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P5 and P6 Parents’ Workshop 2021
“Helping your child to Understand
and Solve Word Problems”
• Get students to be familiar with the recall of basic mathematical facts/rules and formulae automatically and without hesitation.
• It has also shown that students who can’t recall number facts automatically often cannot calculate accurately and also struggle with even higher order thinking skills
Factual FluencyImproving Confidence and Achievement in Numeracy (ICAN)
One of the key structures of ICAN
Time was set aside in Math lesson to practise basic number facts
regularly
Different forms: Speed Test, Class Practice and Games using fact cards
Eases the pupils’ cognitive load when learning new concepts
Factual Fluency
• Systematic approach to scaffold
students in problem solving
• Students use it as a checklist when they
are solving word problems
• Implemented across levels P1 – P6
STAR Framework
STAR Framework
CUBA Strategy:• Circle the
numbers• Underline the key
words• Bracket what we
need to find• Draw Arrows to
link data with information
Mathematical Processes:• Thinking skills
and heuristics• Reasoning
Review:• NTUC (Number Transfer, Units, Calculation) check• Check if the answer is reasonable
MEAL Strategy:• Model• Equation• Algorithm• Last Answer
Four classes A, B, C and D raised money for a charity.
Classes A and B raised a total of $108. Together, classes
B, C and D raised a total of $180. The total amount of
money raised by all 4 classes is 5 times the amount that
class B raised. [How much money] did [class B] raise?
6 units = $108 + $180= $288
1 unit = $288 ÷ 6= $48
STAR Checklist
Stop
Think
Act
Review
A, B, C, D
B
$108 + $180
?
1 unit
1 unit
1 unit
1 unit
1 unit
1 unit
Class B raised $48.#
Model Drawing
1) Fractions: Remainder Concept
2) Whole Numbers: Before and After
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Fractions: Remainder Concept (branching method indicated by arrows)
Firdaus’ stamp
collectionat first
Gave cousin 14
Left with
[1 -14
]
Gave sister 59
Left with 80(in the end)
Fraction:
[1 -59
]
Firdaus gave his cousin 14
of his stamp collection.
He gave his sister 59
of the remainder and had 80 stamps left.
How many stamps did he have at first?
STAR Approach to Problem-Solving
Firdaus gave his cousin 14
of his stamp collection.
He gave his sister 59
of the remainder and had 80 stamps left.
How many stamps did he have at first?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Fractions: Remainder Concept Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
Cousin
80
1 unit
9 units = ?
Sister
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Fractions: Remainder ConceptStep 3:
I will write out the
steps of my solutions
Firdaus gave his cousin 14
of his stamp collection.
He gave his sister 59
of the remainder and had 80 stamps left.
How many stamps did he have at first?
4 small units = 801 small unit = 80 ÷ 4
= 209 small units = 20 × 9
= 180
3 big units = 1801 big unit = 180 ÷ 3
= 604 big units = 60 × 4
= 240
Firdaus had 240 stamps at first.
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Fractions: Remainder Concept Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
Firdaus gave his cousin 14
of his stamp collection.
He gave his sister 59
of the remainder and had 80 stamps left.
How many stamps did he have at first?
Alternative method:
Cousin
80
1 unit
Sister
Using a different method to check (when big units can be divided equally):1. Find 1 unit
• 80 ÷ 4 = 202. Find 12 units
• 20 × 12 = 240
Whole Numbers:Before and After
• 2 things have equal at first or at the end
• Keywords like “after”, “at first” , “in the end” and “equal”
Don’t be confused with Work Backwards Method, where no information of “Before” situation is given at all.
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Whole Numbers: Before and After
Paul(same)
- $145
Left with 4 unitsKen
(same)- $64
Left with 1 unit
Paul and Ken had an equal amount of money at first.
Paul spent $145 and Ken spent $64.
After that, Ken had 4 times as much money left as Paul.
How much did each of them have at first?
Paul and Ken had an equal amount of money at first.
Paul spent $145 and Ken spent $64.
After that, Ken had 4 times as much money left as Paul.
How much did each of them have at first?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Whole Numbers: Before and After Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
1 unit 1unit 1 unit 1 unit
1 unitPaul
Ken $64
$145
$145
After finding the value of 1 unit, we can add $145 to find out how much Paul had at first. That gives us what ‘each of them’ had at first.
1. Find 3 units2. Find 1 unit
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Whole Numbers: Before and AfterStep 3:
I will write out the
steps of my solutions
Paul and Ken had an equal amount of money at first.
