STU Seminar on The Model Method in Mathematical Problem Solving at NTUC Centre, Singapore 10 April...
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Transcript of STU Seminar on The Model Method in Mathematical Problem Solving at NTUC Centre, Singapore 10 April...
word problemsmodel method
of solving mathematical
Yeap Ban HarNational Institute of Education
Nanyang Technological UniversitySingapore
Slides are available for download fromwww.mathz4kidz.com
SEMINAR
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
“
”
educationmathematics
Move 3 sticks to get two squares.
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
Wellington Primary School, Singapore
visualization
“…development and improvement of a person’s
intellectual competencies...” Singapore Ministry of Education 2006
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
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
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
Cheryl has $20 less than David.Cheryl and David have $148 altogether,Find the amount of money Cheryl has.
Cheryl
David 20
$148
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.
see abstract ideasmodel method
helps average learners
Emil spent 2/5 of his savings to buy a gift and 1/6 of the remainder to buy a snack.Emil then has $7.50 left. Find the amount Emil spent on the gift.
5 units = $7.50
1 unit = $1.50
4 units = $1.50 x 4 = $6
Emil spent $6 on the gift. How about he 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
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
Machine A
Machine B 12
Every minute Machine A prints 12 pages more than Machine B. Machine A and Machine B together print a total of 528 pages in 3 minutes. At this rate, how many pages does Machine B print in 1 minute?
176
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 choco;ates 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
Monday
Tuesday
Wednesday
Thursday
Friday
20
20 20
20 20 20
2020 20 20
Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday?
At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?
A
B
156 kg
72 kg
At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?
A
B 28
156 kg
72 kg
3 units = 156 kg – 72 kg = 84 kg
1 unit = 28 kg
Each shop sold 64 kg of rice.
preliminary examination
model method primary school
Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
Mrs Liu spent 1/5 of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
Mrs Liu spent 1/5 of her monthly salary on a handbag, 1/4 of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
3 units = $1890
Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
Mrs Liu spent 1/5 of her monthly salary on a handbag, 3/8 of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
5 units = $1890
Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
Mrs Liu spent 1/5 of her monthly salary on a handbag, 4/7 of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.
12 units = $1890
There were 192 apples and pears in a box. John removed 2/5 of the apples from the box and he added 24 pears into the box. As a result, there was an equal number of apples and pears left in the box. How many more apples than pears were there in the box at first?
apples
pears 24
192
There were 192 apples and pears in a box. John removed 2/5 of the apples from the box and he added 24 pears into the box. As a result, there was an equal number of apples and pears left in the box. How many more apples than pears were there in the box at first?
apples
pears 24
192 + 24
8 units = 216
8 units = 160 + 56
1 unit = 27
apples
pears
2 27 2727 27
24
192
27
?
Apples = 27 x 5 = 135
Pears = 27 x 3 – 24 = 81 – 24 = 57
There were 135 – 55 – 2 = 78 more apples than pears at first.
A librarian counted the number of adults in the library and found that 2/5 of the number of women was equal to 2 times the number of men. When another 12 men entered the library and 45 women left the library, the ratio of the number of women to the number of men became 5 : 2.
men
women
12
45
30 5 units = 30 + 45 = 751 unit = 15
Men = 2 x 15 = 30
Women = 10 x 15 = 150
leaving examinationother heuristics
primary school
Draw a Diagram
David and Michael drove from Town A to Town B at different speeds. Both did not change their speeds throughout their journeys. David started his journey 30 minutes earlier than Michael. However, Michael reached Town B 50 minutes earlier than David. When Michael reached Town B, David had travelled 4/5 of the journey and was 75 km away from Town B.
Michael
David
75 km4/5
4 x 75 km = 300 km
(a) Town A to Town B is 375 km.
(b) 50 min 75 km
10 min 15 km
1 h 6 x 15 km = 90 km
(c) 50 min 1/5 of the journey250 min whole journey
Michael took 80 min less.He took 170 min.