Three rows of four
  29. 29. Textbook StudyObserve how equal grouprepresentation evolves into array andarea models. Also observe how themultiplication tables of 3 and 6 arerelated on the flights of stairs.
  30. 30. They begin with equal group representation.
  31. 31. 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 30
  32. 32. In Primary 2, students learnmultiplication facts of 2, 5, 10 and 3and 4. In Primary 3, they learn themultiplication facts of 6, 7, 8 and 9.
  33. 33. Later, the array meaning ofmultiplication is introduced.
  34. 34. Square tiles are subsequently used to lead tothe area representation of multiplication.
  35. 35. Lesson 2Multiplication of multi-digit numberstaught in a problem-solving approach.
  36. 36. Lesson 2 August 6, 2012
  37. 37. Lesson 2 August 2, 2012 30 9 39 x 6 6       Method 1 Method 2 39 x 6 = 40 x 6 = 240 30 9
  38. 38. Lesson 3Use digits 1 to 9 to make a correctmultiplication sentence =.
  39. 39. Open Lesson at Broomfield, Colorado
  40. 40. Students who were already good in the skill of multiplying two-digit numberwith a single-digit number were asked to make observations. They wereasked “What do you notice? Are there some digits that cannot be used taall?”
  41. 41. Multiplication Around UsDo you see multiplication in these workof art around the venue of theconference? Hilton Oak Lawn, IL
  42. 42. Lesson 4We studied the strategies to helpstruggling readers as well as thoseweak in representing problemsituations.
  43. 43. Lesson 4 August 6, 2012
  44. 44. Lesson 5 August 2, 2012 In the end ... At first …Alice 20Betty 10 Charmaine Dolly
  45. 45. Lesson 5Question: How do we help students set up the model?Students are introduced to the idea of using arectangle to represent quantities – known andunknown. Paper strips are used. Later, only diagramsare used. Advanced skills like cutting and moving arelearned in Grades 4, 5 and 6. How is the idea ofbar model introduced in Grades K – 3?Lesson 5 shows a basic bar model solution in Grade5.
  46. 46. Lesson 5 August 6, 2012 Carl $4686 Ben
  47. 47. Differentiated instruction for students who have difficultywith standard algorithms. Use number bonds.
  48. 48. 2x + x = 4686 3x = 4686Students in Grade 7 may use algebra to deal with such situations. Bar model isactual linear equations in pictorial form.
  49. 49. Lesson 6Let’s look at the emphasis on visualization andgeneralization in a task from a different topic –area of polygons.
  50. 50. Differentiated InstructionIs it true that the area of the quadrilateral ishalf of the area of the square that ‘contains’ it?Why is the third case different from the firsttwo? What are your ‘conjectures’?
  51. 51. It was observed that the area of the polygon ishalf of the number of dots on the sides of thepolygon. Thus, the polygon on the left has 22dots on the sides and an area of 11 squareunits. Is this conjecture correct?
  52. 52. One of the participants used theresults to find the area of thistrapezoid. The red triangle has 3dots on the sides (hence, area of1.5 square units). The brown onehas 6 dots. The purple one has 6dots, Hence, the area of these twotriangles is 3 square units each.
  53. 53. What • Visualization • Generalization • Number Sense How • Tell • Coach • Model • Provide OpportunitiesTampines Primary School, Singapore
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