1. Raffles Institution
Year Two Research Education
Project Report 2011
Modifying The Method Of Teaching Word Problems
By
Team Leader : Muthu (18)
Team Members : Soorya (24)
: Mohamed Haseef Bin Mohamed Yunos (14)
: Jackie Tan (26)
Class : Secondary 2G
Teacher-Mentor : Mrs. Suhaimy
Raffles Institution Research Education
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2. Contents
PAGE NUMBER
1. Acknowledgements 4
2. Abstract(Overview of Project) 5
3. Introduction (Chapter 1) 6
- Singapore Primary School Education in the 6
21st century
- DFC Journey 6
- Research Findings 6
- Hypothesis 9
- Research Question 9
- Aims(Objectives Of Project) 9
- Need of Study(Campaigning for Change) 9
4. Methodology (Chapter 2) 11
- Thought Process (Brainstorming of Solutions) 11
- Analysis of Current Situation & Solution 12
- Preparation For Action Week 12
- Action Week 15
- Modified Teaching Method 16
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4. Acknowledgements
We owe our special thanks to Mrs. Suhaimy, teacher of Raffles Institution, English
Department, Singapore, for her suggestion, valuable guidance, encouragement,
sustained support and interest in the completion of this work. It was largely because of
her that our project was a success. She was able to see the loopholes in our project and
thus, always guided us to the right path. Our thanks are due to her, for opening our
mind‟s eye into the avenues of research.
We profoundly thank Mdm Aisah Bte Mohd Osman, an experienced Maths teacher for
providing the necessary information on the research topic and for kindly accepting our
questions to her. She has been very co-operative with our team and was always there
to help us. Mdm Aisah also did a lot of very important favours such as guiding us in the
designing of the worksheets and also suggesting new ideas to improve our project.
Hence, from the bottom of our hearts, we would like to thank you, Mdm Aisah, for all
your help.
Our thanks are rendered to our friends of Class 2G, Raffles Institution for their precious
help and support as well as the encouragement during the course of this project.
We would also like to show our greatest appreciation to each and every one of our
family members for without them, we would never have the spirit to continue this project
till the end. They also have helped us in many other ways, especially by giving new
ideas to improve our project and spending their time and effort to guide us from the start
till the end.
Last but not least, we would like to thank all those people and friends who have helped
us in one way or another. Although your names may not be mentioned here, we would
just like to say that we remember and appreciate all the help that you have given us in
the course of this project.
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5. Abstract (Overview of Project)
The project aims to help upper Primary students, who have difficulties in solving
complex word problems, improve their level of proficiency by introducing a modified
teaching method into the school curriculum. Through the interview and survey, the real
reason behind the students‟ inability to perform well in Mathematics was found.
39 primary five students whose mark ranges from 50 to 91 marks in their Semestral
Assessment 1 in Mathematics were the participants in this project. They took part in a
survey and Mdm Aisah Bte Mohd Osman, a Maths teacher in Meridian Primary School,
was interviewed prior to the implementation of the project to find out the challenges that
students face in Mathematics. From the survey and interview it was found that most of
the students were not able to perform well in Mathematics because they were not able
to apply the concept had they learned especially in multi-steps, complex word problems.
The pupils also feedback that they lost significant marks due to careless mistakes .and
their inability to complete the paper on time. Through the survey and interview the root
problem and topics to focus on were identified.
The team brainstormed for ideas on how to motivate and help pupils overcome the
barrier of solving multi-steps word problems. The team came out with the idea of
designing worksheets that break down word problems into simpler concepts. 5 such
worksheets were given to students with time frame to simulate exam conditions to help
pupils manage time better. Finally, pre and post tests were given to examine the effect
on the experiment. The results from the post-test revealed remarkable improvements.
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6. Introduction (Chapter 1)
Singapore Primary School Education in the 21st century
A child in Singapore undergoes six years of primary education, comprising a four-year
foundation stage from Primary 1 to 4 and a two-year orientation stage from Primary 5 to
6. At the foundation stage, the core curriculum comprising English, the Mother Tongue
and Mathematics are taught, with supplementary subjects such as Music, Art & Craft,
Physical Education and Social Studies. Science is included from Primary 3. To
maximize their potential, students are streamed according to their learning ability before
advancing to the orientation stage. At the end of Primary 6, students sit for the Primary
School Leaving Examination (PSLE). It was noticed that students struggled during the
PSLE examination and this was very disturbing. They were in need of help and thus,
this project aims to help these students.
DFC Journey
After watching the design for change video, the team was greatly inspired and
motivated to help the less fortunate or less intelligently inclined people. We felt that they
had been suffering a lot. Unlike us, we have everything we want. In addition, we also
thought that if we as the younger generation do our part, what will the future generation
be? Thus, we wanted to do our part to help and contribute to the society.
Research Findings
Researches have shown that Mathematics is the toughest subject that is tested in
PSLE. The PSLE Maths exam has received complaints from students and even parents
that the questions set are tough. For example, the 2005 PSLE Maths paper was set so
hard that the pupils could not finish the paper on time and started crying over the marks
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7. lost. The questions set were not textbook oriented but more on the application of
concepts learnt.
Through intensive searches through the internet and through journals there were many
factors that contributed towards students‟ inability to handle Mathematics paper at
PSLE. From one of these searches, an interesting comment in CollegeNet forum was
found. The following was quoted from a blogger as to why Maths is difficult:
“Some teachers throw formulas and theorems at you and give you a vague
explanation of how it works and what its usefulness is.”
After much thought, the team agreed that the comment was actually true. Based on our
own experiences, most teachers in Singapore teach a formula but do not explain the
concept behind the formula. Instead of exploring the derivation at that particular formula,
teachers generally will go on to the practice questions immediately. It was discovered
that the problem arises when the student does not understand the concept behind the
formula.
Doing a word problem correctly is an essential and important factor for a student‟s
success in Mathematics. The primary school Maths papers have a high percentage of
word problems ranging from 2 to 6 marks each. Therefore, if a student does not have
the ability to handle word problems correctly, there is a high probability that this student
will fail the Mathematics examination.
“One of the most important skills that children need to master is their ability to
become independent thinkers and problem solvers.” (Grace, 2010)
This quote from Ms Elizabeth Grace further supports the facts that word problems are
extremely important in the Mathematics examination in this context of time.
Most students are able to do simple 2 or 3 marks word problems but many of them are
unable to do the multi-steps word problems with the weightage of 4 to 6 marks each.
This is mainly because those questions tests a few Mathematical concepts combined
together and thus, the answers usually require many different steps. This was
mentioned by one of the researchers in Mathematics:
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8. “Students can solve most one-step problems but have extreme difficulty trying to
solve non-standard problems, problems requiring multi-steps, or problems with
extraneous information.” (Carpenter et al., 1981)
Hence, it can be clearly seen that there is a serious problem that needs attention and
should be dealt with quickly otherwise students will continue to struggle. A revolutionary
method of teaching which is more effective than the standard method of teaching should
be adopted so as to help students achieve the results that they desire.
Besides this, the problem of making careless mistakes is also another serious issue.
Many students lose marks due to careless mistakes. However, this problem is really just
due to the fact that students do not check their work.
