Successfully reported this slideshow.
Upcoming SlideShare
×

# Rye Bar Model

1,850 views

Published on

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

Published in: Education, Technology
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

### 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 />