Modul TOPS Jan 2006 Latest

8/14/2019 Modul TOPS Jan 2006 Latest

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TECHNIQUES OF PROBLEM SOLVING

INTRODUCTION

TOPS ( Technique Of Problem Solving ) is a comprehensive program for the

development of problem-solving skills and strategies. It has been designed to complement

existing mathematics textbook program. TOPS has instructional materials for the primary

schools. This modules provide the core for a program in one of the most important of

mathematical areasproblem solving. TOPS Module can be used to make students aware

that many problems can be solved in more than one way. It can be also

used to encourage students to communicate in English during the teaching and learning

activities.

Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 1


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COMMITTEE MEMBERS

Advisor : Dr. Goh Kok Keng

Chief of Academic Management Sector

Chairman : En. Mohd. Nasir b. Hj. OthmanChief of Curriculum Unit

Vice Chairman : En. Ridza b. Hussin

Assistant Director of Science & Mathematics

Module Coordinator : En. Huzaimi b. Hj. Mohd. Hashim

Primary Mathematics Officer

Module Writers : Pn. Aneesha bt. Hamid ( Leader) - SK Pulau BetongEn. Ibrahim b. Mohd Ariffin - SKPK Jalan Hutton

Tn. Hj. Ahmad Nizar b. Salleh - SK Sg. Kechil

Tn. Hj. Osman Kechik - SK Mutiara Perdana

En. Tung Fook Yen - SJK (C) Kim Sen

Pn. Liau Chooi Chin - SJK (C) Sg. Lembu

Pn. Shahbanou bt. Mohamed - SK Kg. Jawa

Pn. Saadiah bt Hassan - SK Juara

Pn. Azrin bt. Abdul Ghafar - SKPK Jalan Hutton

Pn. Norijah bt. Hassan - SK Kebun SirehPn. Vanidamani a/p K. Karuppayah - SJK (T) Ladang Alma



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CONTENT

Introduction 2

Objectives 5

Problem Solving Strategies 6 7

Polyas model 8

Whole Numbers 9 26

Fractions 27 28

Decimals 29 31

Money 32 36

Time 37 40

Length 41 42

Mass 43 44

Volume of Liquid 45 47

Shape & Space 48 51

Data Handling 52 56

Worksheets 57 90

Acknowledgements 91

Bibliography 92


Topic 1

Topic 2

Topic 3

Topic 4

Topic 5

Topic 6

Topic 7

Topic 8

Topic 9

Topic 10


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OBJECTIVES

The objectives of this program are to improve students performance

at solving problems correctly and make students aware of problem solving

strategies. TOPS module was designed to encourage the students to

communicate during the teaching and learning activities with the teacher

playing an active role leading the students through each experience.



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PROBLEM SOLVING IN MATHEMATICS

Problem Solving is an instructional program designed to prepare

students for future problem solving experiences by building their

confidence dealing with real-world situations that involve numbers that

exists in three different modes, namely as content, ability, and learning

approach.



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Choosing

The

Operation

Working

Backwards

Using

LogicGuessing

And

Checking

Make a

table

Chart/

systematic

Identifyin

g patterns

and

sequences

Finding

Facts

Draw a

dia ram

Problem

Solving

Strategie

s

PROBLEM SOLVING STRATEGIES


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PROBLEM SOLVING USING POLYAS MODEL

Understanding the problem

Devising a plan

Carrying out the plan

Looking back at the solution.

02 Mac 2006 TOPS JPN PENANG

Flowing Chart Of Problem SolvingSTART

Incorrect

Incorrrect

Understanding the problem

i. Read and understand

ii. Extract the pointsiii. Interpretate the problem

Incorrect

END

Select appropriate solution strategies Devising a plan

Implement solution

Does the strategic possible?

Carrying out the plan

Check the answer

Is it a correct solving ?

Correct

Looking back the solution

TOPIC 1 : WHOLE NUMBERS



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LEARNING AREA : ADDITION WITH THE HIGHEST TOTAL OF

100 000.

LEARNING OUTCOME : SOLVE ADDITION PROBLEMS.

SUGGESTED TEACHING AND LEARNING ACTIVITIES.

Step 1

Teacher asks pupils to read and understand the problem given.

Step 2

Teacher asks questions and pupils write down what is given and what to find.

Step 3

Pupils underline the key word and choose the operation.e.g. Total The key word is total and the operation is addition

Step 4Pupils solve the problem and check them.

e.g.

CHOOSING THE OPERATION

There are 25 317 Mathematics books and 32 451 English books in a bookshop. Findthe total number of books in the bookshop.

Given 25 317 Mathematics32 451 English books

Find Find total number of books ?Operation Total / Addition (+)

Solve

25 317 Check 57 768+ 32 451 - 32 4 51

_______ _________

57 768 25 31 7_______ _________

Answer There are 57 768 books in the bookshop.

Try this !



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Solve the problems

1. There are 30 000 blue cards, 50 000 red cards and 20 000 yellow cards.How many cards are there altogether ?

Given

Find

Operation

Solve Check

Answer

2.


11 200 76 000

20 456 81 000

10 00 20 000


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What is the sum of the largest number and the smallest number given

above.


Given Largest number - _____________________Smallest number - _____________________

Find

Operation

Solve Check

Answer


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3. Pak Abu sold 3 500 eggs on Monday. He sold 6 900 eggs on Tuesday.What is the total number of eggs sold ?


Given

Find

Operation

Solve Check

Answer


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100 000.

LEARNING OUTCOME : SOLVE ADDITION PROBLEMS.


Step 1Teacher asks pupils to read and understand the problem given.Step 2

Teacher guides pupils to make a table.Step 3

Teacher guides pupils to fill in the table by drawingStep 4

Pupils check the answers.

e.g. MAKING TABLE AND DRAWINGS

If one table with 4 seated and two tables with 6 seated, how many tables are needed

for 20 seats?

Number of Tables Number of People



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100 000

LEARNING OUTCOME : SOLVE ADDITION PROBLEMS


Step 1

Teacher asks pupils to read and understand the problem given.Step 2

Teacher asks questions and pupils write down what is given and what to find. Plan whatstrategy to use.Step 3

Pupils underline the key words to write the number sentence.Step 4

Pupils implement the plan. Then, check the solution.e.g.

