1. Raffles Institution Year Two Research Education Project Report 2011 Modifying The Method Of Teaching Word Problems ByTeam Leader : Muthu (18)Team Members : Soorya (24) : Mohamed Haseef Bin Mohamed Yunos (14) : Jackie Tan (26)Class : Secondary 2GTeacher-Mentor : Mrs. Suhaimy Raffles Institution Research Education 1|Page
2. Contents PAGE NUMBER1. Acknowledgements 42. Abstract(Overview of Project) 53. 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) 94. 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 2|Page
4. AcknowledgementsWe owe our special thanks to Mrs. Suhaimy, teacher of Raffles Institution, EnglishDepartment, Singapore, for her suggestion, valuable guidance, encouragement,sustained support and interest in the completion of this work. It was largely because ofher that our project was a success. She was able to see the loopholes in our project andthus, always guided us to the right path. Our thanks are due to her, for opening ourmind‟s eye into the avenues of research.We profoundly thank Mdm Aisah Bte Mohd Osman, an experienced Maths teacher forproviding the necessary information on the research topic and for kindly accepting ourquestions to her. She has been very co-operative with our team and was always thereto help us. Mdm Aisah also did a lot of very important favours such as guiding us in thedesigning 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 allyour help.Our thanks are rendered to our friends of Class 2G, Raffles Institution for their precioushelp 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 ourfamily members for without them, we would never have the spirit to continue this projecttill the end. They also have helped us in many other ways, especially by giving newideas to improve our project and spending their time and effort to guide us from the starttill the end.Last but not least, we would like to thank all those people and friends who have helpedus in one way or another. Although your names may not be mentioned here, we wouldjust like to say that we remember and appreciate all the help that you have given us inthe course of this project. 4|Page
5. Abstract (Overview of Project)The project aims to help upper Primary students, who have difficulties in solvingcomplex word problems, improve their level of proficiency by introducing a modifiedteaching method into the school curriculum. Through the interview and survey, the realreason 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 SemestralAssessment 1 in Mathematics were the participants in this project. They took part in asurvey 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 thatstudents face in Mathematics. From the survey and interview it was found that most ofthe students were not able to perform well in Mathematics because they were not ableto 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 .andtheir inability to complete the paper on time. Through the survey and interview the rootproblem and topics to focus on were identified.The team brainstormed for ideas on how to motivate and help pupils overcome thebarrier of solving multi-steps word problems. The team came out with the idea ofdesigning worksheets that break down word problems into simpler concepts. 5 suchworksheets were given to students with time frame to simulate exam conditions to helppupils manage time better. Finally, pre and post tests were given to examine the effecton the experiment. The results from the post-test revealed remarkable improvements. 5|Page
6. Introduction (Chapter 1)Singapore Primary School Education in the 21st centuryA child in Singapore undergoes six years of primary education, comprising a four-yearfoundation stage from Primary 1 to 4 and a two-year orientation stage from Primary 5 to6. At the foundation stage, the core curriculum comprising English, the Mother Tongueand Mathematics are taught, with supplementary subjects such as Music, Art & Craft,Physical Education and Social Studies. Science is included from Primary 3. Tomaximize their potential, students are streamed according to their learning ability beforeadvancing to the orientation stage. At the end of Primary 6, students sit for the PrimarySchool Leaving Examination (PSLE). It was noticed that students struggled during thePSLE examination and this was very disturbing. They were in need of help and thus,this project aims to help these students.DFC JourneyAfter watching the design for change video, the team was greatly inspired andmotivated to help the less fortunate or less intelligently inclined people. We felt that theyhad been suffering a lot. Unlike us, we have everything we want. In addition, we alsothought that if we as the younger generation do our part, what will the future generationbe? Thus, we wanted to do our part to help and contribute to the society.Research FindingsResearches have shown that Mathematics is the toughest subject that is tested inPSLE. The PSLE Maths exam has received complaints from students and even parentsthat the questions set are tough. For example, the 2005 PSLE Maths paper was set sohard that the pupils could not finish the paper on time and started crying over the marks 6|Page
7. lost. The questions set were not textbook oriented but more on the application ofconcepts learnt.Through intensive searches through the internet and through journals there were manyfactors that contributed towards students‟ inability to handle Mathematics paper atPSLE. From one of these searches, an interesting comment in CollegeNet forum wasfound. 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 ourown experiences, most teachers in Singapore teach a formula but do not explain theconcept behind the formula. Instead of exploring the derivation at that particular formula,teachers generally will go on to the practice questions immediately. It was discoveredthat the problem arises when the student does not understand the concept behind theformula.Doing a word problem correctly is an essential and important factor for a student‟ssuccess in Mathematics. The primary school Maths papers have a high percentage ofword problems ranging from 2 to 6 marks each. Therefore, if a student does not havethe ability to handle word problems correctly, there is a high probability that this studentwill 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 areextremely 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 areunable 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 combinedtogether and thus, the answers usually require many different steps. This wasmentioned by one of the researchers in Mathematics: 7|Page
