Complete Book of Basic Mathematics_Group 1

7/27/2019 Complete Book of Basic Mathematics_Group 1

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KPLSPM

Semester 2Coursework For

Basic Mathematics

Topic : Non-Routine ProblemSolving

Prepared by :

Name : Ka Kai FongI.C No & Matrix. No : 891030-01-5089 & 0661-0707

Name : Chan Chew FongI.C No & Matrix. No : 890808-23-5214 & 0658-0707

Name : Nin Chiou CheeI.C No & Matrix. No : 890430-08-6180 & 0669-0707

Name : Tee Meng Fung

I.C No & Matrix. No : 890518-23-5064 & 0674-0707

Unit : KPLSPM PS / BI / BC Ambilan Julai 07

Course : Basic Mathematics Semester 2

Lecturers name : Encik Razali Bin Ibrahim

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Institut Pendidikan Guru Malaysia,Kampus Perlis.


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Date of submission : 7 March 2008

Contents

Task Sheet 02

Introduction 03

NON ROUTINE PROBLEM 1

Problem 1 04Solution for Problem 1 05Justification for Problem & Solution 1 06Similar Problem 1 07Solution for the Similar Problem 1 with the best method 08


Problem 2 09Solution for Problem 2 10-11Justification for Problem & Solution 2 12Similar Problem 2 13Solution for the Similar Problem 2 with the best method 14


Problem 3 15Solution for Problem 3 16-18Justification for Problem & Solution 3 19

Similar Problem 3 20Solution for the Similar Problem 3 with the best method 21

References 22

Collaboration Form 23

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INTRODUCTION TO NON-ROUTINE PROBLEM SOLVING

Futurists continue to stress that our future is going to undergo change at a rate

even greater than present generations have experienced. This implies that todays and

future problems will have a dynamic component. Such problems change or evolve as theyare being studied. It is evident then that a fundamental skill for dealing with the future is

active problem solving, i.e., the ability to solve problems which are undergoing change

during the process of resolution. There are many types of problems that students

encounter in their mathematics classes, but most are considered routine problem solving

activities. These usually involve the direct application of an algorithm to a word problem.

On the other hand, non-routine problem solving, stresses the use of heuristics

and often requires little to no use of algorithms. Unlike algorithms, heuristics areprocedures or strategies that do not guarantee a solution to a problem but provide a more

highly probable method for discovering the solution. Building a model and drawing a

picture of a problem are two basic problem-solving heuristics. Other heuristics include

describing the problem situation, making the problem simpler, working backwards, and

classifying information.

Non-routine problem solving focus on a higher level of interpretation and

organization of the problem rather than on application of an algorithm. These problems

tend to encourage logical thinking, expand students understanding of concepts, develop

mathematical reasoning power, develop students abilitiesto think in more abstract ways,

and allow for a transfer of mathematical skills to unfamiliar situations. Teachers usually

have a more difficult time gathering these types of problems since there may not be many

included in the textbooks they are using in their classrooms. The internet can be a helpful

resource in providing non-routine problem solving activities for elementary school

students. The internet can be a helpful resource in providing non-routine problem solving

activities for elementary school students.

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PROBLEM 1

Chew was a tired young boy. He had been gone for a long time collecting mushrooms.Chew was the oldest child and that meant lots of chores for him. But he didnt mind thatmuch. He was almost home now. All he had to do was to go over two drawbridges that

crossed two dangerous rivers.

Chew came to the first river. The drawbridge was raised. Normally all he had to do was topush a lever and the bridge came down. To Chews surprise, the lever was surrounded byan iron cage with a lock on it. He could not reach the lever unless he opened the lock. Itmust be his pesky younger sister, Chiou, playing one of his practical jokes. Oh well,thought Chew, Ill just open the lock. Below show the lever at the drawbridge.

SOLUTION FOR PROBLEM 1

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INSTRUCTION TO OPEN THE LOCK

Place the numbers 1 to 6, one in each circle so that the sum of the four numbers along any

of the three sides of the triangle is 10. There are 6 circles and 6 numbers to place in thecircles. Each circle must have a different number in it.

1

25 3

4 6


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Method 1 (Identify Sub Goal)

Goal (A+B+C)=(C+D+E)=(E+A+F)=10

Sub Goal 1 = (1+4+5) =10Sub Goal 2= (5+2+3) =10Sub Goal 3 = (3+1+6) =10

Method 2 (Construct a table)

Group FirstNumber SecondNumber ThirdNumber TotalI 1 4 5 10

II 3 2 5 10

III 3 1 6 10

Method 3 (Draw a diagram)

JUSTIFICATION FOR PROBLEM & SOLUTION 1

5

1

25 3

4 6


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We choose this question because:

i) it is suitable for primary schools student level.ii) it requires the skill of summation which students will learn since from standard

one.iii) The question will build a creative thinking among the student.iv) it is a quite challenging problems.