“Check all answers for accuracy and reasonability, backtracking line by line; and
reserve time on tests for a final check. If you practice being careful as you work
homework problems, you can overcome the problem of “careless” or “stupid”
mistakes. But it is interesting that many students would prefer to blame their
intelligence or their carelessness before their effort becomes the variable.” (Keith
& Cimperman, 1992)
This quote supports the fact that the problem of making careless mistakes can be
avoided if the students check and backtrack their answers for accuracy. Furthermore,
this quote also claims that students blame their intelligence or their carelessness for
making careless mistakes. However, if they take the extra effort to check their work
thoroughly, they will be able to spot their careless mistakes and edit their answer.
Many students have been reminded time and again to check their work by their
teachers and parents. However, the problem is that the teacher or parent does not
explain clearly to their child or student how to check their work. During a research done
by Wiens on careless mistakes, he stated that the students “didn‟t spend as much time
reviewing their tests as I would like them to because they had never been taught how to
check over their work; they thought they were doing what I was asking them to do just
by looking over their test for neatness.” Hence, it is very important that the teacher
guide the students in terms of explaining clearly how to check their work.
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9. Hypothesis
The team believe that students will be able to answer Maths questions well if they
understand the concepts. To explore this believe, the question, “When does Maths
become difficult?” was included in the survey. As expected, majority of the pupils
surveyed responded that they are not able to apply the concepts they have learned.
Thus, our hypothesis is that the students will be able to answer complex word problems
which require multi-steps answers that test different concepts if they are able to break
down the problems into simpler steps.
Research Question
In this project we hope to address the following question:
“Do simplifying words problems into simpler concepts improve students‟
achievements?”
Aims (Objectives of Project)
Our main goal is to help students handle multi-steps word problems by breaking down
the problems into basic steps that help scaffold students‟ understanding so that
eventually they will be able to handle the word problems in the complex form.
Need of Study (Campaigning For Change)
This project could be a breakthrough in the teaching of Mathematics especially in the
teaching of multi-steps word problems. Through this project we hope students will
develop better skills in problem solving and it will also help to build students‟ critical
thinking skills and a strong foundation in Mathematics. We also hope to enlighten
teachers with an approach that could bring about better results in students‟ performance
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10. and motivate them towards the learning of Mathematics. Parents could also adopt this
method to effectively guide and support their children in the area of problem solving.
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11. Methodology (Chapter 2)
Thought Process (Brainstorming of Solutions)
A few solutions were derived after the team brainstorm for ideas and getting
feedback from teachers. The first solution was to teach the students in a fun way
by incorporating games during the Mathematics lessons to motivate students. The
team believed that engaging students in this manner during lessons would motivate
them to do better. Students tend to remember things better when they have fun
and are more engaged.
The second solution was to ask students in groups to take turn to make a
presentation of the lesson taught. The teacher will teach the students in the normal
way. However, instead of the normal way of assessing their learning through tests
and exams, they are tested in a creative way. They would be required to make a
presentation on the lesson that was taught. The presentation would be just a short
one and would include whatever the students had learnt during the lesson. From
their presentation, the teacher would be able to know if they students had
understood the lessons. Prior to the presentation, the students would be asked to
read up on the topic. This method would enable students to have a chance to
revise the topic and they would remember the topic better.
The last solution was to break the complicated Mathematics word problem into
simpler concepts and manageable parts. By breaking the word problem into
simpler concepts and having a question on each concept, the students would be
able to finally complete the complex word problems. A pre-test and a post-test
consisting 5 very complex word problems would be used to measure the
effectiveness on this method.
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12. Analysis of Current Situation & Solution
The team deliberated on the three solutions before deciding on the most effective
solution. Team members debated on the pros and cons of each solution before
making the decision. The team felt that the first solution was too childish and upper
students might not like games. Besides this, the students might end up playing the
games for fun and not learn anything from them. The second solution was not
feasible due to the time constraints. The group presentation might take up too
much time so the teacher in-charge might not be willing to participate in this
project. Furthermore, students might get bored after sometime and do their
presentations half-heartedly. The team collectively agreed that the last solution was
the most attractive and sound. However, some members had some doubts on the
effectiveness of the method. The other criticism was it would require a lot of time
and effort to design worksheets and tabulate the result as well as explain the
results. However, since the third solution was the most viable, the group decided to
put in lot of hard work to complete this project.
Preparation For Action Week
Work allocation (What had to be done & Who did it)
There was quite a lot of work that had to be done. We had to ensure that they were
progressing along the correct path. We had to first of all, find an appropriate group
of students who would want to cooperate with us. However, with Haseef‟s help we
managed to find a teacher teaching Primary-5 Mathematics to help us implement
the project. Moving on, we needed a strategy to teach them. One that was different
from their current one and that would be impactful. This was strategized by Jackie
and Soorya. The effectiveness of the method was assessed by Mdm Aisah during
the interview and confirmed by the students survey. Hence, after verifying, we finally
came up with another method. After this the next task was to implement this
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13. method. The method was to have a pre-test consisting 5 questions which were
totally different from one another. Then, create 5 different worksheets with 4
questions each of them focusing on 1 of the 5 question set in the pre-test. Finally,
we had a post-test to measure the effectiveness of the method. We decided to
measure the effectiveness of the method by comparing the pre-test and pos-test
results.
From our survey, students said that it would be preferable to be taught in small
groups. Hence, we broke up the class into groups of 8.
The next task was to set all the worksheets. The task was carried out by all the
team members. It took us quite a long time to set the worksheets and edit them as
we were neither professionals nor a teacher. We struggled a bit but we managed to
do it well, especially with the help of Mdm Aisah who guided us along the way
correcting us as we set the worksheets. Then, the next part was to print out and
assign the worksheets to all the students. This was mainly done by Haseef who co-
ordinated with the P5 teacher to find suitable time slots which we could use to
conduct the lessons. Finally, we bought snacks and issued it to them freely during
their breaks and whenever they did well, as promised.
Timeline of Tasks
The team knew what needed to be done so we planned a timeline. The timeline was
as follow:
Find a group of students and create a strategy to teach them – By 8th July
Design the worksheets – By 18th July
Start on the action week – Dates: 21st, 22nd, 25th, 26th, 27th, 28th and 29th of
July
Complete marking the worksheets and key in the results – By 2nd August
Start on the report – By 30th July
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14. Resource Management
We had enough resources and we made references to some of the Primary-5
Mathematics worksheets and assessment books when preparing the worksheets
and one of our biggest resource was Mdm Aisah who gave us some important tips
and guided us in the preparation of the worksheets.
Risk Management
As the saying goes, “It is better to be safe than sorry”, we did some conducted the
survey and interview to ensure that the proposed method is sound and viable. The
only risk that we took was to implement that new method. However, we thought
through the process carefully to minimize the risk. As our project involve students,
we had to ensure that there were no detrimental effects on the students‟ learning.
On the other hand, the possibility of success was high.
Who is involved?
There were quite a lot of people involved in this project. First of all, the group of
students who took part in this project were very involved and committed and
motivated. Next their teacher helped us with the logistics. The team members were
very committed and shared the workload equally and every member contributed by
carrying out the task assigned without fail.
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15. Action Week
Participants (Who is affected)
The participants were 39 primary five students aged between 10 and 11 years. These
students were chosen because of the mix ability nature of the group as their
Mathematics marks ranges from 50 to 91 in their Semestral Assessment 1 examination.