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 andshould be dealt with quickly otherwise students will continue to struggle. A revolutionarymethod of teaching which is more effective than the standard method of teaching shouldbe 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 justdue 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 beavoided if the students check and backtrack their answers for accuracy. Furthermore,this quote also claims that students blame their intelligence or their carelessness formaking careless mistakes. However, if they take the extra effort to check their workthoroughly, 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 theirteachers and parents. However, the problem is that the teacher or parent does notexplain clearly to their child or student how to check their work. During a research doneby Wiens on careless mistakes, he stated that the students “didn‟t spend as much timereviewing their tests as I would like them to because they had never been taught how tocheck over their work; they thought they were doing what I was asking them to do justby looking over their test for neatness.” Hence, it is very important that the teacherguide the students in terms of explaining clearly how to check their work. 8|Page
9. HypothesisThe team believe that students will be able to answer Maths questions well if theyunderstand the concepts. To explore this believe, the question, “When does Mathsbecome difficult?” was included in the survey. As expected, majority of the pupilssurveyed 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 problemswhich require multi-steps answers that test different concepts if they are able to breakdown the problems into simpler steps.Research QuestionIn 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 downthe problems into basic steps that help scaffold students‟ understanding so thateventually 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 theteaching of multi-steps word problems. Through this project we hope students willdevelop better skills in problem solving and it will also help to build students‟ criticalthinking skills and a strong foundation in Mathematics. We also hope to enlightenteachers with an approach that could bring about better results in students‟ performance 9|Page
10. and motivate them towards the learning of Mathematics. Parents could also adopt thismethod to effectively guide and support their children in the area of problem solving. 10 | P a g e
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. 11 | P a g e
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 WeekWork 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 12 | P a g e
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 13 | P a g e
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. 14 | P a g e
15. Action WeekParticipants (Who is affected)The participants were 39 primary five students aged between 10 and 11 years. Thesestudents were chosen because of the mix ability nature of the group as theirMathematics 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 theiropinions on the method of teaching of Mathematics would be invaluable.InstrumentationA survey was designed to gather feedback on students‟ perception of Mathematics. Thekey elements in the survey include students‟ difficulties in Maths, the reasons for losingmarks 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 questionnairewas prepared to test its effectiveness. Appropriate transitions and section introductionswere also added. Prior to being finalized, the questionnaire was pre-tested on a smallnumber of respondents. These respondents were from Raffles Institution and throughthis survey pre-testing, we were able to ensure that our questions were easilyunderstood and straightforward. Through this survey, the group was able to identifytopics students are weak in and the reasons why they do not do well. These arefactored into the design of the project.We also interviewed an experienced Maths teacher, Mdm Aisah Bte Mohd Osman, whohas been teaching upper primary Mathematics for more than 25 years. She has vastand deep knowledge on the teaching of Mathematics in Primary schools. The questionswere designed based on the current method of teaching Mathematics, the type ofquestions teachers usually set in exam papers and students‟ ability in handling suchquestions. From the interview, the team triangulate on the topics to focus on and theapproach to be taken. 15 | P a g e
16. A pre-test and a post-test were used to measure the effectiveness of the methodadopted. The pre-test and the post-test were the exact worksheets made up of 5complex word problems on topics students‟ have difficulties in.The Modified Teaching MethodThe modified teaching method basically breaks down multi-steps or complex wordproblems into basic steps/concepts that help scaffold students‟ understanding so thateventually 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 studentshave difficulties in under exam condition prior to the implementation of the project. Themain aim of this pre-test is to gauge the students‟ ability in solving complex wordproblems before the implementation of the modified teaching approach. The pre-testwas 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 inevery worksheet is similar to one question in the pre-test worksheet. The first 3questions in all the five worksheet were scaffolding questions to help pupils break downthe fourth question into simpler steps and concepts. For example, if question1 of thepre-test tested the concept of changing fraction, balancing ratio and changingpercentage, then the worksheet 1 would have a question testing each concept and thelast question will be similar to the question 1 of the pre-test. Students were given onlyone 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 8and along with the teacher‟s help; we taught each group on how to avoid carelessmistakes and explain the concepts that the students were not very clear with as well asthe answers. This was to ensure that the pupils understand how to break the complexproblems into simpler steps and concepts. The splitting of the class enabled better 16 | P a g e