+ 33 268 + 18 175 = 99 077

Working Backwards

Solve Check

99 007 47 564

- 18 175 + 33 268

______ 18 175

80 832 ______

- 33 268 99 007

______ ______

47 564

______


The sum of three numbers is 99 077. Two of the numbers are

33 268 and 18 175. What is the third number ?


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TRY THIS !


The sum of three numbers is 44 563 . Two of the numbers

are 12 009 and 18 200. What is the third number ?

SOLUTION CHECK


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LEARNING AREA : SUBTRACTION WITHIN 1 000 000

LEARNING OUTCOME : SOLVE SUBTRACTION PROBLEMS.


Step 1


Step 2

Teacher asks questions and pupils write down what is given and what to find. Plan whatstrategy to use.

Step 3

Pupils underline the key words to write the number sentence.Step 4

Pupils implement the plan. Then, check the solution.

e.g.

What number subtract 7 500 give a difference of3 700?

7 500 = 3 700

Strategy

Working backward

Solve the problem Check the solution.

7 500 = 3 700 11 200

7 5003 700 _________+ 7 500 3 700________ _________11 200

________

Try this !


11 200


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1. What number subtract 8 200 give a difference of7 560?

_____________ = ____________

Strategy

Working backward

Solve the problem Check the solution.



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LEARNING AREA : SUBTRACTION WITHIN 100 000

LEARNING OUTCOME : SOLVE SUBTRACTION PROBLEMS.


Step 1


Step 2

Teacher asks questions and pupils write down what is given and what to find.e.g. How many people visited the travel fair on Saturday?

Step 3

Pupils underline the key word and choose the operation.e.g. Difference The key word is difference and the operation is subtraction.


e.g.CHOOSING THE OPERATION

1. 20 536 people visited the zoo on Saturday and 25 906 peopleon Sunday. Find the difference in the number of visitors for the two days.


Given Saturday 20 536 peopleSunday - 25 906 people

Find Find the difference in the number of visitors.

Operation Difference / Subtraction ( )

Solve Check

25 906 5 370 20 536 + 20 536

5 370 25 906

Answer 5 370 people.


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Try this!

1. Raju has 13 045 stamps. He gives 1 542 stamps to Kumar. How manystamps are left?

2. Find the balance if 32 400 cars were sold from 50 000 cars duringthe holiday promotion.

3. Hamidah has 480 eggs. She sells 175 of them. How many eggs are left?


Given

FindOperation

Solve Check

Given

Find

Operation

Solve

Answer


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Given

Find

Operation

Solve

Answer


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LEARNING AREA : MULTIPLICATION WITH THE HIGHEST

PRODUCT OF 100 000

LEARNING OUTCOME : SOLVE MULTIPLICATION PROBLEMS


Step 1Teacher shows multiplication flash cards and pupils give the answers.

Step 2


Step 3

Teacher asks questions and pupils write down what is given and what to find.

Step 4Pupils underline the key word and choose the operation.

Step 5

Pupils solve the problem and check them.e.g. Times The key word is times and the operation is multiplication.


Huzi has 5 250 stamps. Imah has 5 times as many stamps as Huzi. How many stamps

does Imah have?Given Huzi has 5 250 stamps

Imah has 5 times

Find Find the number of stamps Imah hasOperation Times / Multiplication (x)Solve Check

5 250 5 250x 5 5 250

_______ 5 25026 250 5 250_______ + 5 250

26 250_________

Answer 26 250 stamps



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Try this!

Encik Raju buys 20 boxes of chocolates. There are 2 620 chocolates in each box. Howmany chocolates does he buy altogether?


Given

Find

Operation

Solve Check

Answer


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LEARNING AREA : DIVISION WITH THE HIGHEST DIVIDEND

OF 100 000

LEARNING OUTCOME : SOLVE DIVISION PROBLEMS


Step 1Teacher asks 2 pupils to divide 20 books equally among themselves. Pupils answer.

Step 2


Step 3

Teacher asks pupils to draw the diagram related to the questions given.


e.g. Divide equally The key word is divide equally and the operation is division.


There are 3 030 books. Rina arranges them onto 6 shelves equally. How many books doesshe put on each shelf ?

e.g : 1


3 030


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e.g :2

Answer : 505 books

Try this

1050 marbles are packed equally into 15 plastic bags. How many marbles are there in eachplastic bag.

Draw a diagram from the question above.


3 030


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LEARNING AREA : MIXED OPERATION

LEARNING OUTCOME : SOLVE MIXED OPERATION PROBLEMS


Step 1


Step 2

Teacher asks questions and pupils solve the problem.

Step 3

Pupils underline the key words to write the number sentence.

Step 4

Teacher guides the pupils to identify the patterns and sequence of the problem.

CHOOSING THE OPERATIONA farmer puts 4 000 mangosteens equally into twenty baskets. Count the number ofmangosteens in 15 baskets.


Given 4 000 mangosteens , 20 baskets, 15 baskets

Find Find the number of mangosteensOperation Equally/division ()

multiply (x)Solve Check200

20 4000 15 3000

- 40 - 30

0 0

0 0

0 0

200 200

x 15 x 20

1000 4000

200

3000

Answer 3 000 mangosteens


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Try this

CHOOSING THE OPERTION

There are 2 430 green flags in a store. Red flags exceed green flags by 216. The numberof blue flags is 508 less than the red flags. How many blue flags are there in the store?


Given

Find

Operation

Solve Check

Answer


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e.g 2

+ =

Try this.

Azrin ate of a fruit cake and Banu ate of the fruit cake. How much fruit cake did theyeat altogether?

Draw the diagram from the above information.



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TOPIC 3 : DECIMALS

LEARNING AREA : DECIMAL NUMBERS

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING ADDITION, SUBTRACTON,

MULTIPLICATION AND DIVISION OF DECIMAL

NUMBER.


Step 1


Step 2

Teacher guides the pupils to find facts in a list given

Step 3Teacher asks the pupils to answer the questions.

