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    Mathematics in Everyday Life

    Siv DomeijKerstin DomeijChristina Lind

    Komvux, rnskldsvik Sweden

    Can the use of hands-on exercises from situations ineveryday life affect the students attitude to

    mathematics?

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    Foreword

    Thank you to- our students on mathematics course A at Komvux Open Learning Centre whoresponded to our questionnaires and worked with our laborative boxes. Special thanks to

    those who allowed themselves to be interviewed and open-heartedly shared with us theirexperiences of studying mathematics.- our tutor at the Department of Education at Ume University, Chatrine Johansson andLena lander, who guided us through organisational strategies and report writing.- Lena Bostrm who helped us with the section on learning styles and also shared herexperience as a researcher with us.- Barbro Grevholm who helped us to find literature and encouraged us in our work.- Kunskapslyftet which contributed to the financing.

    rnskldsvik January 2002

    - English at work, Cathrine Sjdin, who helped us with the English version of the report.

    rnskldsvik April 2003

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    CONTENTS

    INTRODUCTION ..................................................................................................4

    AIM..........................................................................................................................5

    TARGET GROUP ..................................................................................................6

    PARTICIPANTS ....................................................................................................6

    ENVIRONMENT ...................................................................................................6

    IMPLEMENTATIONBackground...................................................................................................7Students attitudes to mathematics at the beginning of the course...............7Hands-on boxes.........................................................................................8

    Miscellaneous ...............................................................................................8

    RESULTS/ANALYSISAttitudes to mathematics at the beginning of the course..............................9Reasons for a negative attitude ..................................................................10Attitudes to mathematics after the course...................................................11Evaluation of hands-on boxes in a big group..........................................11

    DISCUSSION

    Result..........................................................................................................13Looking into the future...............................................................................13

    REFERENCES .....................................................................................................14

    APPENDICESQuestionnaire..............................................................................................15Hands-on boxes.......................................................................................17

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    Mathematics in everyday life

    Siv DomeijKerstin Domeij

    Christina LindKomvux, rnskldsvik Sweden

    Can the use of hands-on exercises from situations in everyday life affect the

    students attitude to mathematics?

    INTRODUCTION

    For some years we have offered mathematics courses at an Open Learning Centre. Thismeans that the students work individually, following their own plan. They can start at anytime during the term and they decide themselves how long they will study and thenumber of lessons per week. We find support for this form of working in theGovernments bill on adult learning and the development of adult education:The government believes that adult education must be based on the needs andconditions of the individual and must therefore be carried out with great flexibility.(Information sheet p. 3, Utbildningsdepartementet, U01.003February 2001)

    The syllabus also describes a more individual approach:In their teaching of mathematics, schools must strive to enable the students to:- develop confidence in their own ability to learn more mathematics, to think

    mathematically and to use mathematics in different situations.- develop the ability to reflect on their experience of concepts and methods inmathematics and their own mathematical activities.

    (www3.skolverket.se/skolverket.se/kursinfo/00_01/skolform/21/amne/urskr/_MA.html )

    In your work as a teacher of mathematics you meet students with different attitudes to thesubject of mathematics. Brandell & Wallin write:The study of mathematics is an area full of emotions with reactions which can vary from

    easy and fun to boring and difficult and even incomprehensible andmeaningless (Brandell,Wallin: Nmnaren 1998:2 sid. 3)

    A negative attitude to mathematics is something we have witnessed too. We have alsonoticed that the students have problems relating school mathematics to reality. There area number of earlier studies concerning this subject e.g. Boaler who writesA great number of studies have shown that many students cannot use their schoolmathematics in unknown situations outside school

    (Boaler (bearb. Emanuelsson): Nmnaren 1997:3 p. 16)

    In a study from Singapore you can readStudentst in school must see how mathematics can be used in real situations. We mustencourage their ability to avoid working superficially with the information in the maths

    problem.

    (Foong Pui Yee & Koay Phong Lee (vers. redakt.): Nmnaren 1998:4 p. 10-11)

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    In this study you can also readMany of the problems in school textbooks are unrealistic. These problems probably do

    not motivate the students to solve problems; they only emphasize the students opinionthat mathematics has nothing to do with real life. In order to change this opinion we mustemphasize even more the connection between mathematics in school and the world

    around.