17. monitoring of the students‟ learning. We could focus on each student and hencemaximise learning.After students had completed the five worksheets, a post-test was administered. Thepost-test had exactly the same questions as the pre-test to ensure the validity andreliability of the instrument used to measure the effectiveness of the method. 17 | P a g e
18. Results (Chapter 3)Impact of ActionsAnalysis of SurveyFigure 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 foundratio the most difficult while 84.6% (33) of the students thought Percentage was themost difficult topic. Based on this data the team incorporated Percentage in all the 5worksheets that made used of the modified teaching method.Figure 1. The Difficult Topic In Maths. 18 | P a g e
19. Figure 2 reflects the reason why Maths is difficult to the students. 25.6% (10) of thestudents responded that they find Maths difficult when they did not have enoughpractice. 38.5% (15) of the students reflected that the difficulty in Maths is because ofmany 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 wasquite clear that they are not able to handle multi-steps word problems as they were notable 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 RespondentsFigure 2. Reasons For Difficulty In Maths 19 | P a g e
20. Figure 3 reflects the students‟ preference in the way Maths is taught. 12.8% (5) of thestudents 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 teamadopted 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 RespondentsFigure 3. Preference In The Way Taught 20 | P a g e
21. Figure 4 illustrates the motivational factor. 38.5% (15) of the students preferred snacksduring breaks, 17.9% (7) of them wanted soft music, 25.6% (10) of them wanted tokenprizes to be given to those who did well and 20.5%(8) needed frequent complimentsfrom the teacher. The team decided to reward students with snacks during their breaksso 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 RespondentsFigure 4. Motivational Factors 21 | P a g e
22. Analysis of Pre-Test & Post-Test ResultsFigure 5 displays the average marks scored by the students for the Pre-Test, the 5Worksheets and the Post-Test. The average marks of all the 5 worksheets are muchhigher than the average mark for the pre-test. This means that students are able tohandle complex word problems much better when they are broken down into simplesteps. Also, there is a remarkable improvement of the average marks from the pre-testto the post-test from 3.1 to 6.7 respectively. This is very significant considering theshort 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 0 t t 1 2 3 4 5 es es et et et et et T -T he he he he he e- st Pr ks ks ks ks ks Po or or or or or W W W W W Worksheet NameFigure 5. Average Marks for Pre-Test, 5 Worksheets and the Post-Test 22 | P a g e
23. The students were able to handle the complex word problems more effectively aftergoing through 5h of the modified teaching method. 87.2% of the students showedimprovement in the Post-Test. Figure 6 clearly displays the variation in marks betweenthe 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 39Figure 6. Pre-Test & Post-Test Results of 39 Pupils.Based of the above results it can be concluded that modified teaching method wherestudents were taught to break complex word problems into simple steps/concepts hascontributed significantly towards students‟ better achievements. 23 | P a g e
24. Discussion (Chapter 4)In today‟s world, Mathematics is one of the most important subjects one has to be goodin order to be marketable. Therefore, it is very disturbing when some of the primaryschool students are still performing badly in Mathematics. This is the main reason for ustaking up the challenge to introduce the modified teaching method to the 39 Primary fivestudents. Our main aim is that we hope through this project we are able to design achange to the current teaching method for Mathematics, and possibly other subjects aswell, to a better and more effective method of getting the concepts across to thestudents so that they can perform better in Maths.The results clearly indicated that our project is a success. After just 5 hourly session ofusing the modified teaching method, the students were able to show remarkableimprovements in their achievements score. 87.2% (34) students score higher marks inthe Post-Test than the Pre-Test. There are 3 pupils who even achieved full marks forthe 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 mostprobably need more time/ sessions to assimilate this form of learning.Students most likely find Percentage a difficult topic as students do not understand theconcept 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 thestudents were able to substitute fixed values in a percentage formula with values givenin the question. They were also trying their best to break the question down into smallerparts. As we invigilated them during the post-test, they were making attempts tounderline keywords and checking back the answers to avoid careless mistakes. Themarked improvement in the results of the post-test and their understanding of ourstrategy showed us how close we were to success.We also agree with „kids‟ development‟ website that „the basis of all future learning liesin the ability to break down a problem into manageable parts until a solution is 24 | P a g e