Step 4

Pupils solve the problem and check them



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FINDING FACTS IN A LIST

0.15 kg each

1.2 kg each

1.5 kg each

Find The Facts

1. What is the weight of an apple? ________________

2. A banana weighs _______________

Use The Facts

3. What is the total weight of the fruits listed above?

____________________________

4. What is the difference between a pineapple and an apple in grams?

____________________________

5. If an apple weighs 0.15 kg, what is the total weight of 6 apples in grams?

____________________________

Answer:1. 0.15 kg2. 1.2 kg3. 2.85 kg4. 1350 g5. 900 g



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Try this!

1200 g 170 g 195 g

Find the facts

1. What is the weight of the bananas? __________________________

2. An apple weighs __________________________

Use The Facts

3. What is the total weight of the fruits listed above ? __________________

4. What is the difference of weight between the bananas and the carrot ?

______________________________.

5. What is the total weight of the 4 apples?

______________________________.



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TOPIC 4 : MONEY

LEARNING AREA : MONEY UP TO RM 10 000

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING MONEY UP TO

RM 10 000


Step 1


Step 2

Teacher guides pupil to complete the bill given.

Step 3

Pupils answer the questions and check the answer.

COMPLETING TABLE

RM 1500.00 RM 69.90 RM 399.90

Complete the bill below

Quantity Item Price per Unit Price

1

2

3

Television

Table Lamp

Camera

_____________

_____________

_____________

_____________

TotalAnswers:

1, RM 1500.00 / RM 1500.002. RM 69.90 / RM 139.803. RM 399.90 / RM 1199.70

Total RM 2839.50



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Try this

3 bottles of soya sauce cost RM 1.50 per bottle. 5 kg sugar cost RM 1.40 per kg. 1 cartonof mineral water costs RM 18.00. Find the total amount of the things bought and completethe table.

Quantity Item Price Per Unit Price

Total



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TOPIC 4 : MONEY

LEARNING AREA : MONEY UP TO RM10 000

LEARNING OUTCOMES : (vii) Solve problems involving money up to RM10 000


Step 1


Step 2

Teacher asks questions and pupils answer. Teacher calls out pupil andSimulate the situation given in the problem given.

Step 3

Teacher guides pupils to make a table and listing to check the answers.

Step 4

Teacher asks pupils to use trial and error strategy to get the answer for the sameproblem.

Step 5

Check all the answers.



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e.g.

Awin, Dino and Pam received a total of RM45.Awin got RM4 more than Dino. Pam got

RM1 less than Dino. How much money did Dino receive ?

Simulation

The teacher distributes RM45 to Awin, Dino and Pam.

First she gives Awin RM4. Then Dino takes RM1 and so does Awin from the teacher. Lastly, the teacher divides the balance of the money equally to

Awin, Dino and Pam. All of them count their money .

The Result :

Name of pupils

Amount

received The difference

Awin RM 18

Dino RM 14

RM 4

RM 1

Pam RM 13

FINDING ANSWER BY MAKING A TABLE.

NAME FIRST

STEP

SECOND STEP THIRD STEP AMOUNT

RECEIVED

AWIN RM4 Add RM1 Add RM13 RM18

DINO - RM1 Add RM13 RM14

PAM - - RM13 RM13

TRY THIS !

Use Trial and Error strategy to determine the answer.Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 34


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Awin, Dino and Pam received a total of RM45. Awin got RM4 more than Dino. Pam got

RM1 less than Dino. How much money did Dino receive ?

TRIAL AND ERROR

TRIAL AWIN DINO PAM TOTAL

1st

2nd

3rd

Answer : ____________________________________________

TOPIC 5 : TIME

LEARNING AREA : TIME DURATION



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LEARNING OUTCOME : CALCULATE THE START OR THE END OF AN EVENT

FROM A GIVEN DURATION OF TIME AND READ THE START OR END OF AN

EVENT.


Step 1

Teacher asks pupils about their favourite T. V. program.

Step 2

Teacher discusses the T. V. Schedule given. Teacher guides pupils to findfacts in the schedule. Ask questions and pupils write down the answers.e.g. What time does the movie begin?

Step 3

Pupils use the facts to answer the questions given.

e.g. FINDING FACTS IN A SCHEDULE

T.V. SCHEDULE

FIND FACTS

1. What time does the movie begin ?________________________

2. Which program begins at 8:40 ? __________________________

3. What time does the music program begin ? ______________________

4. What time does the music program end? ________________________USE THE FACTS


TIME PROGRAM

8:00 a.m. NEWS

8:15 a.m. MUSIC

8:40 a.m. SPORTS

9:00 a.m. MOVIE

10:30 a.m. COOKING

11:00 a.m. CARTOONS

12:00 noon ABOUT TOWN


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5. What is the duration of the news program ? _______________________________

6. Which program is one hour long? _______________________________

7. Which program is 30 minutes long? _____________________________

8. What is the duration of the music program? ______________________

9. Which program is longer, the sports show or the cookingshow? _____________________________

10. Which program is the longest? _____________________________

11. What is the duration of this TV program? _______________________



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TOPIC 5 : TIME

LEARNING AREA : BASIC OPERATION INVOLVE TIME

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING BASIC OPERATION OF

TIME


Step 1Teacher asks pupils to read and understand the problem given.

Step 2

Pupils state the start and end of the event.

Step 3

By using drawings, teacher guide pupils to calculate the duration of the event.

MAKING DRAWINGS

Pn. Neesha jogs every morning. She starts at 6 oclock and finishes at 7:30 am. How longdoes she jog?


6:00 am 7:00 am 7:30 am

1 hour hour

Answer 1 hour / 1 hour 30 minutes


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Try this!

A test starts at 8:00 a.m. and end at 9:15 a.m. How long is the test?

start end



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TOPIC 6 : LENGTH

LEARNING AREA : MEASURING LENGTH

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING BASIC OPERATION ON

LENGTH


Step 1Teacher practices mental calculations and estimation involving length.Step 2

Teacher asks pupils to measure the actual length of the object.Step 3

Teacher asks pupils to read and understand the story given.Step 4

Teacher asks pupils to answer the questions from the storyStep 5

Pupils solve the problem.

FINDING FACTS IN A STORY

Ijah is 150 cm tall. Arin is 10 cm shorter than Ijah. Anis is 15 cm taller than Arin.