    In our teaching we also meet many people with dyslexia. The way in which mathematicalproblems are presented is very important to them.The presentation of mathematical items should be done in a manner which allows

    different forms of presentation. Students should be more actively involved in the learningprocess, for example through experiments and group cooperation

    (Malmer: Nmnaren 1996:4 p. 37)

    Lately the concept of learning styles has been in focus in the classroom situation. Theconnection between the study of mathematics and learning styles is far too big a subject

    to explore in depth within this project, but the following short presentation of thesedifferent styles is given as a brief introduction.Visual people: They can remember best what they see. For some it could be in the formof a text or, for others, a picture. The information is then turned into their own notes orpictures.Auditive people: Listeners who prefer oral instructions. They also want to discuss andthrough dialogue reinforce their knowledge.Kinaesthetic people: They prefer to learn through practical activity which they developthrough emotions and physical activityTactile people: They want to work manually, often with fine motor skills, when they arelearning.

    This section concerning learning styles is summarized from Bostrm: Frn undervisningtill lrande (Bostrm 1998)In this study the following is also pointed out:another basic idea with learning styles is that the students themselves ask questionsand search for answers and thereby also decide the way they want to work with different

    problems. (the above book, p. 78)The traditional methods of learning, visual and auditive learning are not very effective.

    Discussing, learning by doing and teaching others, so that you immediately transfer what

    you have learnt, results in the best retention of knowledge and definitely not lectures.(Bostrm 1998 p. 78 -79)

    Against a background of the points mentioned above we have felt it necessary tosupplement our teaching of mathematics with other methods than just traditional textbookstudies. To make our teaching closer to real life we have tried to devise experimentaltasks. To make them suit the Open Learning Centre they consist of hands-on boxeswith all instructions and materials included.

    AIM

    In our project we want to examine the attitude to mathematics of the students on the

    mathematics A course when they begin their studies at Komvux, a municipal college offurther education.

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    We clarify our aim through the following questions:- Can we make students more motivated to use mathematics in everyday life?- Can we increase their understanding of mathematical problem solving?- Can we do this by using tasks from everyday life in which the students themselves haveto look for facts and use hands-on material which are connected to real life situations?

    - Can we change the students negative attitude towards mathematics by introducing it inanother way?First we want to give initial questionnaires to all our students and then, based on theirresponses, select some people for interview in order to follow their attitudes tomathematics before, during and after the course.

    TARGET GROUP

    During the year 2001 we had about 200 students altogether at Komvuxs Open LearningCentre for mathematics. Age and sex can be seen in figure 1 below. The project included

    the students who started their studies at the beginning of January and September 2001,approx. 100 people.

    Members of the group

    0

    10

    20

    30

    40

    50

    -21 22-31 32-41 42-51 52-

    Age (Years)

    Number

    Men

    Women

    Figure 1. Members of the group

    PARTICIPANTS

    Those who carried out the project work as teachers at the Mathematics Open LearningCentre at Komvux in rnskldsvik, Sweden. Our names are Christina Lind, KerstinDomeij and Siv Domeij. We are all highly qualified teachers of natural science andmathematics. Furthermore, each of us has approx. 30 years experience of teachingmathematics and science, mostly chemistry and biology. This experience is fromdifferent levels of the school system.

    ENVIRONMENT

    The project has been carried out in rnskldsvik, a municipality with 56 000 inhabitants.The towns commercial life is dominated by industry comprising both big and small

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    companies. Komvux is a college with many different fields of activity: Swedish forimmigrants, education for people with dyslexia, courses at compulsory and upper-secondary level (general subjects and nursing). The number of students is approx. 2000 inall and there are approx 100 teachers and administrative staff. Last year numbers declinedconsiderably.

    The Mathematics Open Learning Centre offers the upper secondary courses A, B and C.The number of students during the spring term 2001 was approx. 220 people working onapprox. 260 courses, and during the autumn term 2001 approx. 180 persons on 220courses. Four teachers shared 3,3 (respectively 3,1) teaching posts. Each student isallocated a teacher who is responsible for help with planning of studies, tests and marks.New students can begin studying each week and they make an individual timetable fortheir studies (i.e. they plan how many courses per term, how many weeks they will studyand how many lessons per week). A teacher is available 18,5 hours per week. One to fourteachers are on duty at any one time depending on how many students have planned tocome. Times for tests are provided three times a week. Depending on the pace of studythe student can choose how many tests they want to have during the course. If there are

    enough students working on the same point, it is possible to bring them together forexplanatory lessons. Otherwise brief guidance is given at the students desks, eitherindividually or in small groups.

