Problem-Solving Items in
PSLE Mathematics
Yeap Ban Har
National Institute of Education
Nanyang Technological University
Organised by Association of Mathematics Educators &
Department of Science and Mathematics Singapore Polytechnic
Singapore Mathematics
Curriculum (1992, 2001)
New Directions in Assessment
 Examinations are here to stay
 Changes in emphasis
 Changes in format
 Not necessarily paper-and-pencil
 Not necessarily individual
 Not necessarily independent
Item Types in PSLE
What is the value of 84  7 – 4  2?
(1) 56
(2) 16
(3) 14
(4) 4
PSLE Items
Computation must not be
tedious
Item Types in PSLE
A piece of wire is bent to form the rightangled triangle shown below.
Find the area of the triangle.
16 cm
Answer: _________ cm2
20 cm
12 cm
PSLE Items
Selecting data is now
required
Item Types in PSLE
The figure is made up of four identical
squares each of side 2 cm.
What is the perimeter of the figure?
(1) 16 cm
(2) 20 cm
(3) 24 cm
(4) 32 cm
Item Types in PSLE
The figure is made up of four identical
squares each of side 2 cm.
What is the perimeter of the figure?
(1) 16 cm
(2) 20 cm
(3) 24 cm
(4) 32 cm
PSLE Items
Concepts are tested
alongside procedures
Item Types in PSLE
A rectangular piece of paper, coloured
on one side, is folded to form the shape
shown below.
What is the area of the rectangular piece
of paper before it was folded?
Item Types in PSLE
(1) 24 cm2
(2) 40 cm2
(3) 48 cm2
(4) 56 cm2
PSLE Items
Expects hands-on learning
in the classroom
Singapore Mathematics
Curriculum (1992, 2001)
More Than Computational
Fluency
What is the reading indicated on the
weighing scale shown?
PSLE Items
Practical skills are tested
too
More Than Computational
Fluency
What is the reading indicated on the
weighing scale shown?
More Than Computational
Fluency
The figure shows a line XY and three
points R, S and T.
More Than Computational
Fluency
Draw a straight line from
point X to one of the
points R, S or T so as to
form an angle between
50o and 70o at X.
Draw a perpendicular to
XY passing through point
T.
Computation?
What is the missing number in the box?
4 2 2
  
11 11 11
1

11
Computation?
1 + 2 + 3 + 4 + …….. + 94 + 95 + 96 + 97
When the first 97 whole numbers are added
up, what is the digit in the ones place of this
total?
(1) 1
(2) 2
(3) 3
(4) 8
Computation?
1 + 2 + 3 + 4 + …….. + 94 + 95 + 96 + 97
1 + 2 + 3 + 4 + …….. + 94 + 95 + 96 + 97
1 + 2 + 3 + 4 + …….. + 94 + 95 + 96 + 97
1 + 2 + 3 + 4 + …….. + 94 + 95 + 96 + 97
1 + 2 + 3 + 4 + …….. + 94 + 95 + 96 + 97 + 98 + 99
Singapore Mathematics
Curriculum (1992, 2001)
Life becomes harder for those who perceive
these to be computational items.
There are pupils who perceive mathematics
to be computations.
Those who are a little critical would ask
themselves if there are more elegant methods
to get the answer. Those who are a little
creative would be able to figure different
ways to do the same tasks.
Perception, critical thinking and creative
thinking are part of habits of mind.
The PSLE Format
It lasts for 2 hours 15 minutes.
There are 15 multiple-choice questions for 25% of the
total marks.
• 5 1-mark questions (5%)
•10 2-mark questions (20%)
The first format tests really basic knowledge. The second
format tests a range of competencies including problemsolving proficiency.
The PSLE Format
There are 20 short-answer tasks for 20%. They are all 1mark item. If units are required, they are indicated. If
working is necessary, they can be done but will not be
considered for credit. They are meant to test basic skills.
Many can be done mentally.
The PSLE Format
There are 15 structured and long-answer tasks for 55%.
•Three 2-mark tasks (6%)
•Three 3-mark tasks (9%)
These two types tend to test basic skills and simple
problem solving.
The PSLE Format
There are 15 structured and long-answer tasks for 55%.
•Five 4-mark tasks (20%)
•Four 5-mark tasks (20%)
These two types tend to test problem-solving proficiency.
Some tasks are demanding.
Problem Solving
Lee and Chan both drove from Town P to Town Q.
They started their journeys at different times.
Lee drove at an average of 45 km/h and took 40
minutes.
Chan drove at an average speed of 72 km/h and
reached Town Q at the same time as Lee.
Problem Solving
Lee and Chan both drove from Town P to Town Q.
They started their journeys at different times.
Lee drove at an average of 45 km/h and took 40
minutes.
Chan drove at an average speed of 72 km/h and
reached Town Q at the same time as Lee.
Speed = Distance  Time
45 = Distance  2/3
Problem Solving
Lee and Chan both drove from Town P to Town Q.
They started their journeys at different times.