Paul spent $145 and Ken spent $64.
After that, Ken had 4 times as much money left as Paul.
How much did each of them have at first?
3 units = $145 - $64= $81
1 unit = $81 ÷ 3= $27
Paul at first = $ 145 + $27= $172
Each of them had $172 at first.
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Whole Numbers: Before and After Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
Paul and Ken had an equal amount of money at first.
Paul spent $145 and Ken spent $64.
After that, Ken had 4 times as much money left as Paul.
How much did each of them have at first?
Alternative method:
Ken should also have $172 at first.
1 unit 1unit 1 unit 1 unitKen $64
$172
Check if the value of 1 unit is the same.4 units = $172 - $64
= $1081 unit = $108 ÷ 4
= $27
HEURISTIC Framework
HEURISTIC Framework
1) Supposition
2) Guess and Check
3) Working Backwards
Heuristic Skills
Supposition
• Supposition questions usually have the following characteristics:Usually 2 criteria (2 variables found in a question)to fulfilWhen all criteria are fulfilled, answers obtained can be considered correct
• Method: Assume 1 part of the final answer to fulfil 1 of the criteria
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Supposition
Number of three-mark questions: 10
Number of five-mark questions: 10
Number of correct answers: 15
Score: 57
What do we need to find?• Number of CORRECT
three-mark questions• Number of CORRECT
five-mark questions
In a test, each pupil had to answer 10 three-mark questions and
10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
Supposition
In a test, each pupil had to answer 10 three-mark questions and
10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
Fulfil 2 final answers to achieve the full marks for the question:• Number of correct three-mark questions• Number of correct five-mark questions
Fulfil 2 criteria when answering the question:• 15 correct answers• 57 marks
Choose either:• SuppositionOR• Guess & Check
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Step 3:
I will write out the
steps of my solutions
SuppositionIn a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
Assume that Ting Ting answered 15 five-marks questions correctly
(1) 15 x 5 = 75 (Number of marks Ting Ting would have scored if she scored 15 five-mark questions correctly)
(3) 5 – 3 = 2 (Difference in marks between a five-mark and three mark question)
(2) 75 – 57 = 18 (Difference in marks between assumed marks and real marks)
(4) 18 ÷ 2 = 9 (number of three-mark questions Ting Ting answered correctly)
(5) 15 – 9 = 6 (number of five-mark questions Ting Ting answered correctly)
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
5 m
- 23 m- 23 m- 23 m
- 23 m - 23 m - 23 m
- 23 m- 23 m- 23 m
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
Supposition
In a test, each pupil had to answer 10 three-mark questions and
10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
Assume that Ting Ting answered 15 three-marks questions correctly
(1) 15 x 3 = 45 (number of marks Ting Ting would have scored if she scored 15 three-mark questions correctly)
(2) 5 – 3 = 2 (Difference in marks between a five-mark and three mark question)
(3) 57 – 45 = 12 (Difference in marks between assumed marks and real marks)
(4) 12 ÷ 2 = 6 (number of five-mark questions Ting Ting answered correctly)
(5) 15 – 6 = 9 (number of three-mark questions Ting Ting answered correctly)
Alternative method:Assume Ting Ting answered 15 three-marks questions correctly.
Guess and Check
• Guess and Check questions usually have the following characteristics:Usually 2 criteria (2 variables) to be used as a “Check” for “Guesses” of correct/incorrect answersWhen all criteria are fulfilled, answers obtained can be considered correct
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Guess and Check
Guess: - How many correct three-mark questions?- How many correct five-mark questions?
Check:- 15 correct answers- 57 marks
STAR Approach to Problem-Solving
In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Guess and Check
Guess: - How many correct three-mark questions?- How many correct five-mark questions?
Check:- 15 correct answers- 57 marks
Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
We can use Guess and Check to find possible combinations of correct three-mark and five-mark questions in a table
No. of correct three-mark questions
Marks from three-mark questions
No. of correct five-mark questions
Marks from five-mark questions
Marks scoredNo. of correct
answersCHECK
7 7 x 3 = 21 8 8 x 5 = 40 21 + 40 = 61 15 X
8 8 x 3 = 24 7 7 x 5 = 35 24 + 35 = 59 15 X
9 9 x 3 = 27 6 6 x 5 = 30 27 + 30 = 57 15
STAR Approach to Problem-Solving
In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Guess and CheckStep 3:
I will write out the
steps of my solutions
STAR Approach to Problem-Solving
In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.
