Problem Solving Using Model Drawing 2013
Problem Solving Using Model Drawing Edition 2013
Based on latest MOE Primary Mathematics Syllabus
Step-by-Step Example
Ample questions to drill on
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Pustaka Abdul Hafidz Attamimi © Problem Solving Using Model Drawing
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Problem Solving Using Model Drawing 2013 Your Achievement Record
Made easy for teacher, parents or tutor to take necessary action for immediate follow up for the student concern.
After the student has done the exercises and tested by teacher, please fill up the schedule below.
UNIT 1
TOPIC
MARKS
REMARK
FOLLOW UP ACTION
FUNDAMENTAL MENTAL STRATEGY
WHOLE NUMBERS 2
REVISION TEST 1 REVISION TEST 2 FACTIONS
3
REVISION TEST 3 REVISION TEST 4 FACTIONS
4 REVISION TEST 5 DECIMALS 5
REVISION TEST 6 Ratio 6
REVISION TEST 7 REVISION TEST 8 CHALLENGING PROBLEMS 7
REVISION TEST 9 REVISION TEST 10 FUNDAMENTAL PROBLEM SOLVING STRATEGIES
8
REVISION TEST 11 REVISION TEST 12
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Problem Solving Using Model Drawing 2013
CONTENT UNIT 1 STRATEGY 1
FUNDAMENTAL MENTAL STRATEGY FORMING TENS IN ADDITION STRATEGY EXERCISE 1 - 2 ......................................................................
STRATEGY 2
PAY MORE THAN GET BACK LATER STRATEGY EXERCISE 3 - 4 ......................................................................
STRATEGY 3
ADD MORE THAN RETURN STRATEGY EXERCISE 5 - 6 ......................................................................
UNIT 2
WHOLE NUMBERS PRACTICE STEP BY STEP 1 - 5 .......................................... REVIEW 1 ............................................................................ PRACTICE STEP BY STEP 6 - 10 ........................................ REVIEW 2 ............................................................................ REVISION TEST 1 .................................................................. PRACTICE STEP BY STEP 11 - 15 ........................................ REVIEW 3 ............................................................................ PRACTICE STEP BY STEP 16 - 20 ........................................ REVIEW 4 ............................................................................ REVISION TEST 2 ..................................................................
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Problem Solving Using Model Drawing 2013 UNIT 3
FACTIONS PRACTICE STEP BY STEP 21 - 25 ...................................... REVIEW 5 ............................................................................ PRACTICE STEP BY STEP 26 - 30 ...................................... REVIEW 6 ............................................................................ REVISION TEST 3 .................................................................. PRACTICE STEP BY STEP 31 - 35 ...................................... REVIEW 7 ............................................................................ PRACTICE STEP BY STEP 36 - 40 ...................................... REVIEW 8 ............................................................................ REVISION TEST 4 ..................................................................
UNIT 4
FACTIONS PRACTICE STEP BY STEP 41 - 45 ...................................... REVIEW 9 ............................................................................ PRACTICE STEP BY STEP 46 - 50 ...................................... REVIEW 10 .......................................................................... REVISION TEST 5 ..................................................................
UNIT 5
DECIMALS PRACTICE STEP BY STEP 51 - 55 ...................................... REVIEW 11 .......................................................................... PRACTICE STEP BY STEP 56 - 60 ...................................... REVIEW 12 .......................................................................... REVISION TEST 6 ..................................................................
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Problem Solving Using Model Drawing 2013 UNIT 6
AREA AND PERIMETER PRACTICE STEP BY STEP 61 - 65 ...................................... REVIEW 13 .......................................................................... REVISION TEST 7 ..................................................................
UNIT 7
CHALLENGING PROBLEMS PRACTICE STEP BY STEP 66 - 70 ...................................... REVIEW 14 .......................................................................... REVISION TEST 8 ..................................................................
UNIT 8
FUNDAMENTAL PROBLEM SOLVING STRATEGIES PRACTICE STEP BY STEP 71 - 75 ...................................... REVIEW 15 .......................................................................... PRACTICE STEP BY STEP 76 - 80 ...................................... REVIEW 16 .......................................................................... REVISION TEST 9 ..................................................................