    IMPLEMENTATION

    Background

    Those of us who have worked with the project all have many years of experience ofteaching both in mathematics and science (chemistry and biology). In science there are

    practical experiments; Why not in mathematics as well? We had already tried suchpractical work on a small scale, but then in groups in which everyone worked with thesame task at the same time. When we learned that the organization Kunskapslyftetoffered funding for research in your own classroom we saw an opportunity to increaseand structure this experimental way of working in mathematics, and adjust it to suit theOpen Learning Centre. Through this we wanted to examine if we could change thenegative attitude towards mathematics, which we sensed that many of our students had.Our application for funding was granted and we were granted 40% of a teaching post fortwo terms.

    Students attitudes towards mathematics at the beginning of the course.

    We started with a questionnaire in order to examine the attitude towards mathematicsamong our students (Appendix 1). We asked them what thoughts, feelings andassociations they had when they heard the word mathematics. On a six-point scale theyestimated if mathematics was Difficult Easy, Threatening Fun, and A lot offigures all over the place Logical. It was also possible for them to make their owncomments. We also asked which course they had studied at the senior level of the nine-year compulsory school, as well as their grades and attitude from that time. Then weasked them why they wanted to study mathematics now. The alternatives were: Toimprove an earlier grade, to acquire a qualification for higher education, to fill up the

    timetable to get enough points enough for the study grant , interest in mathematics,need to improve mathematical skills. The last question dealt with their use of

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    mathematics in everyday life. From the questionnaire we selected six students with anegative attitude towards mathematics. They were interviewed at the beginning and alsolater at the end of the course. The interviews at the beginning were based on the answersfrom the questionnaire. Questions were asked to clarify the mostly very short answersgiven in the questionnaire. The students responses were noted down and these notes

    were shown to the students.

    Hands-on boxes

    Meanwhile we also made hands-on boxes with practical, everyday, mathematical tasks.We already had some ideas for tasks, but during the work many new ideas arose out ofeveryday situations. Some ideas also grew out of studies of literature and study-visits. Wefound material for the boxes at home, in newspapers, in weekly advertising leaflets fromshops in the neighbourhood and in recycling-bins. We have also purchased some goodsspecially for the boxes, mostly in second-hand shops. The boxes themselves are fromcopying paper carton lids from college. The practical tasks were of different degrees of

    difficulty, as marked on the box, and dealt with different aspects of the mathematics Acourse. Here we simply make a short presentation of some of them. A wider range isincluded in appendix 2.Numeric calculation: Whats the price of a glass of squash? In the box you find an emptybottle of squash on which you can read the volume, how much water you should add, andthe price. The volume of the glass can be measured with a measuring glass or a ruler (andthen calculated)Percentage: Comparison of the same goods in different sized packaging. This can be donewith two bottles of shower gel, a small one with a volume of 250 ml and another of 400ml and the text Now 60% bigger. Is the text correct? The big bottle has no price. Whatwould be a reasonable price for it? A further question can be asked, since there was a

    temporary discount offer on the smaller bottle. How many per cent discount will you getwhen using the coupon?Geometry in combination with large and small numbers: The dripping tap. Calculate theprice of the water-leak for a year. You can use a graduated measure, a watch and a bill fordomestic water.Functions: Car-rental contract. With a Moroccan car-rental contract, (written in Arabic,German, French and English, which was appreciated by many of our immigrants withArabic as a native language), decide what alternative is best if you want to rent a car forthree days. You must decide yourself on a reasonable mileage. The task must bepresented as a graph and the cost calculated in SEK based on a given exchange rate.The students were encouraged to work with the boxes alongside the same point in theirbooks. We collected running evaluations from our students in the form of a questionnairein which we asked what they thought of this way of working, the tasks and if theirunderstanding of maths had been affected by working with the boxes. It was possible forthem to give supporting evidence and also propose improvements.

    Miscellaneous

    The work with the report began. We read some literature to find support for our theories.We also made a study visit to Paris where we visited, for example, the museum Cit desSciences et de lIndustrie. During the autumn term 2001 we continued our studies, with

    questionnaires, interviews with six new students and work with new hands-on boxes.To emphasize the importance of the practical work we introduced as an obligatory task

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    for all our students on the mathematics A course at the Open Learning Centre the handingin of solutions to three boxes.

    RESULTS/ ANALYSIS

    Attitudes to mathematics at the beginning of the course

    The result of the initial questionnaire is shown as a diagram and a choice of comments.

