word problemsbar model method
of solving mathematical
Yeap Ban HarNational Institute of Education
Nanyang Technological UniversitySingapore
Slides are available for download fromwww.banhar.blogspot.com or www.mmepdpm.pbworks.com
SEMINAR at RYE CITY SCHOOL DISTRICT
intellectual competenceintroduction
singapore curriculum
curriculum framework
Wellington Primary School, Singapore
Ministry of Education Singapore 2006
an excellent vehicle for the development and improvement of
a person’s intellectual competence
“
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educationmathematics
intellectual competence
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
VisualizationPatterning
Number Sense
“…development and improvement of a person’s
intellectual competencies...” Singapore Ministry of Education 2006
PSLE ItemJohn 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
coaching techniquesmodel method
pre-algebra
Siti
Rahim
29 kg
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?
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?
Siti
Rahim
29 kg
11 kg
11 kg 18 kg
2 units = 18 kg1 unit = 9 kg
Rahim’s clothes is 9 kg.The suitcase is 2 kg.
We can also find the mass of Siti’s clothes (27 kg) if required.
Siti
Rahim x y
x y y yx + y = 11
x + 3y = 29
2y = 29 – 11 = 18
y = 18 ÷ 2 = 9
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?
and primary onemodel method
in kindergarten
Ali has 3 sweets. Billy has 5 sweets.How many sweets do they have altogether?
mental computationsmodel method
alternate methods
Cheryl has $20 less than David.Cheryl and David have $148 altogether,Find the amount of money Cheryl has.
Cheryl
David 20
$148
Let the amount of money that Cheryl has be $y.
y + (y + 20) = 148
2y + 20 = 148
Cheryl has $20 less than David.Cheryl and David have $148 altogether,Find the amount of money Cheryl has.
Cheryl
David 20
$148 - $20 = $128
$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.
Cheryl
David 20
$148
Let the amount of money that David has be $y.
Cheryl
David 20
$148 + $20 = $168
20$168 ÷ 2 = $84
David has $84.
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.
y + (y – 20) = 148
2y – 20 = 148
2y = 148 + 20 = 168
y = 168 ÷ 2 = 84 Cheryl has $64.
see abstract ideasmodel method
helps average learners
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? $1.50How 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
basketball 12
Soccer 12 x 3 = 36
There were 36 students in soccer .
How about 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.
soccer
basketball
3 units = 12
1 unit = 4
8 units = 32
There were 32 students in soccer at first
problem solvingmodel method
new situations
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
girls
34 34
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
girls
34 34
88 – 34 – 34 = 20
34
2 units = 34 – 20 = 14
1 unit = 7
7 x 3 = 21 21 girls wore goggles
leaving examinationmodel method
primary school
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
Jim
Ken
sweets
18
3 parts 12 + 12 + 12 + 12 + 18 = 661 part 22
Half of the sweets Ken bought = 22 + 12 = 34So Ken bought 68 sweets.`
12
12
12
12
12
12
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