UNIT 9
TABLES AND LINE GRAPHS EXERCISE 1 - 5 ..........................................................................
UNIT 10
SYMMETRY EXERCISE 1 - 4 ..........................................................................
UNIT 11
NON ROUTINE PROBLEMS AND THINKING SKILLS EXERCISE 1 - 4 ..........................................................................
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Problem Solving Using Model Drawing 2013 UNIT 1 - FUNDAMENTAL MENTAL STRATEGIES STRATEGY 1:
Forming Tens in Addition Strategy
Example 1
Example 3
Example 2
14 + 18 + 36 + 12
52 - 27 + 18
36 + 19 + 14 =
50 + 19
=
70 - 27
=
50 + 30
=
69
=
43
=
80
EXERCISE 1 Find the following sums by forming tens first. Show your intermediate working clearly. 1)
12 + 19 + 28
2) 27 - 39 + 23
3)
56 + 87 + 44
4) 195 - 229 + 55
5)
32 + 97 + 18 + 13
6) 47 - 98 + 113
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Problem Solving Using Model Drawing 2013 EXERCISE 2 Find the following sums mentally by forming tens.
1)
16 + 39 + 14
2) 36 - 49 + 24
3)
12 + 19 + 28 + 41
4) 32 - 57 + 38
5)
45 + 38 + 15
6) 72 - 88 + 28
7)
175 - 57 + 25
8) 88 + 95 + 12
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Problem Solving Using Model Drawing 2013 STRATEGY 2:
Pay More then Get Back Later Strategy
Example 1
Example 2
95 - 38 = ( 95 - 40 ) + 2 = 55 + 2 = 57
305 - 97 = ( 305 - 100 ) + 3 = 205 + 3 = 208
EXERICE 3 Use the Pay More than Get Back Later Strategy to find the following differences. Show your intermediate working clearly. (1) 82 - 49
(2) 56 - 27
(3) 125 - 89
(4) 71 - 37
(5) 253 - 98
(6) 101 - 76
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Problem Solving Using Model Drawing 2013 EXERICE 4 Find the following differences mentally. (1) 152 - 25
(2) 87 - 69
(3) 73 - 47
(4) 58 - 39
(5) 253 - 98
(6) 101 - 76
(7) 86 - 58
(8) 235 - 128
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Problem Solving Using Model Drawing 2013 STRATEGY 3:
Add More then Return Strategy
Example 1
Example 2
Example 3
86 + 97 = ( 86 + 100 ) + 3 = 186 - 3 = 183
58 + 73 = ( 60 + 73 ) - 2 = 133 - 2 = 131
397 + 69 = ( 400 + 69 ) - 3 = 469 - 3 = 466
EXERICE 5 Use the Add More then Return Strategy to find the following sums. Show all your intermediate working clearly. (1) 76 + 59
(2) 87 + 78
(3) 36 + 98
(4) 297 + 85
(5) 359 + 36
(6) 496 + 58
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Problem Solving Using Model Drawing 2013 EXERICE 6 Use the mental strategy you have learnt to find the following sums mentally. (1) 54 + 78
(2) 68 + 35
(3) 396 + 89
(4) 335 + 87
(5) 89 + 54
(6) 94 + 78
(7) 297 + 84
(8) 698 + 117
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Problem Solving Using Model Drawing 2013 UNIT 2 - WHOLE NUMBERS PRACTICE STEP BY STEP 1
Example 1 Kelvin paid $281.40 for a camera and a radio. The camera cost $87.80 more than the radio. How much did the camera cost?
Solution
Radio $281.40 Camera
$87.80
?
$281.40 - $87.80 = $193.60 $193.60 รท 2 = $96.80 The radio cost $96.80
$96.80 + $87.80 = $184.60 The camera cost $184.60
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Problem Solving Using Model Drawing 2013 Example 2 The total mass of Siti, Emilia and Cindy is 131kg. Siti is 18kg lighter than Cindy and Emilia is 7kg lighter than Cindy. What is Siti's mass?