25. determined‟. We think it is a very useful strategy after having seen the results of usingthe strategy. It actually helps the student to analyse the question better and enablethem to understand it better because as they split a complex question into simpler partsthey 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 toa very productive learning process. The interaction between the students and us in thesmall group tutoring, enabled us to glean valuable insights about the students learningstyle and approach. They were able to ask questions freely and this really aided incarrying out the project smoothly.Furthermore, we have avoided a „convenience sample‟ in our survey. We did not surveyour friends but instead students who are younger than us. This means that theiropinions are different to ours, they are original and not biased. Hence there is apossibility of generalising our results to a larger population.We were very focused and managed our time well as we had fixed timelines tocomplete each task. We abided by the timelines strictly and hence were able tocomplete the project on time. Indeed we have developed good time management,collaborative and communication skills through this project. We share information andcommunicate effectively via the use of technology eg email, sms, video conferencing aswe are not able to meet frequently due to time constraints.However, our project does have its weaknesses. The idea of giving snacks to the pupilsmight not be welcomed by other teachers, MOE or even the parents. This is because, inthe 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 thefindings. We may need to do the project on a bigger scale with a bigger sample size andmore varied sample. For example, we can have students of differing ability and fromdifferent schools.According to Kate Nonesuch in her report „Changing the Way We Teach Math‟, whenshe introduces a teaching strategy that is new to the class she will present it, giving her 25 | P a g e
26. reasons for thinking it would be valuable. She would ask for their reactions, and thenpropose that they try it out for a reasonable length of time and that they evaluate itbriefly at the end of the first week, and more thoroughly after the trial period. We couldhave done the same but due to time constraint, we were unable to do it. This is anotherweakness in our project.As reflected, the weaknesses were mainly due to lack of resources especially timeresource which made it impossible for us to adopt a more rigorous and effectivemethodology.We see value in this project and strongly believe that more and similar projects in thisarea should be explore. We strongly believe in the effectiveness of the modifiedteaching approach and perhaps it should be extended on the teaching method forEnglish because, in Singapore, English is becoming Singlish and the standard ofEnglish is getting worse due to SMS, which do not require proper English. Our projectcould be carried out with different groups of students but one has to bear in mind that itis the pupils‟ learning style should be taken into account.We hope our project can bring about a paradigm change to the teaching method for anysubject because today‟s youth is tomorrow‟s future. The students will achieve betterperformance if they can learn more effectively. We believe that our country‟s educationsystem can do much more to widen the students‟ knowledge and understanding andbridge the learning gap between students.ReflectionWhat 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 trackWhat significant difficulties did you encounter and how did youovercome 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 methodHow 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 ofHow has your experience in the project helped you in yourprofessional 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 March26,2011,http://www.k12.wa.us/research/pubdocs/pdf/mathbook.pdfKate Nonesuch. (2006) Changing the Way We Teach Math. Retrieved April5,2011,http://www.nald.ca/library/learning/mathman/mathman.pdfElizabeth Grace. (2010) Children and Problem Solving. Retrieved June 20,2011,http://www.kidsdevelopment.co.uk/ChildrenAndProblemSolving.htmlJasmine Yin. (2005)Tears over tough Maths Exam. Retrieved July 10,2011,http://sgforums.com/forums/8/topics/156216Donald Deep. (1966) The Effect of an Individually Prescribed Instruction Program inArithmetic on Pupils with Different Ability Levels. Retrieved August8,2011,http://www.eric.ed.gov/PDFS/ED010210.pdfSandra Z. Keith & Janis M. Cimperman (1992) The Hidden Script. Retrieved August20,2011, http://www.tc3.edu/instruct/sbrown/math/faq.htmAndrea Wiens. (2007) An Investigation into Careless Errors Made by 7th GradeMathematics 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 QuestionnairesName(optional): ______________________There are two sections in this survey. You are required to answer all thequestions in both sections truthfully.Your answers will be kept confidential. The time spent in doing this survey isgreatly appreciated.Background InformationPlease circle the appropriate informationGender: Male FemaleRace: 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 belowOn the scale of 1-10, how difficult is Maths to you? (Please circle accordingly) 1 2 3 4 5 6 7 8 9 10Least Difficult Most DifficultStudent’s Perception on MathematicsThere are 5 questions in this section. Please rank the answers from 1 to 4. 1being 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 theeasiest topic and 4 as the most difficult topic.PercentageRatioFractionsWhole number 31 | P a g e
32. 2. Maths becomes difficult whenthere are too many stepsthe teacher is too fastI’m not able to apply the concepts learntI don’t have enough practice3. I usually lose marks in a Maths exam becauseI am not able to solve the multi-steps word problemsI am not able to complete all the questions in timeI am too dependent on the use of calculatorI tend to make careless mistakes4. I will be able to achieve better Maths results throughplay e.g. Math card gameonline learningone-to-one tutoringsmall group (of about 4-5 students) tutoring 32 | P a g e