    Associations with mathematics

    0

    5

    10

    15

    20

    25

    30

    1 2 3 4 5 6

    Difficult Easy

    Percent(%)

    Figure2. Associations with the word mathematics before studies in mathematics A(n=104)

    In response to the question whether mathematics is difficult or easy approx. 60% of the

    answers were on the difficult side. Only a few comments were made in respect to thisquestion but, as an example, the following comment can be given:Hate maths because it is difficult

    Associations with mathematics

    0

    5

    10

    15

    20

    25

    30

    35

    40

    1 2 3 4 5 6

    Threatening Fun

    Perc

    ent(%)

    Figure3. Associations with the word mathematics before studies in mathematics A(n=104)As to whether mathematics is threatening or fun approx. 36% were on thethreatening side and, of these, 6% expressed the most negative alternative. In addition,

    these negative comments were made:

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    Get frightened when I simply hear the word maths, and get a blockage when I mustsolve certain tasks.

    Worst thing I knew. Almost got pain in my stomach from thinking about itGet a blockage just by seeing a task with text.Among the positive comments can be mentioned:

    Have always thought maths is fun and interesting. A challenge to find solutions.Mathematics is fun if you can do it and understand it.

    Associations with mathematics

    0

    510

    15

    20

    25

    30

    35

    1 2 3 4 5 6

    "Figures all over the place" Logical

    Percent(%)

    Figure 4. Associations with the word mathematics before studies in mathematics A(n=104)

    In response to the third question concerning whether mathematics was a lot of figures allover the place or logical approx. 37% thought that they had not seen any logic inmathematics. The comments were few.

    Reasons for a negative attitude

    Attitudes from compulsory school were in many cases negative. Unfortunately, it isimpossible to say how large a percentage, as not everyone had made comments. Thefollowing negative comments can be mentioned:Boring and difficult! Always heard how poor I was at Maths.

    The most boring, worst subject of all.The worst thing that existed.

    Something you had to endure.Tough and difficult.I did not care a bit about maths then because I had a bad teacher.

    There were also positive comments:It was fun and something of a challenge to solve.

    One of the most pleasant subjects.Had a bit of a problem with it at the beginning, but then I loved it.

    By analysing the answers given in the interviews we have been able to conclude that thegreatest cause of problems concerning the attitude to mathematics comes from things thathave happened during the students compulsory education. It has been impossible for thestudent to keep up with the tempo of the class and then they have lost track of the subject.

    Catching up again has been a problem. It has been impossible for the teacher with a biggroup to help them catch up. The students have then lost interest and ended up in a

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    negative spiral. The problems of those with dyslexia have been particularly pronouncedwhen there have been more tasks involving a text. Most of those interviewed have hadproblems with mathematics but have managed better in other subjects. After compulsoryschool they have chosen an education without, or with as little mathematics as possible.Also at work and in private life they have avoided situations in which they have to

    calculate. The results from the questionnaire and the interviews support our theory thatthere is an extensive, negative attitude to mathematics.

    Attitudes to mathematics after the course

    At the interviews at the end of the course we found that attitudes to mathematics hadchanged. Now many students said that they dared to approach the problems and they feltusing mathematics was necessary. Among the reasons for the change of attitude tomathematics, most of the students mentioned that they now felt much more motivated tostudy than during their time at compulsory school. They also said that working at onesown pace was favourable since they avoided stress and comparison with others. This has

    resulted in more self-confidence and mathematics has felt more fun. The practical tasks inthe hands-on boxes have contributed to better understanding and it has been a positiveexperience to recognize problems from real life. For one of the students who had a verydominant tactile learning style the work with the boxes was good, as she could touch thematerial and use more senses than she could when just reading a book.

    Evaluation of the hands-on boxes in a big group

    As we introduced the solving of three boxes as a compulsory item for all students ofmathematics A, we also carried out an evaluation of them.

    What do you think about this way

    of working?

    0

    10

    20

    30

    40

    50

    60

    1 2 3 4 5 6

    Very bad Very good

    Percent(%)

    Figure 5. Evaluation of hands-on boxes - way of working

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    What do you think about the task?

    0

    10

    20

    30

    40

    50

    60

    1 2 3 4 5 6

    Very bad Very good

    Percent(%)

    Figure 6. Evaluation of hands-on boxes - the task.

    Do you feel that your

    understanding of matematics has

    increased?

    0

    10

    20

    30

    40

    50

    60

    1 2 3 4 5 6

    Not at all To a great extent

    Percent(%)

    Figure 7. Evaluation of hands-on boxes - understanding.