Solution
18 kg
7 kg
Siti
131 kg
Emilia Cindy
3 units
= 131kg - 18kg - 11kg = 102kg
Siti
= 102kg รท 3 = 34kg
Siti's mass is 34kg
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Problem Solving Using Model Drawing 2013 QUESTION 1 Peter and Fiona have $142.30 altogether. Fiona has $19.90 less than Peter. How much does Fiona have?
QUESTION 2 Jason, Simon and Linda have 238 stickers altogether. Jason has 25 fewer stickers than Simon. Simon has 46 more stickers than Linda. How many stickers does Simon have?
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Problem Solving Using Model Drawing 2013 QUESTION 3 Mrs Wu bought a television set which cost $987. She bought a piano which cost $3298 more. How much did she spend altogether?
QUESTION 4 The mass of an elephant is 298 kg. A lion weighs 59 kg more than the elephant. Find the total mass of the two animals.
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Problem Solving Using Model Drawing 2013 QUESTION 5 Mrs Smith had $637. She gave all the money to her 4 children. Andrew, Bill, Claire and Daniel. Andrew received the most while Daniel received the least. The difference between the amount Andrew received and the amount each of the siblings received were $20. How much did Andrew receive?
QUESTION 6 Jack, Sam and Tom had a total of 360 marbles. Sam had 20% more marbles than Jack while Tom had 20% less marbles than Jack. How many more marbles did Sam have than Tom?
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Problem Solving Using Model Drawing 2013 PRACTICE STEP BY STEP 2 Example Carol has twice as many stickers as Denise, Elanie has thrice as many stickers as Carol. If they have 71 stickers altogether, how many stickers does Carol have?
Solution
Elaine ? Carol
72
Denise
Total number of units
=6+2+1 = 9 units
1 Unit
= 72 รท 9 = 8 stickers
Carol, 2 units
= 2 units x 8 stickers = 16 stickers
Carol has 16 stickers
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Problem Solving Using Model Drawing 2013 Example At a park, there are 96 girls. There are 724 more boys than girls. How many children are there at the park?
Solution
Girls
96 724
Boys
?
( 96 X 2 ) + 724 =
192 + 724
=
916
There are 916 children altogether.
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Problem Solving Using Model Drawing 2013 QUESTION 1 Linda has 57 local stamps. She has 95 more foreign stamps than local stamps. How many stamps has she altogether?
QUESTION 2 Paul has 86 Chinese storybooks. He has 74 more English storybooks than Chinese storybooks. How many storybooks has he altogether?
QUESTION 3 There are 890 girls in a school. There are 985 more boys than girls. What is the enrolment of the school?
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Problem Solving Using Model Drawing 2013
QUESTION 4 Alice has twice as many stamps as Betty. Mary has 3 times as many stamps as Alice. If Mary has 20 more stamps than Betty, how many stamps do the three girls have altogether?
QUESTION 5 Henry has 4 times as much money as David. David has 3 times as much money as Ryan. If the three boys have a total of $128, how much does Henry have?
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Problem Solving Using Model Drawing 2013 QUESTION 6 In a forest, there are 720 species of flowering plants. There are 2975 more species of non-flowering plants than flowering plants. How many different species of plants are there in the forest?
QUESTION 7 Zainal has $870. Ali has $7250 more than Zainal. How much money have they altogether?
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Problem Solving Using Model Drawing 2013 PRACTICE STEP BY STEP 3
Example 1 Andy had 3 times as many marbles as Tim. Andy bought another 35 marbles and Tim bought another 91 marbles. They now have the same number of marbles. How many marbles did Andy have at first?
Solution
? 35
Andy Tim 91
2 Units
= 91 - 35 = 56 marbles
1 Unit
= 56 รท 2 = 28 marbles
3 Units
= 28 x 3 = 84 marbles
Andy had 84 marbles at first
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Problem Solving Using Model Drawing 2013 Example 2 There are 1484 apples at a fruit stall. There are 227 more apples than pears at the stall. How many apples and pears are there altogether?
Solution 1484
Apples
227
? Pears
1484 - 227 = 1257 There are 1257 pears.