They have also gone through 5 years of Mathematics lessons in school and their
opinions on the method of teaching of Mathematics would be invaluable.
Instrumentation
A survey was designed to gather feedback on students‟ perception of Mathematics. The
key elements in the survey include students‟ difficulties in Maths, the reasons for losing
marks in examinations, their opinions on how they could achieve better results in Maths,
and their suggestions on how to motivate them to learn Maths. A draft questionnaire
was prepared to test its effectiveness. Appropriate transitions and section introductions
were also added. Prior to being finalized, the questionnaire was pre-tested on a small
number of respondents. These respondents were from Raffles Institution and through
this survey pre-testing, we were able to ensure that our questions were easily
understood and straightforward. Through this survey, the group was able to identify
topics students are weak in and the reasons why they do not do well. These are
factored into the design of the project.
We also interviewed an experienced Maths teacher, Mdm Aisah Bte Mohd Osman, who
has been teaching upper primary Mathematics for more than 25 years. She has vast
and deep knowledge on the teaching of Mathematics in Primary schools. The questions
were designed based on the current method of teaching Mathematics, the type of
questions teachers usually set in exam papers and students‟ ability in handling such
questions. From the interview, the team triangulate on the topics to focus on and the
approach to be taken.
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16. A pre-test and a post-test were used to measure the effectiveness of the method
adopted. The pre-test and the post-test were the exact worksheets made up of 5
complex word problems on topics students‟ have difficulties in.
The Modified Teaching Method
The modified teaching method basically breaks down multi-steps or complex word
problems into basic steps/concepts that help scaffold students‟ understanding so that
eventually they will be able to handle the word problems in the complex form.
Pupils were given a pre-test which consist 5 complex word problems on topics students
have difficulties in under exam condition prior to the implementation of the project. The
main aim of this pre-test is to gauge the students‟ ability in solving complex word
problems before the implementation of the modified teaching approach. The pre-test
was not given and none of the questions were discussed with the students.
The modified teaching approach was implemented over a period of two weeks.
Students were given five worksheets consisting 4 questions where the last question in
every worksheet is similar to one question in the pre-test worksheet. The first 3
questions in all the five worksheet were scaffolding questions to help pupils break down
the fourth question into simpler steps and concepts. For example, if question1 of the
pre-test tested the concept of changing fraction, balancing ratio and changing
percentage, then the worksheet 1 would have a question testing each concept and the
last question will be similar to the question 1 of the pre-test. Students were given only
one worksheet per day and a time frame of 30 minutes to complete the 4 questions.
This is to simulate exam conditions.
After students had completed the worksheet, the team split the class into groups of 8
and along with the teacher‟s help; we taught each group on how to avoid careless
mistakes and explain the concepts that the students were not very clear with as well as
the answers. This was to ensure that the pupils understand how to break the complex
problems into simpler steps and concepts. The splitting of the class enabled better
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17. monitoring of the students‟ learning. We could focus on each student and hence
maximise learning.
After students had completed the five worksheets, a post-test was administered. The
post-test had exactly the same questions as the pre-test to ensure the validity and
reliability of the instrument used to measure the effectiveness of the method.
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18. Results (Chapter 3)
Impact of Actions
Analysis of Survey
Figure 1 shows the topics which the students find the most difficult to understand.
.2.6% (1) of the 39 students ranked Whole Numbers as the most difficult topic. 5.1%(2)
of the students ranked Fractions as the hardest topic. 7.7% (3) of the students found
ratio the most difficult while 84.6% (33) of the students thought Percentage was the
most difficult topic. Based on this data the team incorporated Percentage in all the 5
worksheets that made used of the modified teaching method.
Figure 1. The Difficult Topic In Maths.
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19. Figure 2 reflects the reason why Maths is difficult to the students. 25.6% (10) of the
students responded that they find Maths difficult when they did not have enough
practice. 38.5% (15) of the students reflected that the difficulty in Maths is because of
many steps involved, 15.4% (6) of the students finds the teacher too fast and 20.8% (8)
of them could not apply the concepts learnt. Based on the students‟ responses it was
quite clear that they are not able to handle multi-steps word problems as they were not
able to apply concepts well and most likely these are complex word problems.
Therefore, the focus of the project was sound.
Maths Becomes Difficult When
NOT ENOUGH PRACTICE 10
Reasons For When
Maths Becomes
NOT ABLE TO APPLY CONCEPT 15
Difficult
TEACHER TOO FAST 6
TOO MANY STEPS 8
0 2 4 6 8 10 12 14 16
Number Of Respondents
Figure 2. Reasons For Difficulty In Maths
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20. Figure 3 reflects the students‟ preference in the way Maths is taught. 12.8% (5) of the
students like to learn Maths through play, on-line learning or one-to-one tutoring.
However, most students, that is 61.5% (24) prefers small group tutoring. Thus, the team
adopted small group tutoring as part of the modified teaching strategy.
Able To Achieve Better Maths Results Through
SMALL GROUP TUTORING 24
Factors To Achieving
Better Results
ONE - TO - ONE TUTORING 5
ON LINE LEARNING 5
MATHS CARD GAME 5
0 5 10 15 20 25 30
Number Of Respondents
Figure 3. Preference In The Way Taught
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21. Figure 4 illustrates the motivational factor. 38.5% (15) of the students preferred snacks
during breaks, 17.9% (7) of them wanted soft music, 25.6% (10) of them wanted token
prizes to be given to those who did well and 20.5%(8) needed frequent compliments
from the teacher. The team decided to reward students with snacks during their breaks
so as it motivate the students to do well.
Feel Motivated To Learn Maths If
FREQUENT COMPLIMENTS GIVEN BY TEACHER 8
Motivations When
Learning Maths
TOKEN PRIZES FOR THOSE WHO DID WELL 10
SOFT MUSIC AT THE BACKGROUND 7
FREE SNACKS DURING BREAKS 15
0 2 4 6 8 10 12 14 16
Number Of Respondents
Figure 4. Motivational Factors
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22. Analysis of Pre-Test & Post-Test Results
Figure 5 displays the average marks scored by the students for the Pre-Test, the 5
Worksheets and the Post-Test. The average marks of all the 5 worksheets are much
higher than the average mark for the pre-test. This means that students are able to
handle complex word problems much better when they are broken down into simple
steps. Also, there is a remarkable improvement of the average marks from the pre-test
to the post-test from 3.1 to 6.7 respectively. This is very significant considering the
short time spent that the method was introduced.
Average Of All Worksheets
12 11.4
Average Marks
9.7 Pre-Test
10
8.2 Worksheet 1
8 6.7 6.5 Worksheet 2
6 Worksheet 3
4 3.1 Worksheet 4
Worksheet 5
2
Post-Test
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1
2
3
4
5
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et
et
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Pr
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ks
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Po
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Worksheet Name
Figure 5. Average Marks for Pre-Test, 5 Worksheets and the Post-Test
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23. The students were able to handle the complex word problems more effectively after
going through 5h of the modified teaching method. 87.2% of the students showed
improvement in the Post-Test. Figure 6 clearly displays the variation in marks between
the Pre-Test and the Post-Test for the 39 pupils.
