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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.
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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
Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 3
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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Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 6
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.
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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.
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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 ?
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Given
Find
Operation
Solve Check
Answer
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TOPIC 1 : WHOLE NUMBERS
LEARNING AREA : ADDITION WITH THE HIGHEST TOTAL OF
100 000.
LEARNING OUTCOME : SOLVE ADDITION PROBLEMS.
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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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TOPIC 1 : WHOLE NUMBERS
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. 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
______
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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 !
Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 14
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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TOPIC 1 : WHOLE NUMBERS
LEARNING AREA : SUBTRACTION WITHIN 1 000 000
LEARNING OUTCOME : SOLVE SUBTRACTION 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. 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 !
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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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TOPIC 1 : WHOLE NUMBERS
LEARNING AREA : SUBTRACTION WITHIN 100 000
LEARNING OUTCOME : SOLVE SUBTRACTION 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.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.
Step 4Pupils solve the problem and check them.
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.
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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?
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Given
FindOperation
Solve Check
Given
Find
Operation
Solve
Answer
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Given
Find
Operation
Solve
Answer
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TOPIC 1 : WHOLE NUMBERS
LEARNING AREA : MULTIPLICATION WITH THE HIGHEST
PRODUCT OF 100 000
LEARNING OUTCOME : SOLVE MULTIPLICATION PROBLEMS
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
Step 1Teacher shows multiplication flash cards and pupils give the answers.
Step 2
Teacher asks pupils to read and understand the problem given.
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.
CHOOSING THE OPERATION
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?
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Given
Find
Operation
Solve Check
Answer
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TOPIC 1 : WHOLE NUMBERS
LEARNING AREA : DIVISION WITH THE HIGHEST DIVIDEND
OF 100 000
LEARNING OUTCOME : SOLVE DIVISION PROBLEMS
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
Step 1Teacher asks 2 pupils to divide 20 books equally among themselves. Pupils answer.
Step 2
Teacher asks pupils to read and understand the problem given.
Step 3
Teacher asks pupils to draw the diagram related to the questions given.
Step 4Pupils solve the problem and check them.
e.g. Divide equally The key word is divide equally and the operation is division.
CHOOSING THE OPERATION
There are 3 030 books. Rina arranges them onto 6 shelves equally. How many books doesshe put on each shelf ?
e.g : 1
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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.
Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 23
3 030
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TOPIC 1 : WHOLE NUMBERS
LEARNING AREA : MIXED OPERATION
LEARNING OUTCOME : SOLVE MIXED OPERATION 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 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.
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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?
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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.
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
Step 1
Teacher asks pupils to read and understand the problem given.
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
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
Step 1
Teacher asks pupils to read and understand the problem given.
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
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
Step 1
Teacher asks pupils to read and understand the problem given.
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.
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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
Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 36
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
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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?
Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 38
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
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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.
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
Step 1
Teacher practices mental calculation and estimation involving mass.
Step 2
Teacher asks pupils to read and understand the problem given.
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
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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.
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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.
FINDING FACTS IN A TABLE
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
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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.
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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.
SUGGESTED TEACHING AND LEARNING ACTIVITIES.
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 ______________
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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 ______
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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.
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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?
________________
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Ali drank litre of milk. Hersister drank litre of milk
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CHOOSING THE OPERATIONS
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 ?
_________________
CHOOSING THE OPERATIONS
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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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FINDING FACTS IN A TABLE
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
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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
Mathematics Module for Year 4 ( TOPS ) Jabatan Pelajaran Pulau Pinang 2006 81
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
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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
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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
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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
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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
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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
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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.
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