Transcript Using Singaporean Models to Develop Understanding

Using Singaporean Visual Bar
Models to Develop Understanding
Alice Ho & Meg Moss
Please try this Singapore problem:
A bag contains straws of different color. ¼ of
these straws are blue. The ratio of the number
of red straws to that of green straws is 2 : 3.
What is the ratio of the number of blue straws to
that of green straws?
A bag contains straws of different color. ¼ of these straws are
blue. The ratio of the number of red straws to that of green
straws is 2 : 3. What is the ratio of the number of blue straws
to that of green straws?
Blue
5 units
Red
Green
9 units
Answer: Ratio of the number of blue straws to that of green straws
5:9
Using Number Bonding to Add
10/30/16
Concept of
Bar Models to introduce Fractions/Mixed Numbers
Adopting C P A approach
Concrete
Pictorial
Abstract
An approach adopted by Ministry of Education
(Singapore) in introducing basic / fundamental
Mathematical concepts to beginners in Mathematics
10/30/16
Power of concrete materials
such as
* Strips of Paper
*Electric Tape
*Color Ribbon
*Drinking Straw
* Hair Comb
in introducing Bar Models
Bar Models to Solve
Linear Equations
5/6 x = 45
x
=?
5/6 x
1 unit
5 units
45
1 unit
45 ÷ 5
=9
Answer: x = 6 units
=9x6
= 54
You try drawing one.
2/5 x = 14
x =?
2/5 x
1 unit
2 units → 14
1 unit
14 ÷ 2 =
7
Answer : x = 5 units
=7x5
= 35
4 + 2x = 14
4
x
x
4 + 2x = 14
2x = 14 - 4
2x = 10
Answer:
x = 10 ÷
2
x=5
You try drawing one.
4x + 7 = 31
x
x
x
4x + 7 = 31
4x = 31 – 7
4x = 24
Answer:
x = 24 ÷
4
x=6
x
7
3x – 2 = 13
x
x
3x – 2 = 13
3x = 13 +2
3x = 15
Answer:
x = 15 ÷
3
x=5
x
2
You try drawing one.
2x – 3 = 13
x
x
2x – 3 = 13
2x = 13 + 3
2x = 16
Answer:
x = 16 ÷
2
x=8
3
9 more than 5 times a number is equal to 3 less than 7 times
the number. What is the number?
1 unit
9
3
?
2 units → 9 + 3 = 12
1 unit → 12 ÷ 2 =
6
Answer: The number is 6.
Concept of
Picture Models to solve Simultaneous Equations
24 pigs and chickens have a total of 80 legs.
How many pigs are there?
A total of 100 tickets were sold to an event with a total of $484
brought in. If student tickets were sold for $4 and nonstudent tickets were sold for $6, how many of each type of
tickets were sold?
Total 100 tickets
For all
student
tickets
1
2
3
4
$4
$4
$4
$4
……………………………..
99
100
$4
$4
$4 x 100 = $400
With $484 - $400 = $84
Top up
$6 - $4 = $2
to buy each
Non-student
ticket
+$2
+$2
+$2
+$2
1
2
3
4
+$2
….......
84 ÷ 2 = 42
Non-student tickets
42
.....……………....
100 – 42 = 58
Student tickets
100

A multiple choice problem from
PSLE 2015 Paper 2 Question 2 ( 2 marks)
Malek paid $945 for a table and 4 chairs.
The price of a chair was 2/7 of the price of the table.
How much did Malek pay for the table? (2 marks)
Mark paid $945 for a table and 4 chairs. The price of a chair was
2/7 of the price of the table. How much did Mark pay for the
table?
Price of
1 chair : 2 units
1 table : 7 units
Price of 4 chairs : 2 x 4 = 8 units
1 table
= 7 units
Mark paid
?
15 units → $945
1 unit → $(945
÷15)
= $63
Amount paid for the table
= 7 units
= $63 x 7
= $441 (Answer)
To contact
Meg Moss
Email: [email protected]
Phone: 828-774-4242
Alice Ho
Email: [email protected]
Whats App: +65 96662987
Questions
from the audience
Introduction
MODEL DRAWINGS
*Visual Models...Number Bondings
>Tree Format
>Horizontal Format
*Picture Models...Simultaneous Equations
>Grouping
>Replacement
*Bar Models... Fractions/Mixed Numbers
>Part/Whole Model
>Partition/Subdivision
*Bar Models...Linear Equations
>Comparison Model
Jo’s car can travel 163 miles on 6.4 gallons of gas. How far can
the car travel on a full tank of 18 gallons?
Gas
6.4 gallons
1 unit
Travel
163 miles
18 gallons
……….........
Answer: Distance travelled
= 2.8125 x 163 miles
= 458.4375 miles
18 ÷ 6.4
= 2.8125
60 newspapers cost $27. Find the cost of 16 newspapers.
60 newspapers
1
2
3
..............................................................................
4
Cost $27
1 newspaper cost $27 ÷ 60 =
$0.45
1
16 newspapers
1
2
3
4
.................................
Answer:
16 newspapers cost = 16 x $0.45
= $7.20
16
60
A recipe for salad dressing uses 2 ozs of olive oil for each 1 oz of
vinegar. If 42 ozs of salad dressing are needed. How many
ozs of each ingredient should be used?
3 ozs
dressing
1 portion
Ingredients
Olive Vinegar
Oil
Olive oil
14 x 2 ozs
= 28 ozs
1
2
42 ozs dressing
42 ÷ 3 = 14
portions
3
14
Vinegar
= 14 x 1 oz
= 14 ozs
Answer: 420 ozs dressing contain 28 ozs of olive oil and 14 ozs vinegar.
Concept of
Visual Models of Number Bondings
Tree format
Diagram
Number Sentences
Horizontal Format
Diagram
Number Sentences

Singapore annual
PSLE(Primary School Leaving Examination)
Typically every 12 year-old Singaporean child will take this annual exam consisting
of 2 papers with 48 Questions to be completed in 150 minutes awarded 100 marks

Paper 1 consists of 30 Questions to be completed in 50 minutes awarded 40 marks

Paper 2 consists of 18 Questions to be completed in 100 minutes awarded 60 marks
Performance of Singapore PSLE 2015 Mathematics
National Performance
Grade A* to C (above 50 marks)
Grade A* to A (above 85marks)
For more information on other subjects English,Science & Mother Tongue
Google: PSLE 2015 Results
85.5%
45.4%