Find The Facts

1. What is the height of Ijah ? ___________________

2. The height of Arin is _________________________3. Anis is ________________________ tall.

Use the Facts

4. What is the height of Ijah in meters. _______________________5. What is the difference of height between Anis and Arin ? _________6. Find their total height in meters. ___________________________

Answers:1. 150 cm 4. 1.5 m2. 140 cm 5. 15 cm3. 155 cm 6. 4.45 m



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Try this!

Diah has 3 colour ribbons. The length of the red ribbon is 1.5 m. The blue ribbon is 207 cmand the yellow ribbon is 0.8m.

Find the facts

1. Which is the longest ribbon ? _____________________________2. The shortest ribbon is __________________________________3. What is the length of the red ribbon ? ______________________

Use the facts

1. If one red ribbon is 1.5m, what is the length of 10 red ribbons in centimeter?_______________________________

2. Calculate the difference between the blue ribbon and the yellow ribbon?_______________________________

3. Find the total length of the red and blue ribbon. _____________________



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TOPIC 7 : MASS

LEARNING AREA : MEASURING MASS

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING BASIC OPERATIONS WITH

MASS.


Step 1

Teacher practices mental calculation and estimation involving mass.

Step 2


Step 3

Teacher guides pupils to read the measurement from the weighing scale.

Step 4

Pupils answer the question asked and check the answer.

FINDING FACTS IN A PICTURE

Picture A Picture B

1. The weight of tomatoes in picture A is ________________.

2. The weight of clock in picture B is ____________________.

3. Which is heavier ? _________________.

4. Find the weight of 10 similar tomatoes from picture A. __________________.

5. Find the weight of picture A and B in grams. _______________________.



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Try this

A B

1. The weight of the chicken is __________________.

2. The weight of the fish is _____________________.

3. Which is heavier? A chicken or a fish? _____________________.

4. Find the weight of 8 chickens. ____________________.

5. Find the weight of the chicken and the fish in grams. ______________.



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TOPIC 8 : VOLUME OF LIQUID

LEARNING AREA : MEASURING VOLUME OF LIQUID

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING VOLUME OF LIQUID


Step 1

Teacher practices mental calculation and estimation involving volume of liquid..

Step 2

Teacher asks pupils to measure the volume of liquid using a measuring cylinder.

Step 3

Teacher guides pupils to estimate the volume of liquid shown below.

Step 4

Teacher asks pupils to answer the questions and solve the problem.

FINDING FACTS IN A TABLE

CONTAINER VOLUME OF LIQUID

______________ ml

______________ ml

______________ ml

1. The cup contains _____________ ml of water

2. There is ____________ ml of ink in the bottle.

3. The cylinder contains _____________ ml of water.



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Use the facts

4. If the water from the cup is poured into the cylinder, what is the total amount ofwater in the cylinder now?

_________________________

5. What is the difference between the volume of water in an ink bottle and a cup?

_________________________

Try this

Container Volume of Liquid

( Estimation )

Aquarium A

_________________ ml

Aquarium B

_________________ ml

Aquarium C

_________________ ml

Find the Facts

1. Aquarium A contains _____________ ml of water.

2. There is ____________ ml of water in aquarium B.

3. Aquarium C contains ______________ml of water.



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Use The Facts

4. If the water from aquarium A is poured into aquarium C, what is the total amount ofthe water in aquarium C now?

____________________

5. What is the difference between the volume of water in aquarium C and aquarium B?

____________________



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TOPIC 9 : SHAPE AND SPACE

LEARNING AREA : TWO DIMENSIONAL SHAPES

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING PERIMETER AND AREA OF

TWO DIMENSIONAL SHAPE.


Step 1Teacher guide pupils to abstract information from the table given.

Step 2

Pupils work in groups

Step 3

Teacher asks pupils to present their work.

Step 4Pupils check the answer.


Fill in the table

Length Breadth Shapes Perimeter Area

4 cm 6 cm

1.5 m 2.5 m

1.5 m 15 m

Answers:

1. rectangle / 20 cm / 24 cm

2. rectangle / 8 m / 3.75 m

3. rectangle / 33 m / 22.5 m



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Try this!

Fill in the table from the story below.

The base length of a model house is 15 m and breadth 8 m. Find the perimeter and thearea of the model house.

Length Breadth Shape Perimeter Area



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TOPIC 9 : SHAPE AND SPACE

LEARNING AREA : THREE DIMENSIONAL SHAPES

LEARNING OUTCOME : SOLVE PROBLEM INVOLVING VOLUME OF CUBES AND

CUBOIDS


Step 1Teacher show real object to the pupils.

Step 2

Teacher asks pupils to measure the object

Step 3

Teacher helps pupils to create story from the above object.

USING LOGIC

?

?

?

Make a short story from the information above.

Try this

2 m

3 m

6 m

Complete a story from the diagram given



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An aquarium is _____________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________



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TOPIC 10 : DATA HANDLING

LEARNING AREA : PICTOGRAPH

LEARNING OUTCOME : SOLVE A GIVEN PROBLEM BY ORGANISING AND

INTERPRETING NUMERICAL DATA IN PICTOGRAPH.


Step 1Teacher guides pupils to specify the problem.

Step 2

Teacher asks pupils to collect data from the pictograph shown.

Step 3

Pupils interpret and discuss the result.

FINDING FACTS IN A PICTOGRAPH

Complete the table based on the problem below

The pictograph below shows the number of points obtained by 3 pupils in diagram.

Brahim

Osman

Nizar

represent 5 points

Brahim has 20 points. Osman has 25 points and Nizar has 40 points.



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Try this!

Complete the table based on the problem below.

The pictograph represent the number of books read by 3 pupils per month.

Liau

Tung

Vani

represent 10 books

Liau needs 40 books. Tung needs 30 books and Vani needs 60 books.

a. Who read the least number of books?

b. What is the difference between the number of books read by Vani and Liau?



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TOPIC 10 : DATA HANDLING

LEARNING AREA : BAR GRAPH

LEARNING OUTCOME : SOLVE A GIVEN PROBLEM BY

ORGANISING AND INTERPRETING

NUMERICAL DATA IN BAR GRAPHS.


Step 1

Teacher shows the graph and pupils discuss about the graph given.

Step 2

Teacher asks questions and pupils find the facts from the graph given.

Step 3Pupils use the finding facts strategy to solve the problem given.