    From this evaluation we can see that the way of working and the task got very highmarks from the students. Understanding did not increase to the same extent, but wasmostly on the positive side. In our evaluation we have not separated the different tasks, asno tendency to differ could be noticed. Some comments:It is fun to count something real.

    You experience maths more naturally and appreciate what help it gives.Good not to have a key. You have to think a little extra.If you have avoided maths during compulsory school it is difficult to have enough time

    for all the tasks in the book and then for the boxes too.Personally, I need someone to remind me of the tasks, since I dont give myself time. My

    aim all the time is to hurry on to the next chapter. What a pity!

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    DISCUSSION

    Result

    The negative attitude seen in many of our students at the beginning of the course has

    changed and become more positive. A variety of reasons can be given for this. One of thereasons has been their work with the practical boxes. The solutions to the hands-onboxes have been clear and well structured, considerably better than to those tasks in themaths textbook. As there were no keys to the practical tasks the students had to reflectand estimate if the answers were reasonable. Hopefully our students have become moreaware as consumers because a lot of discussions around best buys have taken place.Other reasons, which have affected their attitudes to mathematics, have been that theyhave now had the opportunity to work at their own pace and they have been moremotivated to study in general.We have not tried to examine which of these factors has been the most important, since itprobably varies from one individual to the next. The main point is, nevertheless, that their

    attitude towards mathematics has improved.Working with the project has also affected us as teachers. We have become even moreaware of the anxiety for mathematics which many people feel. Our awareness of theimportance of introducing mathematics in a practical way has increased. It has alsobecome obvious to us how important it is to reflect on your own daily work anddocument it.

    Looking into the future

    As an extension of the project it would be desirable to systemize the practical tasks andtry to cover the whole course. A plan of where you find the corresponding items in the

    maths book would also be of great value. Then it would be easier for the students tochoose either the box or the book. Otherwise the workload could be too heavy for them.Another extension of the project is to work out practical tasks for the more theoreticalcourses B and C.However, the very best point to work on is a change of teaching methods in compulsoryschool so that attitudes to mathematics never need to be so negative.

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    References

    Utbildningsdepartementet: Faktablad U01.003februari 2001

    Skolverket: Kursplan Matematik A (SKOLFS 2000:5)

    Brandell & Wallin: Frn elit till massutbildning. Nmnaren 1998:2

    Boaler (bearbetn. Emanuelsson): Projektorientering ger bttre resultat.Nmnaren 1997:3

    Foong Pui Yee & Koany Phong Lee (vers. redaktionen): Problem medverklighet i skolan. Nmnaren 1998:4

    Malmer, G: Matematiksvrigheter och dyslexi - ett frsummat samband.Nmnaren 1996:4

    Bostrm, L (1998): Frn undervisning till lrande (Brain Books)

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    Appendix 1: Enkt (Questionnaire)

    Namn: (Name)______________________________

    Vi genomfr en kompetensutveckling i samarbete med Pedagogiska institutionen, Umeuniversitet och Kunskapslyftet. Vi ska under vrterminen bygga upp ett sjlvinst ruerandematerial som ni ska kunna anvnda fr att ka er matematiska frstelse. Det skainnehlla laborativa uppgifter och vardagliga matematiska problem. Ni kommer att futfra en del av dessa uppgifter under vren. Vi vill underska om dessa uppgifter harvarit till ngon hjlp fr din inlrning och drfr kommer vi att intervjua ngra av ersenare under terminen.

    Vi vill att du besvarar dessa frgor s att vi fr veta lite om din instllning till matematikinnan du brjade lsa matematik hr p komvux.

    (We are carrying out a research project in cooperation with the Department of Educationat the University of Ume and Kunskapslyftet. During the spring term we will deviseself instructional materials, which you can use to improve your mathematicalunderstanding. They will consist of practical tasks and mathematical problems fromeveryday life. You will carry out some of these tasks during the spring. We intend toexamine if these tasks have been of some help to you in your learning and therefore wewill interview some of you later during the term.

    We want you to answer these questions in order to let us know a little about yourattitudes to mathematics before you began to study mathematics at Komvux.