We choose the third methodwhich is draw a diagram because:

i) clear to show and would ot get cofuse easily.

ii) the student will get the answer more quickly.

iii) the student will easily to get the real picture of the situation.

iv) the first and the second solution seem to be more difficult for primay schools

student to understand.

v) the student have not learn how to construct a function, so the first solution will

not be suitable for them.

vi) The student will be get confuse with the numbers that appear twice in the table.

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SIMILAR PROBLEM 1

Fong was a tired young boy. He had been gone for a long time collecting mushrooms.Fong was the oldest child and that meant lots of chores for him. But he didnt mind thatmuch. He was almost home now. All he had to do was to go over two drawbridges thatcrossed two dangerous rivers.

Fong came to the first river. The drawbridge was raised. Normally all he had to do was topush a lever and the bridge came down. To Fongs surprise, the lever was surrounded byan iron cage with a lock on it. He could not reach the lever unless he opened the lock. It

must be his pesky younger brother, Nick, playing one of his practical jokes. Oh well,thought Fong, Ill just open the lock. Below show the lever at the drawbridge.

7

INSTRUCTION TO OPEN THE LOCK

Place the numbers 1 to 9, one in each circle so that the sum of the four numbers along any

of the three sides of the triangle is 20. There are 9 circles and 9 numbers to place in thecircles. Each circle must have a different number in it.


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SOLUTION FOR SIMILAR PROBLEM 1

Best Method (Draw a diagram)

3

9 8

1 4

7 2 6 5

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PROBLEM 2

How many bread are in the basket if

(a) There are fewer than 2 dozen bread, and(b) Counted 3 at a time, there is none left over, and(c) Counted 5 at a time, there are 1 left over, and

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Method 1 (Identify Sub Goal)

Sub Goal 1 There are fewer than 2 dozen bread, and

Sub Goal 2 Counted 3 at a same time, there is none left over

Sub Goal 3 Counted 5 at a time, there are 1 left over, and

Sub Goal 1 = { 23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 }Sub Goal 2= { 21,18,15,12,9,6,3,0 }Sub Goal 3 = { 21,16,11,6,1 }

ANSWER : 21


Sub Goal 1 There are fewer than 2 dozen bread, and

Sub Goal 2 Counted 3 at a same time, there is none left over


Goal 23 22 21 20 19 18 17 16 15 14 13

1 2

3

Goal 12 11 10 9 8 7 6 5 4 3 2 1 0

1

2

3

ANSWER : 21

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Method 3 (Draw a diagram)

Sub Goal 1 There are fewer than 2 dozen bread, and ASub Goal 2 Counted 3 at a same time, there is none left over B

Sub Goal 3 Counted 5 at a time, there are 1 left over, and C

ANSWER : 21

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i) it is suitable for primary schools student level.ii) it requires the skill of multiplication which students will learn since from

standard two.iii) it requires the skill of accuratecy while solving the problemiv) it train the student to be more patient so that they can get the answer only if

they solve the three given clues.

We choose the second methodwhich is construct a table beacuse:

i) it is clear enough to show the final answerii) it will reduce the mistake while solving which of the clue.iii) the risk to get the wrong answer while by using the first method and thrid

method is too high.iv) primay schools studet have not learn about set therefore the first and

third method will be difficult for them.

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SIMILAR PROBLEM 2

How many lemons are in the basket if

(a) There are fewer than 22 lemons, and(b) Counted 5 at a time, there are none left over, and(c) Counted 6 at a time, there are 3 left over, and

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Best Method (Construct a table)

Sub Goal 1 There are fewer than 22 lemons, and

Sub Goal 2 Counted 5 at a time, there is none left over, and


Sub Goal 21 20 19 18 17 16 15 14 13 12 11

1

2

3

Sub Goal 10 9 8 7 6 5 4 3 2 1 0

1

2 3

ANSWER : 15

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PROBLEM 3

There is a career fair in St. Francis High School last Saturday. There are six booth tookpart in that career fair which are profession of teaching, science, nursing, athlete,photography, journalism. However, the no label for each booth and every student isconfusing. As the committee of the career fair, you are responsible to do the label for eachbooth according to the clues given.

a) teaching booth is the firstb) Those who took care of the booth between teaching booth and journalism booth

wore white uniformc) athlete booth and science booth are at the middle of the rowd) there is a camera at the booth next to the science boothe) there are many laboratory apparatus at the booth next to the photograph booth

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Sub Goal 1 Teaching booth is the first

Sub Goal 2 Those who took care of the booth between teaching boothand journalism booth wore white uniform

Sub Goal 3 Those at the third booth from front wore sport wear andlooked muscular

Sub Goal 4 There are many types of camera at the booth next to theathlete booth

Sub Goal 5 There are many laboratory apparatus at the booth next to thephotograph booth

Teacher T Scientist SAthlete A Photographer P

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Nurse N Journalist J

Sub Goal 1

1 2 3 4 5 6T ? ? ? ? ?