Step 4

Pupils implement the plan. Then, check the solution.



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FINDING FACTS

1. How many pupils like to play badminton ?

_________ pupils like to play badminton.

2. How many pupils like to play ping pong ? __________________

3. The number of pupils play basketball is ___________________.

4. The number of pupils like to play football is _______________.

USING THE FACTS

1. What is the total number of pupils in year 4?

There are ______________ pupils in Year 4.

2. Find the difference between the number of pupils playing badminton andfootball. ____________________ pupils.

3. What is the most popular game? __________________.



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Try this!

The above bar graphs shows the number of different types of cars soldby a company in January.

1. Which car sells the most ?

______________________________________________________

2. Which car sells the least ?

______________________________________________________

3. Find the total number of cars sold in the month of January?

_____________________________________________________



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FINDING FACTS

Find the facts.

1. The smallest number is ________________

2. The largest number is ________________

3. The place value of digit 2 in the circle is ____________

4. The value of digit 5 in the rectangle is ____________

5. 8 261 round off to the nearest thousand is ____________

6. Write the number in the square in words.

_______________________________________________________

7. Partition the number in the triangle.

_______________________________________________________

8. Arrange all the above numbers in ascending order.

__________ , _________, _________, __________, __________

9. Arrange all the above numbers in descending order.

_________ , _________, __________, __________, ___________

10. 43 000 is rounded off to the nearest thousands from ______________


32 560 4 290 61 536 8 261


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USING FACTS

MARBLESRED BLUE GREEN YELLOW WHITE

10 265 12 0005

9 375

45 432

36 000

1 What is the total of the red and the white marbles?

________________

2 Find the difference between the yellow and the bluemarbles.

________________

3 Find the total of the green marbles in 15 boxes.

________________

4 Divide the white marbles into 100 boxes equally.

________________

5 Ali bought a box of red and blue marbles. Tina bought a

box of yellow marbles. What is the difference betweentheir marbles?

________________



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USING LOGIC

You are a Detective.

Draw a circle around the numbers that fits Clue 1.Draw a box around the numbers that fits Clue 2.The answer has both a circle and a box.

1. Clue 1 . The number is odd.

Clue 2. The number is more than 100.

The number is _______

2. Clue 1. The number is less than 1 000.

Clue 2. The number is greater than 500.

The number is ________

3. Clue 1. The number is even.

Clue 2. The number is not 2 244.

The number is _______

4. Clue 1. You say the number when you count by 20.

Clue 2. You say the number when you count by 30.

The number is ______


769

2 010

473

172

35

107

200

1 004

1 235

2 244

765

3 242

40

60

90

100


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GUESSING AND CHECKING

Pick a number from the star.

Use the number to solve the problem.

Does it work ? If not, try another number.

1. What is the mystery number ? _________

Add 5 to it.

Subtract 4 and you get 10.

2. What is the mystrery number ? _________

Subtract 10 from it.

Add 6 and you get 11.

3. What is the mystery number ? ________

Add 10 to it.

Add 15 again and you get 60.

4. What is the mystery number ? ________

Multiply 5 to it.

Subtract 20 from it and you get 100.


8

9 10

14 15

16 17

25 35

45 65

20 22

24 26


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CHOOSING THE OPERATIONS

1. Who drank more milk?

________________

2. How much milk both of them drank?

________________

3. Find the difference of milk drank betweenAli and his sister?

________________

4. How much milk was left?

________________


Ali drank litre of milk. Hersister drank litre of milk


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A carpenter used2

1of a piece of plywood to make a cupboard.

He used another 10

3

of the plywood to make a desk.

1. Which of the furniture used less plywood ?

_________________

2. How many parts of the plywood are used to

make the furniture ?

_________________

3. How many parts of the plywood were left ?

_________________




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Tan and his friends, Tin and Tun painted a wall. They painted

one-fifth of the wall in blue and two-fifth of the wall in green.

1. What is the fraction of the wall notpainted ?

_________________

2. What is the fraction of the wall painted ?

_________________

3. What is the difference in fraction betweenthe blue and the green wall?

_________________



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FINDING OPERATIONS1 Ali weighs 32.9 kg. Busu weighs 29 kg. Chin

weighs 36.25 kg. What is their total weight?

________________

2 The total length of red wire and blue wire is12.5 m. If the length of red wire is 8.25m, findthe length of red wire?

________________

3 My father buys 6 tins of paint. Each tin contains4.25 l of paint. What is the total volume of thepaint?

________________

4 Container Q can hold 6.5 l of water. Container R

can hold 0.75 l of water less than container Q.How much water can container R hold?

________________

5 Liza, Ana, May and Yani shared 9.4 m of ribbonamong themselves equally. What was the lengthof the ribbon Yani received?

________________



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RM 3.50 RM 5 RM 22.00 RM 2.50

Amir has RM 25.00Amin has RM 50.00Ana has ten ringgit more than Amir

1 How much money they have altogether?

________________

2 Amir needs to buy a school bag and a pair ofsocks. How much has he left after buyingthose things?

________________

3 Ana bought two books and a pen. How muchmoney has she left?

________________

4 Amin has to use half of his money to pay theschool fees. How much more money he needs ifhe wants to buy a book, a pen and a bag?

________________



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TV SCHEDULETIME PROGRAM

8.00 a.m

8.15 a.m

8.40 a.m

9.00 a.m

10.30 a.m

11.00 am

12.00 noon

News

Music

Sports

Movie

Cooking

Cartoons

About Towns

FINDING FACTS IN A SCHEDULE

FIND THE FACTS.

1. What time does the movie begin ? _________________________

2. Which program begins at 8.40 a.m ? _________________________

3. What time does the music program begin ? ____________________

4. What time does the music program end ? _____________________

USING THE FACTS.