33. 5. I will feel very motivated to learn Maths iffree snacks are provided during breaksthere is soft music at the backgroundtoken prizes are given for those who did wellthere 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 InterviewTranscriptInterviewee Mdm Aisah OsmanThis is an interview we conducted with Mdm AIsah Osman, anexperienced Maths teacher with 25 years of experience in theteaching upper primary Mathematics. This transcript of the interviewwill provide a better idea on the current teaching methods inSingapore, improvements that can be made to it and the interviewee’sopinion of our project. TranscriptMuthu:What is your opinion on today‟s teaching Mathematics teaching method especially forPrimary-5 students?Mdm Aisah:I think that today‟s teaching method is effective in producing A-Star students, but that isonly if the learner is fast and good. As you already know, in the educational system inSingapore, students are categorized according to their marks, and the good studentscontinuously get good marks while the poor students continuously get poor marks. Thatis why, though we have students who get very high marks, we still have students whoget very poor marks and the mark range tends to be very vast. Hence, the teachingmethod is good for producing good results from good students but not good in helpingthe 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 hasproduced good results. However, for the weaker students we need have come out witha 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 mannerhow to approach a question especially word problems and how to break down aquestion 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 intheir results. In my opinion, it all lies on the fundamentals, which include the methodthey use to approach a question, and if their fundamentals are correct, they will begood.Muthu:From your experience, which topics do you think P5 students find difficulty in?Mdm Aisah:Ratio and PercentageSoorya: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 waythat everyone would become participativeMuthu:What are some ways we can use to motivate students to do well in Mahtematics and tobe interested, more enthusiastic and participative in class?Mdm Aisah:Frequent compliments are good and giving them rewards works fine tooHaseef: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 theyare taught. It may even achieve better outcomes.Soorya:Our targeted participant in this project is the Primary-5 students. Do you think it is rightchoice?Mdm Aisah:I think you should go ahead with the Primary-5 students as they are the ones who willeventually sit for the PSLE. It is not so possible to conduct such sessions with thePrimary-6 students as it is too near to their PSLE and they need the time to revise. Ialso think introducing this at the P5 level will be suitable as students need time toassimilate 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 andpercentage and focus on multi-steps word problems as students tend to lose a lot ofmarks due to their inability to handle word problems. This would be beneficial for thestudents 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 everystudent grasps what is being taught. 37 | P a g e
38. Appendix 3 – Pre-Test & Post-Test Pre-Test P5 MathematicsName: ________________________( ) Score:________/25Date: _______________ 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) 41 | P a g e
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 Mathematics1. 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) afternoon1/20 20%(of remainder)5/20 100% (of remainder) (1m)5/20 = ¼2 units ¼ (1m)1 unit 1/85 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 MathematicsName: ________________________( ) Score:________/14Date: _______________ 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) 48 | P a g e
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) 49 | P a g e
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) 50 | P a g e
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 Mathematics1. 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 MathematicsName: ________________________( ) Score:________/14Date: _______________ 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) 56 | P a g e
57. Worksheet 2 Answer Key P5 MathematicsName: ________________________( ) Score:________/14Date: _______________ 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 MathematicsName: ________________________( ) Score:________/20Date: _______________ 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 MathematicsName: ________________________( ) Score:________/20Date: _______________ 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) 62 | P a g e
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 63 | P a g e
64. 12/15 – 7/15 = 5/155 units 2515 units 7525 + 75 = 100OR12 units + 8 units = 20 units5 units 251 unit 520 units 100 Answer: 100 bicycles (5m) 64 | P a g e
65. Worksheet 4 P5 MathematicsName: ________________________( ) Score:________/14Date: _______________ 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) 66 | P a g e
67. Worksheet 4 Answer Key P5 MathematicsName: ________________________( ) Score:________/14Date: _______________ 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) 67 | P a g e
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) 68 | P a g e
69. Worksheet 5 P5 MathematicsName: ________________________( ) Score:________/14Date: _______________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) 69 | P a g e
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) 70 | P a g e
71. Worksheet 5 Answer Key P5 Mathematics5. 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% 841% 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) 71 | P a g e
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 $1001/3 + 1/3 = 2/3$100 – $44 = $562 units $56 (1m)1 unit $56/2 = $283 units 3 x $28 = $84 (handphone) (1m)$28 + $44 = $72 (food) (1m)$72 + $84 = $156 (A1) Answer: $156 (4m) 72 | P a g e
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) 73 | P a g e
74. Appendix 5 – Results of Students’ Survey 74 | P a g e
75. Appendix 6 – Results of Pre-Test, Post-Test & 5 Worksheets 75 | P a g e
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