Pre-Test vs Post-Test Result 2011
30
25 25 25 25
Pre Test (25 marks)
Post Test (25 Marks)
20 20 20
18 18
16
Marks
15 15 15 15
14 14 14
13
12
11
10 10 10
9
8
6 6 6 6
5
4 4
3 3
2 2 2 2 2
1 1 1 1 1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Figure 6. Pre-Test & Post-Test Results of 39 Pupils.
Based of the above results it can be concluded that modified teaching method where
students were taught to break complex word problems into simple steps/concepts has
contributed significantly towards students‟ better achievements.
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24. Discussion (Chapter 4)
In today‟s world, Mathematics is one of the most important subjects one has to be good
in order to be marketable. Therefore, it is very disturbing when some of the primary
school students are still performing badly in Mathematics. This is the main reason for us
taking up the challenge to introduce the modified teaching method to the 39 Primary five
students. Our main aim is that we hope through this project we are able to design a
change to the current teaching method for Mathematics, and possibly other subjects as
well, to a better and more effective method of getting the concepts across to the
students so that they can perform better in Maths.
The results clearly indicated that our project is a success. After just 5 hourly session of
using the modified teaching method, the students were able to show remarkable
improvements in their achievements score. 87.2% (34) students score higher marks in
the Post-Test than the Pre-Test. There are 3 pupils who even achieved full marks for
the Post-Test. There are 12.8% (5) students did not show improvements in their Post-
Test, these are the weaker students as seen in the worksheets score who most
probably need more time/ sessions to assimilate this form of learning.
Students most likely find Percentage a difficult topic as students do not understand the
concept well, hence, were not able to apply the concept and get the correct answer.
However, as we marked the worksheets, after a few sessions, we noticed that the
students were able to substitute fixed values in a percentage formula with values given
in the question. They were also trying their best to break the question down into smaller
parts. As we invigilated them during the post-test, they were making attempts to
underline keywords and checking back the answers to avoid careless mistakes. The
marked improvement in the results of the post-test and their understanding of our
strategy showed us how close we were to success.
We also agree with „kids‟ development‟ website that „the basis of all future learning lies
in the ability to break down a problem into manageable parts until a solution is
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25. determined‟. We think it is a very useful strategy after having seen the results of using
the strategy. It actually helps the student to analyse the question better and enable
them to understand it better because as they split a complex question into simpler parts
they are able to visualise the steps that lead to the answers.
One of the strengths of this project is the effectiveness of the approach used. It leads to
a very productive learning process. The interaction between the students and us in the
small group tutoring, enabled us to glean valuable insights about the students learning
style and approach. They were able to ask questions freely and this really aided in
carrying out the project smoothly.
Furthermore, we have avoided a „convenience sample‟ in our survey. We did not survey
our friends but instead students who are younger than us. This means that their
opinions are different to ours, they are original and not biased. Hence there is a
possibility of generalising our results to a larger population.
We were very focused and managed our time well as we had fixed timelines to
complete each task. We abided by the timelines strictly and hence were able to
complete the project on time. Indeed we have developed good time management,
collaborative and communication skills through this project. We share information and
communicate effectively via the use of technology eg email, sms, video conferencing as
we are not able to meet frequently due to time constraints.
However, our project does have its weaknesses. The idea of giving snacks to the pupils
might not be welcomed by other teachers, MOE or even the parents. This is because, in
the name of achieving better learning, we are actually harming the students‟ health.
The small sample size of the participants (39) makes it difficult for us to generalise the
findings. We may need to do the project on a bigger scale with a bigger sample size and
more varied sample. For example, we can have students of differing ability and from
different schools.
According to Kate Nonesuch in her report „Changing the Way We Teach Math‟, when
she introduces a teaching strategy that is new to the class she will present it, giving her
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26. reasons for thinking it would be valuable. She would ask for their reactions, and then
propose that they try it out for a reasonable length of time and that they evaluate it
briefly at the end of the first week, and more thoroughly after the trial period. We could
have done the same but due to time constraint, we were unable to do it. This is another
weakness in our project.
As reflected, the weaknesses were mainly due to lack of resources especially time
resource which made it impossible for us to adopt a more rigorous and effective
methodology.
We see value in this project and strongly believe that more and similar projects in this
area should be explore. We strongly believe in the effectiveness of the modified
teaching approach and perhaps it should be extended on the teaching method for
English because, in Singapore, English is becoming Singlish and the standard of
English is getting worse due to SMS, which do not require proper English. Our project
could be carried out with different groups of students but one has to bear in mind that it
is the pupils‟ learning style should be taken into account.
We hope our project can bring about a paradigm change to the teaching method for any
subject because today‟s youth is tomorrow‟s future. The students will achieve better
performance if they can learn more effectively. We believe that our country‟s education
system can do much more to widen the students‟ knowledge and understanding and
bridge the learning gap between students.
Reflection
What factors contributed to the success of the project ?
- The modified teaching method was an effective teaching approach
- The slides were very impressive with detailed steps to aid pupils‟ understanding
- The vetted worksheets were well structured, with appropriate scaffolding
- Survey was conducted to validate the topics pupils found challenging
26 | P a g e
27. - Member were on task in setting the worksheets and PowerPoint slides and kept
to the time line
- Good team work and collaboration as everyone helped in the different tasks
- Samples provided by the leader helped members to create the worksheets
- Good guidance by LC leader
- Structured homogenous vetted PowerPoint slides and worksheets
- Teacher in-charge guided the team well
- Considerable amount of time was spent on AOC,RQ and CQ to ensure the team
was on the right track
What significant difficulties did you encounter and how did you
overcome them ?
- Time constraints in completing the project: Members communicated via email,
sms and MSN to send and share completed work assigned
- Looking for suitable questions for the worksheets: The team referred to questions
found in challenging assessment books and asked for guidance from Mdm Aisah
- Very weak pupils needed more time to benefit from the project: The project would
be continued by the teacher-in-charge as she had seen the benefit of using the
modified teaching method
How can we improve on the project?
- More challenging similar problem sums for further practice.
- Provide more examples and reinforcement worksheets for weaker pupils
- Make PowerPoint slides accessible to pupils.
- Make slides more attractive through animation
- Get pupils‟ feedback( after the project) from the students eg how the project had
helped them? What could help them even more?
27 | P a g e
28. - Put digital resources(the PowerPoint slides )on E-learning portal for students and
parents to make use of
How has your experience in the project helped you in your
professional development ?
- Able to teach complex word problems using model drawing more effectively
- Use technology effectively as a communication and presentation tool
- Develop better communication and collaborative skills
- Improvement in research skills
- Develop good team spirit
- More familiar with Learning Circle processes, especially AOC RQ etc
28 | P a g e
29. Bibliography (Chapter 5)
Dr Terry Bergeson. (2000) Teaching and Learning Mathematics. Retrieved March
26,2011,http://www.k12.wa.us/research/pubdocs/pdf/mathbook.pdf
Kate Nonesuch. (2006) Changing the Way We Teach Math. Retrieved April
5,2011,http://www.nald.ca/library/learning/mathman/mathman.pdf
Elizabeth Grace. (2010) Children and Problem Solving. Retrieved June 20,2011,
http://www.kidsdevelopment.co.uk/ChildrenAndProblemSolving.html
Jasmine Yin. (2005)Tears over tough Maths Exam. Retrieved July 10,2011,
http://sgforums.com/forums/8/topics/156216
Donald Deep. (1966) The Effect of an Individually Prescribed Instruction Program in
Arithmetic on Pupils with Different Ability Levels. Retrieved August
8,2011,http://www.eric.ed.gov/PDFS/ED010210.pdf
Sandra Z. Keith & Janis M. Cimperman (1992) The Hidden Script. Retrieved August
20,2011, http://www.tc3.edu/instruct/sbrown/math/faq.htm
Andrea Wiens. (2007) An Investigation into Careless Errors Made by 7th Grade
Mathematics Students. Retrieved August 20, 2011,
http://scimath.unl.edu/MIM/files/research/WeinsA.pdf
29 | P a g e
30. Appendices (Chapter 6)
Appendix 1 – Survey Questionnaires
Name(optional): ______________________
There are two sections in this survey. You are required to answer all the
questions in both sections truthfully.