1. What is the duration of the news ? _____________ minutes.

2. Which program is one hour long ? ________________________

3. Which program is 30 minutes long? ________________________

4. What is the duration of the music program? ______________ minutes.

5. Which program is longer, the sports show or the cooking show ?

________________________

6. Which program is the longest ?

_________________________



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CHOOSING OPERATIONS

1 Abu is 9 years old. His mother is 4 times olderthan him. What is his mothers age?

________________

2 The workers work 8 hours daily. They start workat 9.15 a.m. When will they finish their work?

________________

3 Siti started walking to school at 6.45 a.m. Shereached school at 7.00 a.m. How long did shetake to reach her school?

________________

4 How many minutes are there in 1 hour and 15minutes?

________________

5 Convert 235 minutes to hours and minutes

________________



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CHOOSING OPERATIONS

1 A carpenter needs 45 minutes to make a chair.How long does he need to make 12 chairs?

________________

2 Divide 365 minutes by 6

3 Abus eldest daughter is 36 years old. Hissecond daughter is 23 years old. What is thedifference in their age?

4 What is the total number of days in Jun, Julyand August?

5 What is the duration from Friday 7.45 a.m. toSaturday 2.30 p.m in hours and minutes?



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Problem Solving Strategies:

S1 Draw a diagram

S2 Finding Facts

S3 Identifying patterns and sequence

S4 Make a table chart or systematic list

S5 Guessing and checking

S6 Using logic

S7 Working backwards

S8 Choosing the operation



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Sample questionsTopic Questions Strategies

1.2 There are 34 648 male residents in a district. The female residents inthe district are 4285 more than the male residents. How many femaleresidents are there in the district?

______________

S2/S8

1.2 There are 27 750 packets of flour, 14 500 packets of sugar and 8 375packets of curry powder in a warehouse. find the total packets offlour, sugar and curry powder in the warehouse.

______________

S2/S8

1.2 Mr Nathan collects 15 574 aluminium cans and 20 528 bottles. How

many cans does he collect altogether?

______________

S2/S8

1.2 Year 2003 2004 2005Number of carsexported

12 450 23 574

The tableabove shows the number of cars exported by a country in the year

2003 and 2004. In 2005, the number of cars exported was 3970 morethan the number of cars exported in 2004. What was the total numberof cars exported in the three years?

______________

S2/S8

1.2 Mr Tan rears 28 750 ducks and 15 675 chickens. How many ducks andchickens does he rear altogether?

______________

S2/S8



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1.3 There are 52 428 candidates in an examination. If 46 549of them pass, how many of them fail?

______________

S2/S8

1.3 A businessman imported 83 600 oranges. The number of applesimported by him was 7 850 less than the number of oranges. How manyapples were imported by the businessman?

______________

S2/S8

1.3 43 350 text books were distributed to two schools A and B. School Areceived 16 658 text books. How many text books were received by

school B?

______________

S2/S8

1.3 In a tree planning campaign, two states planted 25 140 trees and16 945 trees respectively. What is the difference between thenumber of trees planted by the two states?

______________

S2/S8

1.3 Month May June July

Number oftourists

20 468 25 564

The tableabove shows the number of tourists who visited a national park in themonth of May and June. If the total number of tourists in the threemonths is 88 046, What is the number of tourists in the month of

July?

______________

S2/S8



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1.4 There are 574 nails in one box. How many nails are there in 82 boxes?

______________

S2/S8

1.4 There are 95 bags of aluminium cans for recycling. Each bag contains

280 cans. How many aluminium cans are there altogether?

______________

S2/S8

1.4 There are 1 288 boys and 1 178 girls in a school. If each pupil buys 9exercise books, how many exercise books do all the pupils buy?

______________

S2/S8

1.4 Ahmad imported 8 500 apples. The number of pears imported by himis 8 times as many as the number of apples. How many pears wereimported by Ahmad?

______________

S2/S8

1.4 A factory can install 652 computers a day. How many computers can

be installed by the factory in 30 days?

______________

S2/S8

1.4 There are 42 rubber trees in a row, how many trees are therealtogether in 80 rows ?

______________

S2/S8

1.5 Zainab arranges 95 stamps in each album. She has 4750stamps. How many albums does she need?

______________

S2/S8



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1.5 Pak Ali plants 12 840 rambutan trees in his orchard. There are 24rows altogether, how many trees are there in a row?

______________

S2/S8

1.5 A box can keep 48 packets of biscuits. How many boxes are needed tofill 2160 packets of biscuits?

______________

S2/S8

1.5 A factory produced 34 500 bottles of soy sauce in a week. Thefactory operates everyday except on Sunday. How many bottles of soysauce can the factory produce in a day?

______________

S2/S8

1.5 14 375 boxes of Milo are kept in 5 warehouses equally.How many packets of Milo are there in each warehouse?

______________

S2/S8

1.5 24 660 CD are kept in 15 boxes, how many CD are there

in each box?

______________

S2/S8

6 The total height of Hassan and Kim Seng is 2.8 m . If Hassans heightis 1.4 m. What is Kim Sengs height?

______________

S2/S8

6 A long string is 108 m long and it is cut into 9 equal length. What is thelength of each part?

______________

S2/S8



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6 A ribbon of 26 cm long is used to wrap a parcel, What is the length ofribbon used to wrap 8 parcels?

______________

S2/S8

6 A dictionary is 3 cm thick. What is the total thickness of

24 dictionary?

______________

S2/S8

6 A rope is 520 cm long. A string is 295 cm long. What is the differencein length?

______________

S2/S8

6 A stick is 420 cm long and a plank is 590 cm long. What is the totallength?

______________

S2/S8

6 Manjit is 136.5 cm tall, Velu is 2.3 cm more than Manjit and Lim is4.4 cm less than Velu. What is the height of Lim?

______________

S2/S8

6 A piece of cloth measured 18 m, it is cut into 9 small pieces. What isthe length of each piece?

______________

S1/S2/S8

6 The distance from Susans house to school is 462 m. If Susan walks toschool everyday, how far does she walk in a day?

______________

S1/S2/S8

6 My mother bought 2m of rice paper and she used 0.5 m to make a kitefor herself. What is the length of the rice paper left?

______________

S1/S2/S8

6 A ruler of 1 m long is broken into two parts. One part is 68cm, what is S2/S8



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the length of the other part?

______________

6 Karen used 3 m 75 cm of ribbon to tie a gift and 2 m 45 cm of ribbonto tie a second gift. What is the total length of ribbon did she use?

______________

S2/S8

6 Yusof has 7 m 30 cm of rope. Azmi has 3 m 75 cm of rope less thanYusof. What is the length of rope does Azmi have?

______________

S2/S8

6 The length of an exercise book is 17 cm 6 mm. What is the totallength of 6 exercise books?

______________

S2/S8

6 Daniel is 5 years 6 months old. His uncle is 4 times Daniels age. How

old is his uncles ?