Lee drove at an average of 45 km/h and took 40
minutes.
Chan drove at an average speed of 72 km/h and
reached Town Q at the same time as Lee.
60 minutes --- 45 km
20 minutes --- 15 km
40 minutes --- ?? km
Structured Questions
How far was Town P from Town Q?
How many minutes later than Lee did Chan start
this journey?
Problem Solving
Lee and Chan both drove from Town P to Town Q.
They started their journeys at different times.
Lee drove at an average of 45 km/h and took 40
minutes.
Chan drove at an average speed of 72 km/h and
reached Town Q at the same time as Lee.
72 km --- 60 minutes
12 km --- 10 minutes
Problem Solving
Sam gets $3 more pocket money than Bob
each week.
They each spend $15 per week on food and
save the rest.
When Sam saves $72, Bob only saves $48.
Sam
$72
Bob
$24
$48
Number of weeks = 24  3 = 8
Sam
$72
Bob
$24
$48
How much pocket money does Bob get each week?
Word Problems
Vani was given $4 to spend during
recess. She spent 90 cents on a
chicken wing and 65 cents on a bottle
of mineral water. How much did she
have left?
Typical Word Problem
Mrs Wong has 24 tarts. She packs all
of them into boxes. Each box holds 4
tarts. What is the total number of
boxes she used?
Typical Word Problem
Mrs Wong has 26 tarts. She packs all
of them into boxes. Each box holds 4
tarts. What is the total number of
boxes she used?
PSLE Item
Mrs Wong has 26 tarts. She packs all
of them into boxes. Each box can
hold up to 4 tarts. Which of the
following cannot be the total number
of boxes she used?
(1) 5
(2) 7
(3) 8
(4) 10
PSLE Items
Expect pupils to realise that
a situation differs from
familiar ones and requires
different strategies to solve
PSLE Item
A box of greeting cards was shared
equally among a group of 35 pupils. 7
of them gave all their cards to the rest
of the pupils. As a result, the rest of
the pupils received 2 more cards each.
How many cards were there in the
box at first?
Strategies to Help Pupils
(1) Read the text
(2) Retell the story
(3) Pose questions based on the story
(4) Answer comprehension questions
PSLE Item
A box of greeting cards was shared
equally among a group of 35 pupils. 7
of them gave all their cards to the rest
of the pupils. As a result, the rest of
the pupils received 2 more cards each.
How many cards were there in the
box at first?
PSLE Item
A box of greeting cards was shared
equally among a group of 35 pupils. 7
of them gave all their cards to the rest
of the pupils. As a result, the rest of
the pupils received 2 more cards each.
How many cards were there in the
box at first?
PSLE Item
Miss Tang went to a supermarket to
buy exactly 44 apples for her class
camp. The apples were priced at 45
cents each or in bags of 5 at $2.00 per
bag. What was the smallest amount of
money that Miss Tang could have
spent on the apples?
Modified Item
Miss Tang went to a supermarket to
buy exactly 44 apples for her class
camp. The apples were priced at 45
cents each or in bags of 5 at $2.00 per
bag. What was the smallest amount of
money that Miss Tang could have
spent on the apples?
Thinking Completely
Using Knowledge
Each of the three cards shown is printed
with a different whole number. The
smallest number is 23. When these
numbers are added two at a time, the
sums are 61, 71 and 86. What is the
largest number on the cards?
Using Knowledge
(1) 25
(2) 38
(3) 48
(4) 63
Draw a Model
1
3
In a class, of the pupils are girls and of the girls wear
6
5
spectacles.
3
4
If
of the boys wear spectacles, what fraction of the
pupils wear spectacles?
Guess and Check
B
A
D
C
The figure is a square made up of four parts, A, B, C and D.
C and D are squares and each is ¼ of the figure.
3
Which of the following two parts will add up to form 8 of
the figure?
Draw a Diagram
Solve Part of the Problem
A toy-maker has a rectangular block of wood 30 cm by
14 cm by 10 cm.
He wants to cut as many 3-cm cubes as possible. How
many such cubes can he cut?
Visualization
A carpenter uses identical blocks to make low stools. Each
block is 44 cm long, 15 cm wide and 9 cm thick.
He cuts the length of the block into
three parts A, B and C in the ratio 5 : 3 : 3.
He then nails B and C to A to make a stool
such that there is a gap between B and C.
The stool is shown on the right.
Find the width of the gap.
He cuts the length of the block into
three parts A, B and C in the ratio 5 : 3 : 3.
He then nails B and C to A to make a stool
such that there is a gap between B and C.
The stool is shown on the right.
There are a number of ways the
carpenter can stack up to 10
completed stools one on top of
another. What is the lowest
possible height of the stack of
10 stools?
Educating the Next Generation
How many cubes are there in this stack?
Educating the Next Generation
Cubes of the same size are stacked in a
corner of a box as shown.
How many cubes are there?
Discussion
bhyeap@nie.edu.sg
Thank You
Association of Mathematics Educators
Singapore Polytechnic