Your answers will be kept confidential. The time spent in doing this survey is
greatly appreciated.
Background Information
Please circle the appropriate information
Gender: Male
Female
Race: Indian
Chinese
Malay
Others (please specify):___________
30 | P a g e
31. Results for previous Maths exam: 91 and above
75 - 90
60 – 74
50 – 59
35 – 49
20 – 34
33 and below
On the scale of 1-10, how difficult is Maths to you? (Please circle accordingly)
1 2 3 4 5 6 7 8 9 10
Least Difficult Most Difficult
Student’s Perception on Mathematics
There are 5 questions in this section. Please rank the answers from 1 to 4. 1
being the most appealing/preferred option and 4 being the least appealing/
preferred option.
1. Rank the topics below in the order of their difficulty. Beginning with 1 as the
easiest topic and 4 as the most difficult topic.
Percentage
Ratio
Fractions
Whole number
31 | P a g e
32. 2. Maths becomes difficult when
there are too many steps
the teacher is too fast
I’m not able to apply the concepts learnt
I don’t have enough practice
3. I usually lose marks in a Maths exam because
I am not able to solve the multi-steps word problems
I am not able to complete all the questions in time
I am too dependent on the use of calculator
I tend to make careless mistakes
4. I will be able to achieve better Maths results through
play e.g. Math card game
online learning
one-to-one tutoring
small group (of about 4-5 students) tutoring
32 | P a g e
33. 5. I will feel very motivated to learn Maths if
free snacks are provided during breaks
there is soft music at the background
token prizes are given for those who did well
there are frequent compliments given by the teacher
Thank you for your cooperation in completing the survey!
33 | P a g e
34. Appendix 2 – Transcript Of Interview
Transcript
Interviewee Mdm Aisah Osman
This is an interview we conducted with Mdm AIsah Osman, an
experienced Maths teacher with 25 years of experience in the
teaching upper primary Mathematics. This transcript of the interview
will provide a better idea on the current teaching methods in
Singapore, improvements that can be made to it and the interviewee’s
opinion of our project.
Transcript
Muthu:
What is your opinion on today‟s teaching Mathematics teaching method especially for
Primary-5 students?
Mdm Aisah:
I think that today‟s teaching method is effective in producing A-Star students, but that is
only if the learner is fast and good. As you already know, in the educational system in
Singapore, students are categorized according to their marks, and the good students
continuously get good marks while the poor students continuously get poor marks. That
is why, though we have students who get very high marks, we still have students who
get very poor marks and the mark range tends to be very vast. Hence, the teaching
method is good for producing good results from good students but not good in helping
the poor students to improve.
Muthu:
So how do you think we can improve today‟s teaching method then?
34 | P a g e
35. Mdm Aisah:
As I have said earlier, today‟s students are categorized according to their marks. Hence,
there is need for 2 different teaching methods to address the two groups of students.
We can continue with the current teaching method for the good students as it has
produced good results. However, for the weaker students we need have come out with
a more effective teaching method that suits them better.
Muthu:
How do you think we change the way these students teaching are taught?
Mdm Aisah:
The most effective way in my opinion is to drill them. Teach them in a structured manner
how to approach a question especially word problems and how to break down a
question into simpler steps. By doing this students will understand the problem better,
they can apply the concepts they have learnt and there would be an improvement in
their results. In my opinion, it all lies on the fundamentals, which include the method
they use to approach a question, and if their fundamentals are correct, they will be
good.
Muthu:
From your experience, which topics do you think P5 students find difficulty in?
Mdm Aisah:
Ratio and Percentage
Soorya:
Do you think that today‟s students are interested in the lesson?
Mdm Aisah:
35 | P a g e
36. Some of them are, but some of them are not. Hence, you must captivate them in a way
that everyone would become participative
Muthu:
What are some ways we can use to motivate students to do well in Mahtematics and to
be interested, more enthusiastic and participative in class?
Mdm Aisah:
Frequent compliments are good and giving them rewards works fine too
Haseef:
What do you think of our project? Is it realistic? Do you think there is a need for it?
Mdm Aisah:
I think it is an excellent idea as it will benefit students as well as improve the way they
are taught. It may even achieve better outcomes.
Soorya:
Our targeted participant in this project is the Primary-5 students. Do you think it is right
choice?
Mdm Aisah:
I think you should go ahead with the Primary-5 students as they are the ones who will
eventually sit for the PSLE. It is not so possible to conduct such sessions with the
Primary-6 students as it is too near to their PSLE and they need the time to revise. I
also think introducing this at the P5 level will be suitable as students need time to
assimilate and get used to a certain method.
Jackie:
Do you have any comments on our project?
36 | P a g e
37. Mdm Aisah:
I think that you should just focus on the more challenging topics like ratio and
percentage and focus on multi-steps word problems as students tend to lose a lot of
marks due to their inability to handle word problems. This would be beneficial for the
students as the improvement in marks would encourage and motivate them to do better.
If you just focus on the easy topics you might not see much difference in their marks.
Moreover, don‟t rush when going through with the class. Go slow and ensure that every
student grasps what is being taught.
37 | P a g e
38. Appendix 3 – Pre-Test & Post-Test
Pre-Test
P5 Mathematics
Name: ________________________( ) Score:________/25
Date: _______________
1. Box X and Box Y contained only oranges and apples. In Box X, the ratio of
the number of oranges to the number of apples is 8:9. There are equal
numbers of oranges and apples in Box Y. There are 40% more oranges in
Box Y than in Box X.
If 80 oranges are moved from box Y to Box X, they have an equal number of
oranges in both boxes. How many oranges and apples were in Box X at
first?
38 | P a g e
39. Answer: ________________ (5m)
2. The number of beads John has is 48 more than thrice that of Baba’s. The number
1
of beads Nurhan has is 24 more than 6 of John’s. Nurhan has 12 fewer beads
than Baba. What percentage of the beads does Baba have? Round off your
answer to two decimal places.
39 | P a g e
40. Answer: ____________(5m)
3. Mr Goh had a number of cookies for sale. He gave away 30 of his cookies.
In the morning, he sold 3/5 of the remaining cookies. In the afternoon, he
sold 80% of the cookies he had left. In the end, he was left with 1/20 of the
original amount of cookies. How many cookies did Mr Goh have at first?
40 | P a g e
41. Answer: ___________ (5m)
4. Abba, Browny and Christopher had a total of 630 cards at first. The ratio of
Browny’s cards to Christopher’s cards was 5 : 4. After Abba and Browny
each had lost 50% of their cards, the three girls had 395 marbles left. How
many marbles did Abba have at first?