Ting Ting had 15 correct answers and scored 57 marks.
How many questions of each kind did she answer correctly?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Guess and Check Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
No. of correct three-mark questions
Marks from three-mark questions
No. of correct five-mark questions
Marks from five-mark questions
Marks scoredNo. of correct
answersCHECK
7 7 x 3 = 21 8 8 x 5 = 40 21 + 40 = 61 15 X
8 8 x 3 = 24 7 7 x 5 = 35 24 + 35 = 59 15 X
9 9 x 3 = 27 6 6 x 5 = 30 27 + 30 = 57 15
Working Backwards
• Used when no information of ‘Before’ situation is given at all
• All the information is given at the ‘After’ situation
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Working Backwards
A shopkeeper had some files for sale.
Jack bought 12
of the files and was given 8 files free.
Rebecca bought 12
of the remaining files and was given 3 files free.
The shopkeeper had 54 files remaining.
How many files did the shopkeeper have at first?
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Working Backwards
Files in the shop at first
Jack bought 12
and got 8 free
Remainder:12
of the total number – 8 files
Rebecca bought 12
of remainder and got 3 free
Left with 54 files
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Working Backwards Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files
free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper
had 54 files remaining. How many files did the shopkeeper have at first?
54 remaining 3 Rebecca’s files
12
of remainder12
of remainder
57 57
114
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Working Backwards Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files
free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper
had 54 files remaining. How many files did the shopkeeper have at first?
54 remaining 3 Rebecca’s files
114
Jack’s files8
12
of original12
of original
122 122
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Step 3:
I will write out the
steps of my solutions
Working Backwards
A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files
free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper
had 54 files remaining. How many files did the shopkeeper have at first?
54 + 3 = 57
57 × 2 = 114
114 + 8 = 122
122 × 2 = 244
The shopkeeper had 244 files at first.
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
Working Backwards
A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files
free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper
had 54 files remaining. How many files did the shopkeeper have at first?
Alternative method:
244 ÷ 2 = 122
122 – 8 = 114
114 ÷ 2 = 57
57 – 3 = 54
Alternative method:Checking for calculation errors by counting backwards
Strategies to solve word problems related to Ratio
Based on these concepts:• Constant Part Concept• Constant Total Concept• Constant Difference Concept
Students need to use their calculator to solve these word problems.
Topic: Ratio (relative sizes)
How many times one quantity is as large as another given their ratio?
Solve word problems involving 2 pairs of ratios
Constant Part Concept
• 2 parts (2 quantities) in a word problem.
• There is a change in one part (quantity) while the other part (quantity) remains unchanged.
• Make use of the unchanged part (quantity) to solve the word problem.
STAR Approach to Problem-Solving
Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the
box was 1:2. When 135 more apples were added into the box, the ratio of the number of
apples to the number of oranges became 9:3. How many apples were in the box at first?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Part Concept (PSLE Question)
The number of oranges is unchanged.
Before ratio-- Apples : oranges 1 : 2
135 more apples were put in the boxAfter ratio -- Apples : oranges
9 : 3
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the
box was 1:2. When 135 more apples were added into the box, the ratio of the number of
apples to the number of oranges became 9:3. How many apples were in the box at first?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Part Concept (PSLE Question)
Make use of this constant part concept (orange quantity) to solve the word problem.
before ratio-- Apples : oranges 1 : 2
135 more apples were put in the box
after ratio -- Apples : oranges 9 : 3
Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
STAR Approach to Problem-Solving
Kim had a box of oranges. The ratio of the number of apples to the number of oranges in
the box was 1:2. When 135 more apples were added into the box, the ratio of the number
of apples to the number of oranges became 9:3. How many apples were in the box at
first?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Part Concept (PSLE Question)
Make the units of oranges in both ratios the same (Equivalent Ratio)Before AfterA : O A : O1 : 2 9 : 3
3 : 6 18 : 6
Step 3:
I will write out the
steps of my solutions
X 3 X 2
Note: 6 is the first common multiple of 2 and 3
STAR Approach to Problem-Solving
Kim had a box of oranges. The ratio of the number of apples to the number of oranges in
the box was 1:2. When 135 more apples were added into the box, the ratio of the number
of apples to the number of oranges became 9:3. How many apples were in the box at
first?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Part Concept (PSLE Question)
Before AfterA : O A : O1 : 2 9 : 3
3 : 6 18 : 6
Step 3:
I will write out the
steps of my solutions
X 3 X 2
Multiply the units of apples in each ratio by the same number used to multiply the units of oranges in the same ratio.