1484 + 1257 = 2741 There are 2741 apples and pears altogether.
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Problem Solving Using Model Drawing 2013 QUESTION 1 Helen had 4 times as many stickers as Mary. Helen bought 15 more stickers and Mary bought 36 stickers. They now have the same number of stickers. How many stickers did Helen have at first?
QUESTION 2 Bobby sold 5 times as many magazines as Dennis on Monday. On Tuesday, Bobby sold another 74 magazines and Dennis sold another 166 magazines. If both men sold the same total number of magazines for both days, how many magazines did Bobby sell on Monday?
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Problem Solving Using Model Drawing 2013 QUESTION 3 Ken travelled 287 km on Sunday. He travelled 98 km less on Monday than on Sunday. How far did he travel on the 2 days?
QUESTION 4 1487 of the pupils in a school are girls. There are 799 more girls than boys. What is the enrolment of the school?
QUESTION 5 2237 of the people in an indoor stadium are males. There are 729 fewer females than males. How many people are there in the indoor stadium altogether?
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Problem Solving Using Model Drawing 2013 QUESTION 6 A farmer has 3027 chickens. He has 2388 fewer ducks than chickens. How many chickens and ducks does he have altogether?
QUESTION 7 Linda spent $7832 on a tour. She spent $3985 more than Tom. How much did they spend altogether?
QUESTION 8 There were 3 times as many goldfish as angelfish in an aquarium. After 4 goldfish were removed and 12 more angelfish were added, there was an equal number of goldfish and angelfish in the aquarium. How many fishes were there in the aquarium at first?
P6 MathsExCEL - Problem Solving Using Model Drawing
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Problem Solving Using Model Drawing 2013 PRACTICE STEP BY STEP 4 - Fraction & Ratio Method
Example 1 Sam has 1/5 as many marbles as Jim. Daniel has 2/3 as many marbles as Sam. If Jim has 52 more marbles than Daniel, how many marbles do the three boys have altogether?
Solution - by MODEL DRAWING METHOD (Method 1) Jim ?
Sam Daniel
13 Units
-->
52 marbles
1 Unit
-->
52 รท 13 = 4 marbles
20 Units
-->
20 x 4 = 80 marbles
The three boys have 80 marbles altogether
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Problem Solving Using Model Drawing 2013 Solution - by RATIO METHOD (Method 2)
Given:
x3
Sam : 1 :
Jim 5
Jim 5
: :
Sam 1
15
:
3
Jim 15
: :
Daniel 2
: :
Sam 3
x3
Sam
:
Daniel
3
:
2
Sam 3
:
Daniel 2
15 - 2 = 13 units
13 units
-->
52 marbles
1 unit
-->
52 รท 13 = 4 marbles
20 units
-->
20 x 4 = 80 marbles
The three boys have 80 marbles altogether
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Problem Solving Using Model Drawing 2013 Example 2 32 people shared among themselves a total of $75,000. 3/4 of them receive the same amount of money each. The rest of the people receive three times as much money each. How much money did each person in each receiving group receive?
<-------------- BIG GROUP -------------->
<-SMALL GROUP->
< ------------------------ 3/4 of 32 people ---------------------------------> <------1/4 of 32 -----> No of people in BIG Group = 3/4 of 32 people = 24 people
No of people in SMALL Group = 32 - 24 = 8 people
BIG GROUP 3
: :
SMALL GROUP 1
Big Group = 24 people ( 24 units )
Small Group = 8 people ( 24 units ) 3 units (1 person)
3 units (2 people)
3 units (3 people)
3 units (4 people)
3 units (5 people)
3 units (6 people)
3 units (7 people)
3 units (8 people)
Total Amount = $75 000, Total People = 32 TIP
=
ALWAYS NEED TO FIND ITS EQUIVALENT
Thus total number of units = 24 + 24 = 48 units 48 units 1 unit
--> -->
$75,000 $75,000 รท 48 = $1,562.50
Each person in the BIG Group receives
=
$1,562.50
Each person in the SMALL Group receives
=
$1,562.50 x 3 units
=
$4,687.50
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