Answer: ___________________ (5m)
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42. 5. Mdm Teow always spends a certain sum of her monthly salary and saves
the rest. When she increases her spending by 17%, her savings will be $349.
On the other hand, when she decreases her spending by 7%, her savings
will be $2485. What is Mdm Teow’s monthly salary?
Answer: ______________ (5m)
42 | P a g e
43. Pre-Test Answer Key
P5 Mathematics
1. Box X and Box Y contained only oranges and apples. In Box X, the ratio of
the number of oranges to the number of apples is 8:9. There are equal
numbers of oranges and apples in Box Y. There are 40% more oranges in
Box Y than in Box X.
If 80 oranges are moved from Box Y to Box X, they have an equal number of
oranges in both boxes. How many oranges and apples were in Box X at
first?
Box X
O:A
8:9
80 : 90
Box Y
O:A
1:1
20% 80 (1m)
100% 80 x 5 = 400 (1m)
8 units 400 (1m)
1 unit 400/8 = 50 (1m)
17 units 17 x 50 = 850 (A1)
43 | P a g e
44. Answer: 850 oranges and apples (5m)
2. The number of beads John has is 48 more than thrice that of Baba’s. The number
1
of beads Nurhan has is 24 more than 6 of John’s. Nurhan has 12 fewer beads
than Baba. What percentage of the beads does Baba have? Round off your
answer to two decimal places.
J
B
N
1
6 of 48 = 8
1u 8 + 24 + 12 = 44 (M1)
2u 44 x 2 = 88 (Baba) (M1)
264 + 48 = 312 (John) (M1)
88 – 12 = 76 (Nurhan) (M1)
Total 88 + 312 + 76 = 476
88/476 x 100% = 18.49% (A1)
44 | P a g e
45. Answer: 18.49% (5m)
3. Mr Goh had a number of cookies for sale. He gave away 30 of his cookies.
In the morning, he sold 3/5 of the remaining cookies. In the afternoon, he
sold 80% of the cookies he had left. In the end, he was left with 1/20 of the
original amount of cookies. How many cookies did Mr Goh have at first?
30
Sold in the morning Gave away
80%
Sold in the
Left(1/20)
afternoon
1/20 20%(of remainder)
5/20 100% (of remainder) (1m)
5/20 = ¼
2 units ¼ (1m)
1 unit 1/8
5 units 5/8 (1m)
3/8 30 (1m)
8/8 30/3 x 8 = 80 (A1)
Answer: 80 (5m)
45 | P a g e
46. 4. Abba, Browny and Christopher had a total of 630 cards at first. The ratio of
Browny’s cards to Christopher’s cards was 5 : 4. After Abba and Browny
each had lost 50% of their cards, the three girls had 395 marbles left. How
many marbles did Abba have at first?
Before After
B:C B:C
5:4 10 : 8
10 : 8
A + B + C = 630
½ A + ½ B + C = 395
A + B + 2C = 790 (1m)
790 – 630 = 160(C) (1m)
160/4 x 5 = 200 (B) (1m)
630 – 160 – 200 = 270 (1m, A1)
Answer: 270 (5m)
46 | P a g e
47. 5. Mdm Teow always spends a certain sum of her monthly salary and saves
the rest. When she increases her spending by 17%, her savings will be $349.
On the other hand, when she decreases her spending by 7%, her savings
will be $2485. What is Mdm Teow’s monthly salary?
17% + 7% = 24% (1m)
2485 – 349 = 2136 (1m)
24% 2136
1% 89
117% 89 x 117 = 10 413 (1m)
10 413 + 349 = 10 762 (1m A1)
OR
93% 89 x 93 = 8277
8277 + 2485 = 10 762 (1m A1)
Answer: $10 762 (5m)
47 | P a g e
48. Appendix 4 – Five Worksheets Using Modified Teaching Approach
Worksheet 1
P5 Mathematics
Name: ________________________( ) Score:________/14
Date: _______________
1. Ali and John have red and blue pens. The ratio of Ali’s red pens to blue pens
is 5: 4. Ali and John have an equal number of blue pens. Ali has 40 more red
pens than John. If John has a total of 140 pens, how many red pens does Ali
have?
Answer:__________________ (2m)
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49. 2. Bag A and Bag B contain hockey balls and golf balls. In Bag A, the ratio of
the number of hockey balls to the number of golf balls is 6: 4. There is an
equal number of golf balls in Bag A and Bag B. In Bag B, there are 10% less
hockey balls than golf balls. If there is a total of 200 balls in Bag A, how
many hockey balls are there in Bag B?
Answer:__________________ (3m)
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50. 3. Basket X and Basket Y had blue bottles and red bottles. In Basket X, the
ratio of the number of red bottles to the number of blue bottles was 5: 8.
There were an equal number of blue bottles in Basket X and Basket Y. There
were 260 bottles in Basket X.
If 40 red bottles were moved from Basket X to Basket Y, they would have an
equal number of red bottles. How many bottles were there in Basket Y at
first?
Answer:__________________ (4m)
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51. 4. Shop A and Shop B had tarts and cakes for sale. The ratio of the number of
tarts to the number of cakes in Shop A was 2: 5. There was an equal
number of tarts in Shop A and Shop B. There was 40% more cakes in Shop A
than in Shop B.
If 60 cakes were moved from Shop A to Shop B, there would be an equal
number of cakes. How many cakes and tarts were there in Shop B at first?
Answer:__________________ (5m)
51 | P a g e
52. Worksheet 1 Answer Key
P5 Mathematics
1. Ali and John have red and blue pens. The ratio of Ali’s red pens to blue pens
is 5:4. Ali and John have an equal number of blue pens. Ali has 40 more red
pens than John. If John has a total of 140 pens, how many red pens does Ali
have?
Ali John
R: B R: B
5:4 (5units - 40)? : 4
9u 140 + 40 = 180
1u 180/9 = 20 (1m)
5u 20 x 5=100 (red pens) ( A1)
Answer: 100 red pens (2m)
2. Bag A and Bag B contain hockey balls and golf balls. In Bag A, the ratio of
the number of hockey balls to the number of golf balls is 6:4. There is an
equal number of golf balls in Bag A and Bag B. In Bag B, there are 10% less
hockey balls than golf balls. If there is a total of 200 balls in Bag A, how
many hockey balls are there in Bag B?
Bag A Bag B
H:G H:G
6:4 ?:4
10 units 200 (1m)
1 unit 200/10 = 20
52 | P a g e
53. 4 units 20x4 = 80 (1m)
100% 80 (1m)
1% 80/100
90% 72 (A1)
Answer: 72 hockey balls (4m)
3. Basket X and Basket Y had blue bottles and red bottles. In Basket X, the
ratio of the number of red bottles to the number of blue bottles was 5:8.
There were an equal number of blue bottles in Basket X and Basket Y. There
were 260 bottles in Basket X.
If 40 red bottles were moved from Basket X to Basket Y, they would have an
equal number of red bottles. How many bottles were there in Basket Y at
first?