______years ______months.

S2/S8

6 A wire of 8.68 m long is cut into 4 equal pieces. Find the length of

each piece?

______________

S2/S8

6 After 35 m 75 cm of walkway was cleaned by a group of workers, 9 m45 cm of walkway was left. What is the total length of the walkway?

______________

S2/S8

6 I am 10 years old. In 10 years time, my uncle will be twice my age.How old is my uncle now?

______________

S4



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6 MAKING DRAWINGSIt is 690 km from Butterworth to Melaka.It is 386 km from Melaka to Batu Pahat.Mr. Lim went from Butterworth to Melaka and then to Batu Pahat.Then, from Batu Pahat he went back to Melaka.How far did Mr. Lim travel ?

Mr. Lim traveled ________ km.

Draw a picture to answer the question. Then fill in the blanks.

1. It is 105 km from Kulim to Taiping.It is 216 km from Taiping to Ipoh.

Marina drove from Ipoh to Taiping then to Kulim.She then drove back from Kulim to Taiping.What is the total distance of her traveling?

________________________

2. Kai Chee rode her bicycle 6 km from home to the school and3 km from the school to the football field.She then rode back to the school. From the school, Kai Chee rode 5 kmto her friends house.How far did Kai Chee ride altogether?

________________________

S1


Draw a picturelike this.

|_________________________|__________________|Butterworth Melaka Batu Pahat

Label the

distances.

|_________________________|__________________|

Butterworth Melaka Batu Pahat

386 km690 km

Show Mr. Lims

trip.

|_________________________|__________________|

Butterworth Melaka Batu Pahat

386 km690 km


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7 The weight of a bag is 2.5 kg and the weight of a basket is 1.2 kg. Findthe difference between the weight of the two objects.

______________

S2/S8

7 2424 kg of rambutans are divided into 4 baskets. What is the weight ofeach basket of rambutans?

______________

S1/S2/S8

7 Anita buys 1.5 kg of fish daily. How many kilograms of fish does she buyfor a week?

______________

S2/S8

7 Box A is 270g , box B is 605g and box C is 158g.What is the total weightof the 3 boxes?

______________

S1/S2/S8

7 Ah Beng has 450g of biscuits, his brother has 285g less than him,whereas his sister has 180g more than Ah Beng . Find the total weight ofthe biscuits they have.

______________

S2/S8

7 Add 28 kg to 579 kg then subtract 52kg.

______________

S2/S8

7 The weights of Rizuan and Mutu are 128 kg. If Rizuan weighs 58 kg,what is the weight of Mutu ?

______________



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7 Aishah has 25 kg of sugar. She used 3.5 kg of sugar to bake cakes, 8 kgto cook syrup , 5.5 kg to cook bubur kacang. How much sugar has sheused altogether?

______________

S2/S8

7 The fruit seller has 120 kg of mangoes, he sells to 6 buyers. How manykilograms of mangoes does each buyer buy?

______________

S2/S8

7 A television weighs 14.4 kg. what is the weight of 5 similar televisions?

______________

S2/S8

7 Mrs Lim bought 3.5 kg of prawn, 1.2 kg of spinach and 2.6 kg of chicken.What is the total weight of things she bought?

______________

S2/S8

7 A basket of durians weights 5 kg 380g. If the basket weighs 1.5 kg ,what is the weight of the durians in kg?

______________

S2/S8

7 A bag of rice weighs 6 kg 750 g. A bag of soya beans weighs 4 kg 500 g.Find the total weight of the two bags, in kg.

______________

S2/S8

7 A loaf of bread weighs 300 g. Find the total weight of 25 loaves of thesame type?

______________

S2/S8



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7 Jean collects 14.6 kg of aluminium cans for recycling. He puts thealuminium can in 4 plastic bags equally. Find the weight of aluminium canin each plastic bag.

______________

S1/S2/S8

7 The mass of Chee Meng is 54 kg. Aron and Mac have the same mass. Ifthe total mass of the three boys is 150 kg, find the mass of Aron.

______________

S2/S8

7 Mrs. Tan used 3 kg 350 g of flour to bake some cakes and 1 kg 850 g offlour is left. Find the weight of flour she had, in kg.

______________

S2/S8

8 A bottle has 1.2 litres of cooking oil. It spills out 60 ml. How much oil isleft in the bottle.Give your answer in ml?

______________

S2/S8

8 A boat used 6 litres of diesel oil in a day, how much will it used for 5days?

______________

S2/S8

8 A tank contains 750 ml of water. Another tank contains2 litre of water. What is the total volume of water in ml?

______________

S2/S8

8 A pail which contains 3.5 litres of water was poured into 7 bottles. Whatis the volume of water in each bottle?

______________

S1/2/S8



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8 A container contains 64 litres of drinking water is to be distributedamong 8 person. How much water does each person get?

______________

S1/S2/S8

8 A bowl contains 0.2 litre of soup, what is the total volume of soup in 10bowls?

______________

S2/S8

8 If Hasni drinks 5 ml of fruit juice per day. How much of fruit juice doeshe drink in the month of April?

______________

S2 /S8

8 Find the total volume of three bottles containing 0.5 litre, 1.3 litre and2.4 litre of water respectively.

______________

S1/S2/S8

8 A kettle contains 3 litres of water and a tea pot contains

1.5 litres of water. Find the difference of volume which the kettle andthe tea-pot hold.

______________

S2/S8

8 A car has 35 litres of petrol. After driving for a distance, 16 litres ofpetrol was left, then he filled up the tank with 24 litres of petrol. Whatis the volume of petrol has the car now?

______________

S1/S2/S8



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8 A tin of milk powder is 1.5 litre. What is the total volume of 18 tins ofmilk powder?

______________

S2/S8

8 60 litres of oil is pour into 24 bottles equally. What is the volume of oilin each bottle?

______________

S1/S2/S8

8 A pot can hold 3 l 250ml of water. A pail can hold 2 l 850 mlof watermore than the pot. How much water can the pail hold in litre ?