Sub Goal 2

1 2 3 4 5 6

T N N / J N / J N / J J

Sub Goal 3

1 2 3 4 5 6

T N A N / J N / J J

Sub Goal 41 2 3 4 5 6

T N / P A N / J / P N / J J

ANSWER:

Sub Goal 5

1 2 3 4 5 6T N A P S J

Method 2 (Draw out the situation)

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2

3

5

4

Career Fair


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ANSWER:

No of booth Profession

1 Teacher

2 Nurse3 Athlete

4 Photograph

5 Scientist6 Journalist

Method 3 (Simplify the clues)

Clue 1

Teaching booth is the first

Teacher 1

Clue 2

Those who took care of the booth between teaching booth andjournalism booth wore white uniform

? ?Teacher Nurse Journalist

Clue 3

Those at the third booth from front wore sport wear and lookedMuscular

Athlete 3There are many types of camera at the booth next to the athlete booth

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1 6


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Clue 4 ? ?

Photographer Athlete Photographer

Clue 5

There are many laboratory apparatus at the booth next to the

photograph booth

? ?

Scientist Photographer Scientist

ANSWER:

No of booth Profession

1 Teacher

2 Nurse

3 Athlete4 Photograph

5 Scientist6 Journalist



i) it is suitable for primary schools student level.ii) It will let the student more understand the differet career.ii) it requires the skill of analysis the clues.iii) it requires the skill of thinkig logicallyv) it train the student to be more patient so that they can get the answer only if

they solve the three given clues.

We choose the second methodwhich is draw out the situation because:

i) it is clear enough to show the final answerii) the student will easily to get the real picture of the situation.

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iii) the first and the third solution seem to be more difficult for primay schools

student to understand.

iv) Students may get confuse with the explanation with the method of table.

SIMILAR PROBLEM 3

There are seven students in a class 5 Hero. Your class tutor asks for a name list accordingto their sitting place. Student are sit according to their height. As the class monitor, you areresponsible to complete the task given.

a) Wan sits at the lastb) Fong sits at the middlec) Meng sits between Fong and Anna who is the shortestd) Nin sits beside Syam who is more taller than here) Pupy is shorter than Meng

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Best Method (Draw out the situation)

21

5 HERO

4

Fong


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ANSWER:

No. Name

1 Anna

2 Pupy3 Meng

4 Fong

5 Nin

6 Syam7 Wan

REFERENCES

Reston. (2000), Principles and Standards for School Mathematics, England: NationalCouncil of Teachers of Mathematics.

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murry, H., Olivier, A., &Wearne, D. (1996). Problem solving as a basis for reform in curriculum andinstruction: The case of mathematics. Educational Researcher, 25(4), 12-21.

Silver, E. A. & Kilpatrick, J. (1988). Testing mathematical problem solving. In R. I.Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical

22

1

ANNA

2

Pupy

3

Meng

7

Wan

6

Syam

5

Nin


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problem solving: Vol. 3. (pp. 178-186). Reston, VA: National Council of Teachers ofMathematics.

Johnson, M. (1976). How to solve word problems in algebra: A solved problem approach.New York: McGraw-Hill.

Third International Mathematics and Science Study (1995). [On-line]. Available:http://isc.bc.edu/timss1995.html

Trends in International Mathematics and Science Study (1999). [On-line]. Available:http://lighthouse.air.org/timss/

BORANG REKOD KOLABORASIKERJA KURSUS PENDEK

Name / I.C No. : Ka Kai Fong 891030-01-5089: Chan Chew Fong 890808-23-5214: Nin Chiou Chee 890430-08-6180: Tee Meng Fung 890518-23-5064

Unit : KPLPSM Pengajian Sosial / BI / BC Ambilan Julai 07

Course : Basic Mathematics

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http://isc.bc.edu/timss1995.htmlhttp://isc.bc.edu/timss1995.html


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Lecturers Name : Encik Razali Bin Ibrahim

Date of Submission : 7 March 2008

Date Discussion Issue CommentLecturersSignature

20.2.08

24.2.08

27.2.08

29.2.08

3.3.08

4.3.08

5.3.08

Briefing of the assignment

Discussion on the problem & solution

Discussion about the justification

Discussion on the similar problem and

its solution

First draft of the assignment

Second draft of the assignment

Final check of the assignment

Documents

Complete Book of Basic Mathematics_Group 1