Basket X Basket Y
R:B R:B
5:8 ?:8
13units 260
1 unit 260/13 = 20
5 units 20 x 5 = 100 (1m)
100 – 80 = 20 (Red bottles in Y) (1m)
20 x 8 = 160
160 + 20 = 180 (A1)
OR
260 – 40 = 220 (1m)
220 – 40 = 180 (1m, A1)
Answer: 180 bottles (3m)
53 | P a g e
54. 4. Shop A and Shop B had tarts and cakes for sale. The ratio of the number of
tarts to the number of cakes in Shop A was 2:5. There was an equal number
of tarts in Shop A and Shop B. There was 20% more cakes in Shop A than in
Shop B.
If 60 cakes were moved from Shop A to Shop B, they would have an equal
number of cakes. How many cakes and tarts were in Shop B at first?
Shop A Shop B
T:C T:C
2:5(120%) 2: 100%
60 x 2 = 120
20% 120 (1m)
1% 120/20 = 6
100% 6 x 100 = 600 (1m)
120% 720
5 units 720
1 unit 720/5 = 144 (1m)
2 units 144 x 2 = 288 (number of tarts in shop B) (1m)
720 – 120 = 600 (number of cakes in shop B)
600 + 288 = 888 (A1)
Answer: 888 cakes and tarts (5m)
54 | P a g e
55. Worksheet 2
P5 Mathematics
Name: ________________________( ) Score:________/14
Date: _______________
1. The number of cards Ravi has is 80 more than thrice of Ellie’s. If Ellie has 21
cards, how many cards do they have altogether?
Answer:__________ (2m)
2. Roy has 15 less marbles than Bruno. The number of marbles Jason has is 25
more than thrice of Roy’s. If Bruno has 90 marbles, what fraction of the
total number of marbles does Jason have?
Answer:_____________ (3m)
55 | P a g e
56. 3. The number of pens Ali has is 16 more than 3 times of Barney’s. The
number of pens Chris has is 18 more than 1/4 of Ali’s. If Barney has 32
pens, what percentage of the total number of pens does Ali have?
Round off your answer to 2 decimal places.
Answer: ____________ (4m)
4. The number of beads Syafiq has is 72 more than thrice that of Muthu’s. The
1
number of beads Weng Fei has is 25 more than 6 of Syafiq’s. Weng Fei has
6 fewer beads than Muthu. What percentage of the beads does
Syafiq have? Round off your answer to two decimal places.
Answer: ____________ (5m)
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57. Worksheet 2 Answer Key
P5 Mathematics
Name: ________________________( ) Score:________/14
Date: _______________
1. The number of cards Ravi has is 80 more than thrice of Ellie. If Ellie has 21
cards, how many cards do they have altogether?
Ravi 80
Ellie
1 unit 21
4 units 21 x 4 = 84 (1m)
84 + 80 = 164 (Ravi + Ellie) (A1)
Answer: 164 cards (2m)
2. Roy has 15 less marbles than Bruno. The number of marbles Jason has is 54
more than thrice of Roy. If Bruno has 90 marbles, what fraction of the total
number of marbles does Jason have?
Jason 25
Roy
Bruno 15
57 | P a g e
58. 90 – 15 = 75 (Roy)
1 unit 75
3 units 75 x 3 = 225 (1m)
225 + 25 = 250 (Jason) (1m)
250 + 75 + 90 = 415(Jason + Roy + Bruno)
250/415 = 50/83 (A1)
Answer: 50/83 (3m)
3. The number of pens Ali has is 16 more than 3 times of Barney. The number
of pens Chris has is 18 more than 1/4 of Ali. If Barney has 32 pens, what is
the percentage of the total number of pens does Ali have? Round off your
answer to 2 decimal places.
16
Ali
Barney
18
Chris
1 unit 32/4 = 8
8 x 12 + 16 = 112 (Ali) (1m)
112/4 + 18 = 46 (Chris) (1m)
Total 112 + 46 + 32 = 190
112/190 x 100% ≈ 58.95% (1m, A1)
Answer: 58.95% (4m)
58 | P a g e
59. 4. The number of beads Syafiq has is 72 more than thrice that of Muthu. The
1
number of beads Weng Fei has is 25 more than 6 of Syafiq’s. Weng Fei has
6 fewer beads than Muthu. What percentage of the beads does
Syafiq have? Round off your answer to two decimal places.
Syafiq
25 8 25 8 25 8 72
Muthu 25 8
25
WF
3 units 165 (1m)
1 unit 165/3 = 55 (Syafiq)
6 units 55 x 6 = 330 (1m)
55 + 25 + 6 = 86 (Muthu)
55 + 25 = 80 (Weng Fei)
330 + 86 + 80 = 496 (Total) (1m)
330/496 x 100% ≈ 66.53% (1m A1)
Answer: 66.53% (5m)
59 | P a g e
60. Worksheet 3
P5 Mathematics
Name: ________________________( ) Score:________/20
Date: _______________
1. Mr Li has a few ice cream cones for sold. If he sold, 80% of his ice cream
cones, he would have 30 unsold ice cream cones. How many ice cream
cones does Mr Li have at first?
Answer:__________ (2m)
2. A cake shop has some cakes on sale. On Tuesday, 4/7 of cakes were sold.
On Wednesday, 3/5 of the remaining cakes were sold. If there were 18
cakes left, how many cakes were there at the start?
Answer: ___________ (4m)
60 | P a g e
61. 3. Jackie’s place had some pizzas. There were 10 Vegetarian pizzas. 2/5 of the
remaining pizzas were Hawaiian pizzas and the rest were BBQ pizzas. ½ of
the original number of pizzas was BBQ pizzas. How many pizzas were there
altogether?
Answer: ___________ (3m)
4. Mr Ng had a few bicycles for sale. He donated 25 bicycles to a charity. Then,
on Monday, he sold 7/14 of the remaining cookies. On Tuesday, he sold
50% of the cookies he had left. In the end, he was left with 1/5 of his
original amount of cookies. How many cookies did Mr Ng have at first?
Answer: ___________ (5m)
61 | P a g e
62. Worksheet 3 Answer Key
P5 Mathematics
Name: ________________________( ) Score:________/20
Date: _______________
1. Mr Li has a few ice cream cones for sold. If he sold, 80% of his ice cream
cones, he would have 30 unsold ice cream cones. How many ice cream
cones does Mr Li have at first?
80%
Left
(30)
100% - 80% = 20%
20% 30 (1m)
100% 30 x 5 = 150 (A1)
Answer: 150 ice cream cones (2m)
2. A cake shop has some cakes on sale. On Tuesday, 4/7 of cakes were sold.
On Wednesday, 3/5 of the remaining cakes were sold. If there were 18
cakes left, how many cakes were there at the start?
Morning
1 – 4/7 = 3/7 (1m)
100% - 60% = 40%
40% 18 (1m)
10% 4.5
100% 4.5 x 10 = 45
3 units 45 (1m)
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63. 1 unit 15
7 units 105 (A1) Answer: 105cakes (4m)
3. Jacks made some pizzas. 3/4of them were ham pizzas and the rest were
BBQ pizzas. After selling 40% of the BBQ pizzas and 5/6 of the ham pizzas,
she had 56 pizzas left. How many pizzas did he sell?