STAR Approach to Problem-Solving
Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the
box was 1:2. When 135 more apples were added into the box, the ratio of the number of
apples to the number of oranges became 9:3. How many apples were in the box at first?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Part Concept (PSLE Question)
Before AfterA : O A : O1 : 2 9 : 3
3 : 6 18 : 6
Step 3:
I will write out the
steps of my solutions
Find the difference between the number of units in apples in both ratios. 18u – 3u = 15u (Unitary Method)
Find 1 unit of apples
1u = 135 ÷ 15 = 9
Find the number of apples at first. 3u = 9 X 3 = 27
STAR Approach to Problem-Solving
Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the
box was 1:2. When 135 more apples were added into the box, the ratio of the number of
apples to the number of oranges became 9:3. How many apples were in the box at first?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Part Concept (PSLE Question) Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
Number of apples at first: 27Number of apples in the end : 27 + 135 = 162Number of oranges = 6 x 9 = 54Apples : Oranges = 162 : 54
= 18 : 6= 9 : 3
Check the steps and use the actual number of apples and oranges calculated to express the quantities in the form of ratio as 9 : 3.
Constant Total Concept
• 2 parts (2 quantities) in a word problem. • There is a redistribution of quantities between the 2 parts while the sum/total of the quantities remains unchanged.
• Make use of the unchanged total (sum of the quantities) to solve the word problem.
• Constant Total concept is related to ‘Internal Transfer’ concept.
STAR Approach to Problem-Solving
The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,
the ratio of Jane’s money to Mary’s money became 1:2.
what was the total amount of money they had altogether?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Total Concept (PSLE Question)
Now, Mary has $24 more while Jane has $24 less (same amount of money is redistributed (internal transfer)
Before ratio-- Jane : Mary : Total 3 : 4 : 7
After ratio -- Jane : Mary : Total1 : 2 : 3
No change in total amount of money altogether
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,
the ratio of Jane’s money to Mary’s money became 1:2.
what was the total amount of money they had altogether?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Total Concept (PSLE Question)
Make use of this constant total concept to solve the word problem.
Before ratio-- Jane : Mary : Total 3 : 4 : 7
After ratio -- Jane : Mary 1 : 2 : 3
Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
STAR Approach to Problem-Solving
The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,
the ratio of Jane’s money to Mary’s money became 1:2.
hat was the total amount of money they had altogether?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Total Concept (PSLE Question) Step 3:
I will write out the
steps of my solutions
Make the total number of units in both ratios the sameBefore After
J : M : T J : M : T3 : 4 : 7 1 : 2 : 3
9 : 12 : 21 7 : 14 : 21
X 3 X 7
Note: 21 is the first common multiple of 3 and 7
STAR Approach to Problem-Solving
The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,
the ratio of Jane’s money to Mary’s money became 1:2,
what was the total amount of money they had altogether?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Total Concept (PSLE Question) Step 3:
I will write out the
steps of my solutions
Before AfterJ : M : T J : M : T3 : 4 : 7 1 : 2 : 3
9 : 12 : 21 7 : 14 : 21
X 3 X 7
Multiply the units of Jane’s and Mary’s money in each ratio by the same number used to multiply the total units in the same ratio.
X 3 X 7X 3 X 7
Note the difference in the amount of units of Jane’s money (or Mary’s money) before and after the transfer. Difference is 2u (9u – 7u or 14u -12u)
STAR Approach to Problem-Solving
The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,
the ratio of Jane’s money to Mary’s money became 1:2.
what was the total amount of money they had altogether?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Total Concept (PSLE Question) Step 3:
I will write out the
steps of my solutions
Before AfterJ : M : T J : M : T3 : 4 : 7 1 : 2 : 3
9 : 12 : 21 7 : 14 : 21X 3 X 7X 3 X 7
Find 1 unit of money2u = 24
1u = 24 ÷ 2= 12 (Unitary Method)
Find the total amount of money21u = 12 X 21 = 252
STAR Approach to Problem-Solving
The ratio of Jane’s money to Mary’s money was 3:4 at first.
After Jane gave Mary $24, the ratio of Jane’s money to Mary’s money became 1:2.