    1. Vilka tankar, knslor, associationer fick du nr du hrde ordet matematik? Kryssai lmplig ruta. (What thoughts, emotions, and associations did you have whenyou heard the word mathematics? Tick the appropriate box)

    1 2 3 4 5 6

    Svrt Ltt(Difficult) (Easy)

    Farligt Roligt(Threatening) (Fun)En massa siffror Logiskthit och dit(A lot of numbers (Logical)all over the place)

    Egna kommentarer: (Own comments:)_______________________________

    ______________________________________________________________

    ______________________________________________________________

    ______________________________________________________________

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    2. a) Lste du allmn eller srskild kurs p hgstadiet? (Did you study the

    general or advanced course at compulsory school?)_____________________

    b) Vilket betyg hade du?(What grade did you get?)_____________________

    c) Nr gick du ut nian? (When did you leave compulsory school?) _________

    d) Hur var din instllning till matematik under grundskoletiden? (What was

    your attitude to mathematics during compulsory school?)________________

    ______________________________________________________________

    3. Varfr valde du att lsa matematik? Kryssa i lmplig(a) ruta(or).( Why haveyou now chosen to study mathematics? Tick the appropriate box.)

    Fr att hja tidigare betyg (To improve a former grade)

    Fr att f full CSN-pong (To get the full CSN-grant) Behrighet till hgskola (Qualification for higher education) Verkar vara ett intressant mne (Seems to be an interesting

    subject) Knner behov att frbttra kunskaper i matematik (Feel the

    need to improve my knowledge of mathematics) Annat (Other) ____________________________________________

    4. Hur nskar du att matematikundervisningen skall vara upplagd? ( How

    would you like mathematics studies to be presented?)_________________________________________________________________________________

    ______________________________________________________________

    5. Hur anvnder du matematik i din vardag ? (How do you use mathematics in

    your daily life?) _________________________________________________

    ______________________________________________________________

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    Appendix 2: Examples of boxes

    The price of beauty Mathematics A:Numeric calculations

    Calculate the price per litre of the products.

    (Contents: Price-marked packaging from various perfumes, after-shaves, and nailpolish.)

    Shampoo Mathematics ANumeric calculation

    Calculate the price per litre of shampoos of different brands and the same brand but withpackaging of different sizes.Discuss your result!(Contents: Price-marked packaging from various shampoos)

    Soap Mathematics A

    Numeric calculationWhich soap is the best buy?Discuss your result!(Contents: Price-marked soap packaging. The packaging contains bars of varying

    number and size)

    Washing detergent Mathematics ANumeric calculation

    1. How much cheaper will it be if you buy one 1-litre bottle of Yes compared with two-litre bottles?2. Calculate the price per litre of different washing detergents. Which one is cheapest?(Contents: 1-litre and litre bottles of Yes. Other packaging from washing detergent. Allmarked with prices.)

    Marbles Mathematics APercentage

    1. a) What is the percentage of green marbles in the little net bag?b) What percentage of the green marbles is big?c) How much greater is the percentage of green marbles compared with the blue ones?d) How much smaller is the percentage of blue marbles compared with the green ones?

    2. Make your own net bags with marbles and let your friend answer the questions.(Contents: Net bags with marbles of different colours. Extra net bags and marbles.)

    VAT Mathematics APercentage

    Calculate the percentage VAT that has been added to the prices.(Contents: Receipts from buying clothes, pizza and bus trips)

    The tube of toothpaste Mathematics AGeometry

    How many days will the toothpaste last?(Contents: Some empty tubes of toothpaste, ruler for measuring the size of the hole)

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    Making geometrical shapes of a certain volume Mathematics AGeometry

    Make them from sheets of paper and tape. Measure their volume by filling them withpeas to be transferred to a graduated measure.1. Cuboid measuring 0.5 dm3.

    2. Cube measuring 0.5 dm3

    .3. Cone measuring 0.5dm3.(Contents: Sheets of paper, tape, ruler, and pair of scissors, graduated measure and

    peas)

    The Wheel Mathematics AGeometry

    How many revolutions will the wheel rotate when the tractor covers a distance of 1metre? Calculate this by taking relevant measurements on the wheel and test your resultby driving the corresponding distance with the tractor.(Contents: Toy tractor, ruler)

    Making tubes Mathematics AGeometry

    Calculate the maximum number of tubes that you can make out of the big yellow papersheet. All the pipes must be the same as the enclosed red one.(Contents: Tube of red paper (height 5 cm and diameter 4,1 cm), yellow A-4 paper, pair

    of scissors, ruler and tape)

    The relation between inch and centimetre Mathematics AFunctions

    Use the gauge for measuring the tread on car tyres to find the relation between inch and

    centimetre.a) Write it as a formula.b) Plot a graph(Content: gauge for measuring tread on car tyres)