Bar Models for Elementary Grades

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  • The central of the framework is mathematical problem solving. This ability is dependent of 5 components. Under processes, it states Thinking skills and heuristics Heuristics – problem solving strategy 1 kind o heuristics is model drawing (give a representation)
  • The central of the framework is mathematical problem solving. This ability is dependent of 5 components. Under processes, it states Thinking skills and heuristics Heuristics – problem solving strategy 1 kind o heuristics is model drawing (give a representation)
  • Pictorial representation – helps pupils to visualize
  • Pictorial representation – helps pupils to visualize
  • +
  • Concrete model bars
  • multiplication
  • Cue word method
  • Cue word method
  • Moving the units
  • Moving the units
  • Bar Models for Elementary Grades

    1. 1. Bar Models for Elementary Grades Peggy Foo Marshall Cavendish Institute
    2. 2. Learning OutcomesParticipants should be able to understand the rationale of model method as a heuristic/ problem-solving tool. Draw different types of models to solve a variety of word problems.
    3. 3. OriginDeveloped by a project team in MOE in the 1980sObjective: Help students who have great difficulty withword problems in the early years of primary school.Drawing a pictorial model to represent mathematicalquantities (known and unknowns) and their relationshipsgiven in a problem.
    4. 4. RationaleThe Mathematics Curriculum Framework focuses on mathematical problem solving. Reasoning, communication and connections
    5. 5. Under ‘Processes’ component, One of the heuristics is model method Helps to visualize situations and Maths problems which are usually meant for secondary pupils
    6. 6. Differences Model Method Algebraic Method_________ representation Abstract reasoningMore effective for _______ More suitable for olderpupils who need to see to pupilsunderstandFoundation for algebraic Use of abstract symbolthinking (without the use ofabstract symbol)
    7. 7. Differences Model Method Algebraic MethodPictorial representation Abstract reasoningMore effective for younger More suitable for olderpupils who need to see to pupilsunderstandFoundation for algebraic Use of abstract symbolthinking (without the use ofabstract symbol)
    8. 8. Guidelines Represent the problem using bar(s) The bar(s) are best drawn proportionately Fill in the diagram with all the given information The unknown value/ answer is represented by question mark Interpret the model and write a simpler mathematical statement (e.g. 11 units + 40  84)
    9. 9. Different types of models Part-Whole Model Comparative Model Change/ Transforming Model
    10. 10. Part-Whole Model♠ Shows various parts which make up a whole♠ Find the whole by addition♠ Find the other part by subtraction
    11. 11. Part-Whole Model(using concrete materials)Ann had 5 books.Bill gave her 7 more books.How many books did Ann have altogether?
    12. 12. Part-Whole Model ?John has 20 marblesHe gave 3/5 of it to Peter.How many marbles did John give to Peter?
    13. 13. Part-Whole Model ?John has 20 marblesHe gave 3/5 of it to Peter.How many marbles did John give to Peter? 20 5 unit  20 marbles 1 unit  4 sweets 3 units  3 x 4 = 12 John gave 12 marbles to Peter.
    14. 14. Comparsion Model Show the relationship between 2 quantities when they are compared E.g. compared by showing the difference
    15. 15. Comparsion Model (Try it)Alice had 3 books.She had 9 books less than Beth.How many books did Beth have?
    16. 16. Comparsion Model Alice had 3 books. She had 9 books less than Beth. How many books did Beth have? Alice 3 9 Beth ? 3 + 9 = 12What do you think is the common mistake made by many students?
    17. 17. Comparsion Model(to find the difference)Jess had 12 beads and Ken had 4.How many more beads had Jess thanKen?
    18. 18. Comparsion Model (to find the difference) Jess had 12 beads and Ken had 4. How many more beads had Jess than Ken? 12 Jess Ken 4 ? 12 – 4 = 8What do you think is the common mistake made by many students?
    19. 19. Model drawing promotes conceptualunderstanding via visual representationsrather than “cue words” method. More than ≠ use addition Less than ≠ use subtraction
    20. 20. Comparsion ModelAnn’s age is twice the age of Bill.Bill’s age is 3 times the age of Carol.If there total age is 70, What is the age of Bill?
    21. 21. Ann’s age is twice the age of Bill.Bill’s age is 3 times the age of Carol.If there total age is 70, What is the age of Bill? A B 70 C 10 units 70 1 unit 7 3 units 21 Bill’s is 21 years of age.
    22. 22. Change/ Transforming Model This type of model can be used to solve complex problems The parts can be transformed into smaller units. This type of model is useful for tacking problems which involve before-and- after situations.
    23. 23. At first, Sara had 4/7 of the number of marblesJack had. When Sara received 36 marbles fromJack, both had the same number of marbles. (a) How many more marbles did Jack have than Sara at first? (b) How many marbles were there together?
    24. 24. At first, Sara had 4/7 of the number of marbles Jack had. When Sara received 36 marbles from Jack, both had the same number of marbles. (a) How many more marbles did Jack have than Sara at first? (b) How many marbles were there together? BeforeSJ
    25. 25. After + 36 S J - 36 (a) 3 units  36 1 unit  12 6 units  6 x 12  72 Jack has 72 more marbles than Sara. (b) 22 units  22 x 12 marbles They were 264 marbles altogether.
    26. 26. After + 36 S J - 36 (a) 1 ½ parts  36 1 part  24 3 parts  24 x 3  72 Jack has 72 more marbles than Sara. (b) 11 units  264 marbles They were 264 marbles altogether.
    27. 27. Three halls contained 9,876 chairsaltogether. One-fifth of the chairs weretransferred from the first hall to thesecond hall. Then, one-third of thechairs were transferred from the secondhall to the third hall and the number ofchairs in the third hall doubled. In theend, the number of chairs in the threehalls became the same. How manychairs were in the second hall at first?
    28. 28. Hall 1 (Before) After Hall 1 Hall 2 Hall 3
    29. 29. AfterHall 1Hall 2Hall 3 BeforeHall 1Hall 2Hall 3
    30. 30. Hall 1 Hall 2 Hall 3 12 units  9876 (M1) 1 unit  9876 ÷ 12 = 823 5 units  5 x 823 (M2)= 4115 (A1)There were 4115 chairs in the second hall at first.
    31. 31. Thank you

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