______________

S1/S2/S3/S8

8 A container has a capacity of 20 l 250 ml. There is 12 l 650 ml ofwater in it. How much more water will fill up the container?

______________

S2/S8

8

If 5 pails are needed to fill Tank C, what is the capacity of Tank C? Giveyour answer in liters and milliliters. ______________m

S2/S8

8 A bucket can hold 8.5 l of water. Ming Ming pours 8 buckets of waterinto an empty tank. Find the total volume of water in the tank.

______________

S2/S8


C

500 m


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8 A tank with a capacity of 528 litres is to be filled with water. Ewen uses12 litres pails to carry water from a river to the tank. If she can carry2 pails each time, how many trips must she make to fill up the tank?

______________

S2/S8

8 A gardener used 18.5 litres water a day to water the plants in the schoolcompound. How much water did he use?

______________

S2/S8

8 A painter used 43.5 litre of paint to paint 6 room of equal size. What isthe volume of paint he used for each room?

______________

S2/S8

8 If Robert drinks 10 ml of cough syrup, 5 ml of flu medicine and 10 ml offever medicine. What is the total volume of medicine has he taken?

______________

S2/S8

8 55 ml of chemical solution is needed to carry out an experiment. If 15groups carry out the experiment, how much chemical solution is needed?

______________

S2/S8

8 A car is filled up with 50 l of petrol. On the first day 16.5 l of petrolwas used whereas on the second day, 18.9 l was used. What is the

volume of petrol remaining in the tank?

______________

S2/S8



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9 The figure shows a cube and a cuboid. Find the difference in volumebetween the cube and the cuboid.

______________

S2/S8

9 The figure shows a field with the shape of a rectangle. Find theperimeter of the field.

______________

S2/S8

9 The figure shows a rectangle. If the perimeter of the rectangle is 42cm, what is the length of CD?

______________

S2/S8

9 The length of side A is _________ cm.

______________

S2/S8


6cm

6cm

6cm12cm

5cm3cm

6 cm

66 cm2

A

16cm

45cm

125cm


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9 The base area of a cuboid is 24cm2, Its height is 5 cm. What is thevolume of the cuboid?

______________.

S1/S8

9 Alvin draws a rectangle. The length of the rectangle is 12 cm and itsbreadth is 8 cm. What is its area?

_____________

S1/S8

9 The volume of a cube is 576 cm3. If its base area is 64 cm2, find itsheight.

______________

S1/S8

9 The breadth of a rectangle is 25 cm. Its length is twice as long as itsbreadth. Find the perimeter of the rectangle.

______________

S1/S8

9 A square has side 6 cm. The area of a rectangle is 4 times the area ofthe square. Find the area of the rectangle.

______________

S1/S8

9 The figure below is made up of 3 cm squares. What is its perimeter?

______________

S3/S8


3cm


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9 The figure shows a rectangle. The perimeter of the rectangle is 32 cm.Find the area of the rectangle.

______________

S1/S2

9 The diagram consists of squares of the same size. Find the total area ofall the shaded squares.

______________

S2/S8

9 The diagram shows a cuboid. How many cubes with sides measuring 1 cmare needed to fill up the cuboid?

______________

S2/S8


12cm

18cm

4cm

2cm

2cm

6cm


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10 The bar graph below shows the number of members in 4 familes.

(a) How many members does family W have?

_______________

(b) How many members do family X, Y and Z have altogether?

_______________

(c) How many members does family W have more than family X?

_______________

(d) How many members does family Y have more than family Z?

_______________

(e) Find the difference between the number of members in family W andfamily Y ?

_______________

(f) How many fewer members does family X have than family Z?

_______________

S2/S8


Number of members

1614121086420WXYZFamily


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10 The pictograph below shows the number of toy cars 5 boys have.

represents 5 toy cars

1. Ramli has _______ toy cars.

2. Chin Hin and Mohan have _______ toy cars altogether.

3. _______has the most number of toy cars.

4. _______has the least number of toy cars.

5. Kelvin has _______toy cars more than Ramli.

6. Mohan has _______toy cars more than Chin Hin.

7. Chin Hin has _______ toy cars less than Ramli.

8. Mohan has _______toy cars less than Kelvin.

S2/S8


Ramli Kelvin Chin Hin Mohan Sam


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10FINDING FACTS IN A BAR GRAPH

Our class asked students to choose their favourite number.The graph shows the results.

Our Favourite Numbers

FIND THE FACTS

1. How many students chose 7 as their favourite number? _______

2. Which number was chosen by 3 students? _______

3. What number was chosen by the most students? _______

4. What number was chosen by the fewest students? _______

USE THE FACTS

5. How many more students chose 4 than 2? _______

6. How many students chose a number greater than 7? _______

7. How many students chose a number less than 4? _______

8. How many students chose a favourite number? _______

9. What is your favourite number? _______

S2


Numberofstudents

7

5

3

1

0 1 2 3 4 5 6 7 8 9

Favourite Numbers

Find the bar for 7. Look up to the top of

the bar. Look back to the number of


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10 The table below shows the number of adults and children who went to anamusement park in a week. Use this table to answer questions.

Day Number of children Number of adultsMonday 135 69Tuesday 160 76

Wednesday 128 51Thursday 150 62

Friday 284 175Saturday 293 198Sunday 309 154

On which day of the week were there the most number of visitors?

______________.

On which day of the week were there the least number of visitors?

______________.

How many more children than adults visited the amusement park on Fridayand Saturday?

______________.

If the entrance fee was RM2 for a child and RM5 for an adult, how muchmoney was collected by the amusement park on Sunday?

______________.



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ACKNOWLEDGEMENTS

The Penang Education Department would like to

express their appreciation and gratitude for the

contributions made by the Module Writers and those

who have contributed ideas for the publication of this

module.

BIBLOGRAPHY



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1. Randall I. Charles, Frank K. Lester, JR, ProblemSolving ExperiencesIn Mathematics Grade 2, Addison- Wesley Publishing Company,Auckland .

2. Carole Greenes, George Immerzeel, Problem Solving Skill Sheets,

Level B by Dell Seymour, Publication, Canada.

3. Curriculum Specifications of Mathematics Year 4, Curriculum DevelopmentCentre, Ministry of Education, Malaysia.

Modul TOPS Jan 2006 Latest

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