What was the total amount of money they had altogether?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Total Concept (PSLE Question) Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
Total = $252$252 ÷7 = 36Jane in the end : ($36 X 3) – 24 = $84Mary in the end : ($36 X 4) + 24 = $168Jane : Mary = 84 : 168
= 1 : 2
Check the steps and use the actual amount of money calculated to express the quantities in the form of ratio as 1 : 2.
Constant Difference Concept
•Constant Difference means the difference between 2 parts (before and after ratio) remains unchanged.
• Usually this concept applies in questions related to ‘Age’
STAR Approach to Problem-Solving
At first, the ratio of the number of boys to the number of girls in a chess club was
4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1. In the end, how many
boys were there in the club?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Difference Concept (PSLE Question)
The same number of boys and girls joined the chess club
Before ratio-- Boys : Girls : Difference4 : 1 : 3
After ratio -- Boys : Girls : Difference 3 : 1 : 2
No change in the difference between the number of boys and girls
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
STAR Approach to Problem-Solving
At first, the ratio of the number of boys to the number of girls in a chess club was
4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many
boys were there in the club?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Difference Concept (PSLE Question)
Make use of this constant difference concept to solve the word problem.
Before ratio-- Boys : Girls : Difference 4 : 1 3
After ratio -- Boys : Girls : Difference 3 : 1 : 2
Step 2:
What strategy
should I use?
Have I solved
similar problems
before?
STAR Approach to Problem-Solving
At first, the ratio of the number of boys to the number of girls in a chess club was
4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1. In the end, how many
boys were there in the club?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Difference Concept (PSLE Question) Step 3:
I will write out the
steps of my solutions
Make the difference in the number of units in both ratios the sameBefore ratio After ratio
B : G : Difference B : G : Difference4 : 1 : 3 3 : 1 : 2
8 : 2 : 6 9 : 3 : 6
X 2
Now, the difference in both ratios is 6.
X 3
STAR Approach to Problem-Solving
At first, the ratio of the number of boys to the number of girls in a chess club was
4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many
boys were there in the club?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Difference Concept (PSLE Question) Step 3:
I will write out the
steps of my solutions
Before AfterB : G : Difference B : G : Difference4 : 1 : 3 3 : 1 :2
8 : 2 : 6 9 : 3 : 6
X 3X 2X 2
Multiply the units of Boys and girls in the before ratio by the same number used to multiply the difference in the number of units in the same ratio.
X 2 X 3 X 3
STAR Approach to Problem-Solving
At first, the ratio of the number of boys to the number of girls in a chess club was
4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many
boys were there in the club?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Difference Concept (PSLE Question) Step 3:
I will write out the
steps of my solutions
Before AfterB : G : Difference B : G : Difference4 : 1 : 3 3 : 1 : 2
8 : 2 : 6 9 : 3 : 6
Note the difference in the amount of units of girls or boys before and after. Difference is 6u (8u – 2u or 9u -3u)
STAR Approach to Problem-Solving
At first, the ratio of the number of boys to the number of girls in a chess club was
4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many
boys were there in the club?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Difference Concept (PSLE Question) Step 3:
I will write out the
steps of my solutions
Before AfterB : G : Difference B : G : Difference4 : 1 : 3 3 : 1 : 2
8 : 2 : 6 9 : 3 : 6
Find 1 unit
1u = 6
Find number of boys in the end.
9u = 9 X 6 = 54
STAR Approach to Problem-Solving
At first, the ratio of number of boys to number of girls was 4:1. After
6 boys and 6 girls joined, the ratio of number of boys to number of girls became 3:1.
What was the number of girls in the end?
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Constant Difference Concept (PSLE Question) Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
6 x 3 = 18 (number of girls in the end)18 – 6 = 12 (number of girls at first)
9 x 6 = 54 (number of boys in the end)54 – 6 = 48 (number of boys at first)
Check the steps and use actual number of boys and girls to check against the ratio given.
Before ratioB : G48 : 12 4 : 1 (simplest form)
After ratioB : G54 : 183 : 1 (simplest form)
Everything Changed Concept
• Every part changes, the difference changes, the total changes….Nothing remains the same...no constant variables basically
• Form equations/use unit-and-part concepts• Form equal parts (or units) in order to solve the word
problems.
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)
Before ratio-- Carl : Vijay75 : 1003 : 4 (ratio in its simplest form)
Carl has $200 more & Vijay has $50 less in the endAfter ratio -- Carl : Vijay
2 : 1 (ratio in its simplest form)
Everything changes. No constant variable.
Step 1:
What am I given?
