Emergent Literacy Attitudes in Intermediate Elementary Grades
Bar Models for Elementary Grades
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Transcript of Bar Models for Elementary Grades
Bar Models for Elementary Grades
Peggy FooMarshall Cavendish Institute
Learning Outcomes
Participants 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.
Origin
Developed by a project team in MOE in the 1980s
Objective: Help students who have great difficulty with word problems in the early years of primary school.
Drawing a pictorial model to represent mathematical quantities (known and unknowns) and their relationships given in a problem.
Rationale
The Mathematics Curriculum Framework focuses on mathematical problem solving.
Reasoning, communication
and connections
Under ‘Processes’ component, One of the heuristics is model
method Helps to visualize situations and
Maths problems which are usually meant for secondary pupils
DifferencesModel Method Algebraic Method
_________ representation
Abstract reasoning
More effective for _______ pupils who need to see to understand
More suitable for older pupils
Foundation for algebraic thinking (without the use of abstract symbol)
Use of abstract symbol
DifferencesModel Method Algebraic Method
Pictorial representation Abstract reasoning
More effective for younger pupils who need to see to understand
More suitable for older pupils
Foundation for algebraic thinking (without the use of abstract symbol)
Use of abstract symbol
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)
Different types of models
Part-Whole Model Comparative Model Change/ Transforming Model
Part-Whole Model Shows various parts which make
up a whole Find the whole by addition Find the other part by subtraction
Part-Whole Model (using concrete materials)
Ann had 5 books.Bill gave her 7 more books. How many books did Ann have
altogether?
Part-Whole Model ?
John has 20 marblesHe gave 3/5 of it to Peter.How many marbles did John give to Peter?
Part-Whole Model?
John has 20 marblesHe gave 3/5 of it to Peter.How many marbles did John give to Peter?
5 unit 20 marbles
1 unit 4 sweets
3 units 3 x 4
= 12
John gave 12 marbles to Peter.
20
Comparsion Model Show the relationship between 2
quantities when they are compared
E.g. compared by showing the difference
Comparsion Model (Try it)
Alice had 3 books.She had 9 books less than Beth.How many books did Beth have?
Comparsion ModelAlice had 3 books.She had 9 books less than Beth.How many books did Beth have?
3Alice
?
Beth
9
What do you think is the common mistake made by many students?
3 + 9 = 12
Comparsion Model (to find the difference)
Jess had 12 beads and Ken had 4.How many more beads had Jess than Ken?
Comparsion Model (to find the difference)
Jess had 12 beads and Ken had 4.How many more beads had Jess than
Ken?
4Ken
?
Jess
12 – 4 = 8
What do you think is the common mistake made by many students?
12
Model drawing promotes conceptual understanding via visual representations rather than “cue words” method.
More than use addition Less than use subtraction
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?
Comparsion Model
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?
70
A
B
C
10 units 70 1 unit 7
3 units 21
Bill’s is 21 years of age.
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.
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?
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?
S
J
Before
S
J
- 36
+ 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.
After
S
J
- 36
+ 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.
After
Three halls contained 9,876 chairs altogether. One-fifth of the chairs were transferred from the first hall to the second hall. Then, one-third of the chairs were transferred from the second hall to the third hall and the number of chairs in the third hall doubled. In the end, the number of chairs in the three halls became the same. How many chairs were in the second hall at first?
Hall 1 (Before)
Hall 2
Hall 3
After
Hall 1
After
Before
Hall 2
Hall 3
Hall 1
Hall 2
Hall 3
Hall 1
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.
Hall 2
Hall 3
Hall 1
Thank you