Rye Bar Model

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This presentation on bar modeling was for Grades Four and Five teachers from elementary and middle schools in Rye City School District in New York

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Rye Bar Model

  1. 1. bar model method <br />of solving mathematical<br />word problems<br />SEMINAR at RYE CITY SCHOOL DISTRICT <br />Yeap Ban Har<br />National Institute of Education<br />Nanyang Technological University<br />Singapore<br />yeapbanhar@gmail.com<br />Slides are available for download from<br />www.banhar.blogspot.com or www.mmepdpm.pbworks.com<br />
  2. 2. introduction <br />singapore curriculum<br />intellectual competence<br />
  3. 3. curriculum framework<br />
  4. 4. mathematics<br />Wellington Primary School, Singapore<br />education<br />“<br />an excellent vehicle for the development and improvement of a person’s intellectual competence<br />”<br />intellectual competence<br />Ministry of Education Singapore 2006<br />
  5. 5. Move 3 sticks to get two squares.<br />
  6. 6. Wellington Primary School, Singapore<br />
  7. 7. Wellington Primary School, Singapore<br />
  8. 8. Wellington Primary School, Singapore<br />
  9. 9. Wellington Primary School, Singapore<br />
  10. 10. Wellington Primary School, Singapore<br />
  11. 11. Move 3 sticks to get two squares.<br />
  12. 12. Move 3 sticks to get two squares.<br />
  13. 13. Wellington Primary School, Singapore<br />
  14. 14. “…development and improvement of a person’s intellectual competencies...” <br />Singapore Ministry of Education 2006<br /> <br />Visualization<br />Patterning<br />Number Sense<br />
  15. 15. PSLE Item<br />John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?<br /> <br />19 cm x 5 = 95 cm<br />150 cm – 95 cm = 105 cm<br />105 cm of the copper wire was left.<br />
  16. 16. Primary Mathematics Standards Edition <br />
  17. 17. model method <br />pre-algebra<br />coaching techniques<br />
  18. 18. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. <br />What is the mass of Rahim’s clothes?<br />What is the mass of the suitcase?<br />29 kg<br />Siti<br />Rahim<br />11 kg<br />
  19. 19. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. <br />What is the mass of Rahim’s clothes?<br />What is the mass of the suitcase?<br />29 kg<br />11 kg<br />18 kg<br />Siti<br />2 units = 18 kg<br />1 unit = 9 kg<br />Rahim<br />Rahim’s clothes is 9 kg.<br />The suitcase is 2 kg.<br />11 kg<br />We can also find the mass of Siti’s clothes (27 kg) if required.<br />
  20. 20. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. <br />What is the mass of Rahim’s clothes?<br />What is the mass of the suitcase?<br />x + y = 11<br />x + 3y = 29<br />x<br />y<br />y<br />y<br />Siti<br />2y = 29 – 11 = 18<br />x<br />y<br />Rahim<br />y = 18 ÷ 2 = 9<br />
  21. 21. model method <br />in kindergarten <br />and primary one<br />
  22. 22. Ali has 3 sweets. <br />Billy has 5 sweets.<br />How many sweets do they have altogether?<br />
  23. 23.
  24. 24.
  25. 25. model method <br />alternate methods <br />mental computations<br />
  26. 26. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />Let the amount of money that Cheryl has be $y.<br />Cheryl<br />y + (y + 20) = 148<br />$148<br />2y + 20 = 148<br />20<br />David<br />
  27. 27. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />Cheryl<br />$148 - $20<br />= $128<br />20<br />David<br />$128 ÷ 2 = $64<br />Cheryl has $64.<br />How about David? $84<br />2y + 20 = 148<br />2y = 148 – 20 = 128 <br />y = 128 ÷ 2 = 64<br />Cheryl has $64.<br />
  28. 28. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />Let the amount of money that David has be $y.<br />Cheryl<br />$148<br />20<br />David<br />
  29. 29. Cheryl has $20 less than David.<br />Cheryl and David have $148 altogether,<br />Find the amount of money Cheryl has.<br />$148 + $20 = $168<br />20<br />Cheryl<br />$168 ÷ 2 = $84<br />David has $84.<br />Cheryl has $64.<br />20<br />David<br />Let the amount of money that David has be $y.<br />y + (y – 20) = 148<br />2y = 148 + 20 = 168<br />2y – 20 = 148<br />y = 168 ÷ 2 = 84<br />Cheryl has $64.<br />
  30. 30. model method <br />helps average learners <br />see abstract ideas<br />
  31. 31. Josh spent 2/5 of his savings to buy a gift and 1/6 of the remainder to buy a snack.<br />Josh then has $7.50 left. <br />Find the amount Josh spent on the gift.<br /> <br /> <br /> <br />5 units = $7.50<br />1 unit = $1.50<br />4 units = $1.50 x 4 = $6<br />Josh spent $6 on the gift.<br />How about the snack? $1.50<br />How much is his savings? $7.50<br />
  32. 32. There were three times as many students in soccer as there were in basketball. <br />After 12 students moved from soccer to basketball, there number of students in both sports became equal. Find the number of students in soccer at first. <br /> <br />Soccer  12 x 3 = 36<br />soccer<br />There were 36 students in soccer .<br />How about basketball?<br />12<br />basketball<br />
  33. 33. There were four times as many students in soccer as there were in basketball. <br />After 12 students moved from soccer to basketball, there number of students in both sports became equal. Find the number of students in soccer at first. <br /> <br />soccer<br />basketball<br />
  34. 34. There were four times as many students in soccer as there were in basketball. <br />After 12 students moved from soccer to basketball, there number of students in both sports became equal. Find the number of students in soccer at first. <br /> <br />1 unit = 4<br />soccer<br />8 units = 32<br />There were 32 students in soccer at first<br />basketball<br />3 units = 12<br />
  35. 35. model method <br />new situations <br />problem solving<br />
  36. 36. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day? <br />boys<br />34<br />34<br />girls<br />
  37. 37. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day? <br />88 – 34 – 34 = 20<br />boys<br />34<br />34<br />34<br />girls<br />2 units = 34 – 20 = 14<br />1 unit = 7<br />7 x 3 = 21 21 girls wore goggles<br />
  38. 38. model method <br />primary school <br />leaving examination<br />
  39. 39. Jim bought some chocolates and gave half of them to Ken.  Ken bought some sweets and gave half of them to Jim. <br />Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. <br />How many sweets did Ken buy?<br />PSLE 2009<br />chocolates<br />sweets<br />12<br />Jim<br />18<br />12<br />12<br />12<br />12<br />12<br />Ken<br />3 parts  12 + 12 + 12 + 12 + 18 = 66<br />1 part  22<br />Half of the sweets Ken bought = 22 + 12 = 34<br />So Ken bought 68 sweets.`<br />
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