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Rye Bar Model
 

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

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 Rye Bar Model Presentation Transcript

    • bar model method
      of solving mathematical
      word problems
      SEMINAR at RYE CITY SCHOOL DISTRICT
      Yeap Ban Har
      National Institute of Education
      Nanyang Technological University
      Singapore
      yeapbanhar@gmail.com
      Slides are available for download from
      www.banhar.blogspot.com or www.mmepdpm.pbworks.com
    • introduction
      singapore curriculum
      intellectual competence
    • curriculum framework
    • mathematics
      Wellington Primary School, Singapore
      education

      an excellent vehicle for the development and improvement of a person’s intellectual competence

      intellectual competence
      Ministry of Education Singapore 2006
    • Move 3 sticks to get two squares.
    • Wellington Primary School, Singapore
    • Wellington Primary School, Singapore
    • Wellington Primary School, Singapore
    • Wellington Primary School, Singapore
    • Wellington Primary School, Singapore
    • Move 3 sticks to get two squares.
    • Move 3 sticks to get two squares.
    • Wellington Primary School, Singapore
    • “…development and improvement of a person’s intellectual competencies...”
      Singapore Ministry of Education 2006
       
      Visualization
      Patterning
      Number Sense
    • PSLE Item
      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?
       
      19 cm x 5 = 95 cm
      150 cm – 95 cm = 105 cm
      105 cm of the copper wire was left.
    • Primary Mathematics Standards Edition
    • model method
      pre-algebra
      coaching techniques
    • 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.
      What is the mass of Rahim’s clothes?
      What is the mass of the suitcase?
      29 kg
      Siti
      Rahim
      11 kg
    • 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.
      What is the mass of Rahim’s clothes?
      What is the mass of the suitcase?
      29 kg
      11 kg
      18 kg
      Siti
      2 units = 18 kg
      1 unit = 9 kg
      Rahim
      Rahim’s clothes is 9 kg.
      The suitcase is 2 kg.
      11 kg
      We can also find the mass of Siti’s clothes (27 kg) if required.
    • 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.
      What is the mass of Rahim’s clothes?
      What is the mass of the suitcase?
      x + y = 11
      x + 3y = 29
      x
      y
      y
      y
      Siti
      2y = 29 – 11 = 18
      x
      y
      Rahim
      y = 18 ÷ 2 = 9
    • model method
      in kindergarten
      and primary one
    • Ali has 3 sweets.
      Billy has 5 sweets.
      How many sweets do they have altogether?
    • model method
      alternate methods
      mental computations
    • Cheryl has $20 less than David.
      Cheryl and David have $148 altogether,
      Find the amount of money Cheryl has.
      Let the amount of money that Cheryl has be $y.
      Cheryl
      y + (y + 20) = 148
      $148
      2y + 20 = 148
      20
      David
    • Cheryl has $20 less than David.
      Cheryl and David have $148 altogether,
      Find the amount of money Cheryl has.
      Cheryl
      $148 - $20
      = $128
      20
      David
      $128 ÷ 2 = $64
      Cheryl has $64.
      How about David? $84
      2y + 20 = 148
      2y = 148 – 20 = 128
      y = 128 ÷ 2 = 64
      Cheryl has $64.
    • Cheryl has $20 less than David.
      Cheryl and David have $148 altogether,
      Find the amount of money Cheryl has.
      Let the amount of money that David has be $y.
      Cheryl
      $148
      20
      David
    • Cheryl has $20 less than David.
      Cheryl and David have $148 altogether,
      Find the amount of money Cheryl has.
      $148 + $20 = $168
      20
      Cheryl
      $168 ÷ 2 = $84
      David has $84.
      Cheryl has $64.
      20
      David
      Let the amount of money that David has be $y.
      y + (y – 20) = 148
      2y = 148 + 20 = 168
      2y – 20 = 148
      y = 168 ÷ 2 = 84
      Cheryl has $64.
    • model method
      helps average learners
      see abstract ideas
    • Josh spent 2/5 of his savings to buy a gift and 1/6 of the remainder to buy a snack.
      Josh then has $7.50 left.
      Find the amount Josh spent on the gift.
       
       
       
      5 units = $7.50
      1 unit = $1.50
      4 units = $1.50 x 4 = $6
      Josh spent $6 on the gift.
      How about the snack? $1.50
      How much is his savings? $7.50
    • There were three times as many students in soccer as there were in basketball.
      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.
       
      Soccer  12 x 3 = 36
      soccer
      There were 36 students in soccer .
      How about basketball?
      12
      basketball
    • There were four times as many students in soccer as there were in basketball.
      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.
       
      soccer
      basketball
    • There were four times as many students in soccer as there were in basketball.
      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.
       
      1 unit = 4
      soccer
      8 units = 32
      There were 32 students in soccer at first
      basketball
      3 units = 12
    • model method
      new situations
      problem solving
    • 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?
      boys
      34
      34
      girls
    • 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?
      88 – 34 – 34 = 20
      boys
      34
      34
      34
      girls
      2 units = 34 – 20 = 14
      1 unit = 7
      7 x 3 = 21 21 girls wore goggles
    • model method
      primary school
      leaving examination
    • Jim bought some chocolates and gave half of them to Ken.  Ken bought some sweets and gave half of them to Jim. 
      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. 
      How many sweets did Ken buy?
      PSLE 2009
      chocolates
      sweets
      12
      Jim
      18
      12
      12
      12
      12
      12
      Ken
      3 parts  12 + 12 + 12 + 12 + 18 = 66
      1 part  22
      Half of the sweets Ken bought = 22 + 12 = 34
      So Ken bought 68 sweets.`