(facts/ information/
data)
What am I asked to
find?
How can I make
sense of the
information given to
me?
What can I infer
from the given data?
Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)
Before ratio-- Carl : Vijay3 : 4
After ratio -- Carl : Vijay 2 : 1
Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 2:
What strategy
should I use?
Have I solved
similar problems
before? Form equations /use unit-and-part concepts to solve the word problem.
Before Change After
Carl 3u +200 2p
Vijay 4u - 50 1p
Note: u stands for units and p stands for parts
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 3:
I will write out the
steps of my solutions
Form equations using units and parts.
Vijay (in the end)1p = 4u – 50
Carl (in the end)2p = 3u + 200
Before Change After
Carl 3u +200 2p
Vijay 4u - 50 1p
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 3:
I will write out the
steps of my solutions
Make the parts of Vijay’s money equal to Carl’s money in the end . 1p = 4u – 50 2p = 8u – 100 (twice of 4u-50) Vijay (in the end)
1p = 4u – 50
Carl (in the end)2p = 3u + 200
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 3:
I will write out the
steps of my solutions
2 Parts
2001U 1U 1U
1U 1U1U1U
50
2 Parts
1U 1U1U1U
50
5U = 200 + 100
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 3:
I will write out the
steps of my solutions
From the model.
5U -> 3001U -> 60
Find how much Carl had at first? 3u = $60 x 3 = $180
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 3:
I will write out the
steps of my solutions
2 Parts
2001U 1U 1U
1U ½
u100
1U 1U1U1U
50 spent
Carl
Vijay
Vijay
Now
At first
From Vijay’s models (now and at
first),
1 u + ½ u + 100 + 50 = 4u
4u - 1½ u = 150
2½ u = 150
5u = 150 x 2 (2 sets of 2½ u = 5u)
= 300
1u = 300÷5 = 60
3u = 60 × 3 = 180
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 3:
I will write out the
steps of my solutions
Now,Vijay’s money is ‘equal’ to Carl’s money in the end.
Vijay : Carl 8u – 100 : 3u + 200left equals to right8u -100 = 3u + 2008u – 3u = 200 + 1005u = 300 (unitary method)1u = 60Find how much Carl had at first? 3u = $60 x 3 = $180
STAR Approach to Problem-Solving
Step 2:Think about your plan and strategy you will use
Step 1: Stop and read the
problem carefullyStep 3: Act: Follow your plan and
solve your problem.
Step 4:
Review your answer
Everything Changed Concept (PSLE Question)
Carl had 75% as much money as Vijay. After Carl received $200 from his uncle
and Vijay spent $50, Carl had twice as much money as Vijay.
How much money had Carl at first?
Step 4:
Have I answered the question?
•Is my answer reasonable /
make sense?
•Have I checked my answers?
•Is there a better alternative?
Carl at first : $180Carl in the end: $180 + $200 = $380Vijay at first: $60 x 4 = $240Vijay in the end: $240 - $50 = $190C : V = 380 : 190
= 2 : 1
Check the steps and use the actual amount of money calculated to express the quantities in the form of ratio as 2 : 1 (in the end).
Carelessness in calculation
Cultivate the habit of checking by working backwards after
attempting the question.
Transfer information wrongly from question to working.
With numbers transferred wrongly from the question, the
subsequent working and calculation may be affected and thereby
causing marks to be lost.
Common Mistakes
Transfer final answer wrongly from working to final answer
blank.
Students are recommended to indicate final answer by underlining
in working space.
Common Mistakes
Common Mistakes
Missing units
Forgetting to include units given in 2-marks or more questions.
Decimal notations for money
Dollars and cents must be expressed in 2 decimal places. Example,
$14.50, not $14.5
Reading the question wrongly- missing out the key words.
Ensure your child is familiar with the essential functions of
his/her calculator and only use it for Paper 2 questions.
Practise the use of the tools like protractor and set-squares
for measuring and constructing figures (Mathematical
Instrument set).
Tips for PSLE
Discourage your child to rely on correction tape or liquid
paper(though it is allowed).
Encourage your child to use a blue ballpoint pen for written
answers.
Tips for PSLE
Revisit the rules and formulae.
Have sufficient rest especially the day before the paper!
Discourage your child to attempt solving a question for more
than 10 minutes (Paper 2). Move on to the questions that they
may be able to solve.
Temporary to skip questions that the students have difficulty
to do and to revisit them at the end.
Questions & Answer
Thank you!