1 – 2/5 – 3/5 (1m)
1 unit 10
6 units 60 (1m, A1)
Answer: 60 pizzas sold (3m)
4. Mr Ng had a few bicycles for sale. He donated 24 bicycles to a charity. Then,
on Monday, he sold 2/5 of the remaining cookies. On Tuesday, he sold 40%
of the cookies he had left. In the end, he was left with 1/5 of his original
amount of cookies. How many cookies did Mr Ng have at first?
left
1 – 7/15 = 8/15 (1m)
8/15 ÷ 2 = 4/15
4/15 1 unit
12/15 3 units
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64. 12/15 – 7/15 = 5/15
5 units 25
15 units 75
25 + 75 = 100
OR
12 units + 8 units = 20 units
5 units 25
1 unit 5
20 units 100
Answer: 100 bicycles (5m)
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65. Worksheet 4
P5 Mathematics
Name: ________________________( ) Score:________/14
Date: _______________
1. John, Cristiano and Marcus had a total of 890 beads. The ratio of the
number of beads John has to the number of beads Cristiano has to the
number of beads Marcus has is 2 : 3 : 5. How many beads does Cristiano
have?
Answer: ___________ (2m)
2. Balvis and Ali had a few books in the ratio 3 : 5 respectively. After Balvis
gave away half of his books and Ali gave away 20% of his books, they have
924 books left in the end, how many books did Balvis have at first?
Answer: __________ (3m)
65 | P a g e
66. 3. Jesse, Hafiz and Kenny had a few marbles in the ratio 1 : 3 : 2. After Jesse
and Hafiz lost 18 marbles each, the ratio of the number of marbles Jesse
has to the number of marbles Hafiz has to the number of marbles Kenny
has became 2 : 7 : 5. How mny marbles did they have at first?
Answer: ____________ (4m)
4. Jim, Charlie and Ali had a total of 690 erasers. The ratio of the number of
erasers Charlie had to the number of erasers Ali had was 3:2. After Jim and
Charlie lost half of their erasers, they had a total of 400 erasers left. How
many erasers did Jim have at first?
Answers: ___________ (5m)
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67. Worksheet 4 Answer Key
P5 Mathematics
Name: ________________________( ) Score:________/14
Date: _______________
1. John, Cristiano and Marcus had a total of 623 beads. The ratio of the
number of beads John has to the number of beads Cristiano has to the
number of beads Marcus has is 2 : 3 : 2. How many beads does Cristiano
have?
7 units 623
1 unit 623/7 = 89 (1m)
3 units 89 x 3 = 267 (A1)
Answer: 267 beads (2m)
2. Balvis and Ali had a few books in the ratio 3 : 4 respectively. Then, Balvis
sold half of his books and Ali sold 20% of his books. The ratio of the number
of books Ali has to the number of books Balvis has then became 6:3. If
there were 918 books left in the end, how many books did Balvis have at
first?
Before After
B:A B:A
3:4 3:6
9 s units 918
1 s unit 918/9 = 102
6 s units 102 x 6 = 612 (1m)
6 small units = 4 big units
4 b units 612
1 b unit 612/4 = 153 (1m)
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68. 3 b unit 153 x 3 = 459 (A1)
Answer: 459 books (3m)
3. Jesse, Hafiz and Kenny had a few marbles in the ratio 1 : 3 : 2 respectively.
Jesse and Hafiz lost 18 marbles each. The ratio of the number of marbles
Jesse has to the number of marbles Hafiz has to the number of marbles
Kenny has became 2 : 7 : 5.
Before After
J:H:K J: H : K
1:9:2 2:7:5
3 units 18 (1m)
1 unit 18/3 = 6 (1m)
15 + 45 + 30 = 90
90 units 90 x 6 = 540 (1m, A1)
Answer: 540 marbles (4m)
4. Jim, Charlie and Ali had a total of 690 erasers. The ratio of the number of
erasers Charlie had to the number of erasers Ali had was 3:2. Jim and
Charlie lost half of their erasers. Then, they had a total of 400 erasers left.
How many erasers did Jim have at first?
J + C + A=690
½ J + ½ C + A=400
J + C + 2A=800
800-690=110(A)
110/2 x 3=165(C)
690-165-110=415(J)
Answers: 415 erasers (5m)
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69. Worksheet 5
P5 Mathematics
Name: ________________________( ) Score:________/14
Date: _______________
1. Mrs Tan baked some cakes for sale. After she sold 72% of the cakes, she had 84
cakes left. How many cakes did she bake?
Answer: _________ (2m)
2. Mr Sim used his $8 970 salary to pay for his new bedroom set and food and
saved the rest. The amount of money he spent on the bedroom set was 30%
more than on food and savings. If his expenditure on food was equal to his
savings, how much did Mr Tan pay for the bedroom set?
Answer: __________ (3m)
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70. 3. Darryl set aside a certain amount of money every month to pay for his hand
phone bills and food. If his hand phone bill increases by 1/3, he will have $44 to
pay for his food. However, if his phone bill decreases by 1/3, he will have $100
to pay for his food. How much money does Daryl set aside for his hand phone
bills and food?
Answer: __________ (4m)
4. Mr Lim spends a certain amount of his salary and saves the rest. If he increases
his expenditure by 7%, he can save $3 300. On the other hand, if he reduces his
expenditure by 4%, he can save $4 400. How much does he earn?
Answer: _________ (5m)
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71. Worksheet 5 Answer Key
P5 Mathematics
5. Mrs. Tan earns a certain amount of money. When she spends 72% of her salary,
the remaining amount she has is $644. How much does she earn?
72%
100% - 72% = 28%
28% 84
1% 84/28 = 3 (1m)
100% 3 x 100 = 300 (A1)
Answer: $300 (2m)
6. Mr Tan earns $8970 a month. His monthly salary is used only to pay the
wireless broadband plan, food and for savings. Mr Tan has to pay the wireless
broadband plan 30% more than his expenditure on food as well as his savings
combined. If his expenditure on food is equal to his savings, how much does Mr
Tan has to pay for the wireless broadband plan per month?
Food + Savings = 100%
WBP = 130%
230% $8970 (1m)
1% $8970/230 = $39 (1m)
130% $39 x 130 = $5070 (A1)
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72. Answer: $5070 (3m)
7. Darryl set aside a certain amount of money every month to pay for the phone
bills and food. If his phone bill increases by 1/3, he will have $44 to pay for his
food. However, if his phone bill decreases by ¼, he will have $100 to pay for his
food. How many marbles did Daryl have at first?
$44
$100
1/3 + 1/3 = 2/3
$100 – $44 = $56
2 units $56 (1m)
1 unit $56/2 = $28
3 units 3 x $28 = $84 (handphone) (1m)
$28 + $44 = $72 (food) (1m)
$72 + $84 = $156 (A1)
Answer: $156 (4m)
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73. 8. Mr Lim earns a certain amount of money. He spends a certain amount then
saves the rest. If he increases his expenditure by 7%, he will save $3 300. If he
reduces his expenditure by 4%, he will save $4 400. How much does he earn?
7% + 4% = 11%
$4400 - $3300 = $1100
11% $1100 (1m)
1% $1100/11 = $100
100% $100 x 100 = $10 000 (expenditure) (1m)
4% $100 X 4 = $400 (1m)
$4 400 - $400 = $4 000 (saving) (1m)
$4 000 + $ 10 000 = $14 000 (A1)
Answer: $14 000 (5m)
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74. Appendix 5 – Results of Students’ Survey
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75. Appendix 6 – Results of Pre-Test, Post-Test & 5 Worksheets
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