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11th March 2016, Friday
@ FPS
Programme
Time Activity
3.30 p.m. to 3.45 p.m. Registration
3.45 p.m. to 5.00 p.m. Heuristics Skills - Guess and Check - Making Supposition
Q1. Thomas collected 85 $2 notes and $10 notes during Chinese New Year. He collected a total of $586. How many $10 notes did Thomas collect?
Method 1: Guess and Check
No. of $2 notes
Value of $2 notes
No. of $10 notes
Value of $10 notes
Total value
Check for $586
43 42 43 x $2 = $86 42 x $10 = $420 $86 + $420 = $506 X
38 47 38 x $2 = $76 47 x $10 = $470 $76 + $470 = $546 X
33 52 33 x $2 = $66 52 x $10 = $520 $66 + $520 = $586
Q1. Thomas collected 85 $2 notes and $10 notes during Chinese New Year. He collected a total of $586. How many $10 notes did Thomas collect?
Method 2: Supposition Suppose all the 85 notes are $2 notes,
85 x $2 = $170
$586 - $170 = $416 (shortfall)
For every 1 $10 note that replace a $2 note, $8 will fill the shortfall.
$10 - $2 = $8 extra to fill the shortfall
Thus 416 divided by 8 = 52 $10 notes are needed to fill the shortfall.
Q2. Mrs Tan bought a total of 70 pens and files. Each pen cost $2 and each file cost $5. She paid a total of $203. How many files did Mrs Tan buy?
Method 1: Guess and Check No. of pens
Value of pens
No. of files
Value of files Total value
Check for $203
35 35 35 x $2 = $70 35 x $5 = $175 $70 + $175 = $245 X
40 30 40 x $2 = $80 30 x $5 = $150 $80 + $150 = $230 X
45 25 45 x $2 = $90 25 x $5 = $125 $90 + $125 = $215 X
49 21 49 x $2 = $98 21 x $5 = $105 $98 + $105 = $203
Q2. Mrs Tan bought a total of 70 pens and files. Each pen cost $2 and each file cost $5. She paid a total of $203. How many files did Mrs Tan buy?
Method 2: Supposition
Suppose Mrs Tan bought 70 pens,
70 x $2 = $140
$203 - $140 = $63 (shortfall of $63)
For every 1 file that replace 1 pen, $3 will fill the shortfall.
$5 - $2 = $3 extra to fill the shortfall.
Thus $63 divided by $3 = 21 (21 files are needed to fill the shortfall)
Q3. There are a total of 98 wheels in a carpark. There are a total of 36 cars and motorcycles. How many cars are there in the carpark?
Method 1: Guess and Check
No. of cars No. of car wheels
No. of motorcycles
No. of m/c wheels
Total no. of wheels
Check for 98 wheels
18 18 18 x 4 = 72 18 x 2 = 36 72 + 76 = 108 X
16 20 16 x 4 = 64 20 x 2 = 40 64 + 40 = 104 X
13 23 13 x 4 = 52 23 x 2 = 46 52 + 46 = 98
Q3. There are a total of 98 wheels in a carpark. There are a total of 36 cars and motorcycles. How many cars are there in the carpark?
Method 2: Supposition Suppose there are 36 motorcycles in all,
36 x 2 wheels = 72 wheels
98 - 72 = 26 (shortfall of 26 wheels)
For every 1 car that replace 1 motorcycle, 2 wheels will fill the shortfall.
4 wheels – 2 wheels = 2 extra wheels to fill the shortfall.
Thus 26 divided by 2 = 13 (13 cars are needed to fill the shortfall)
Reflection Time
• So far all the supposition methods are using shortfall.
• How about excess?
• Is supposition method still applicable?
Q4. Thomas collected 85 $2 notes and $10 notes during Chinese New Year. He collected a total of $722. How many $2 notes did Thomas collect?
Method 2: Supposition Suppose all the 85 notes are $10 notes,
85 x $10 = $850
$850 - $722 = $128 (excess)
For every 1 $2 note that replace a $10 note, $8 will be taken away from the excess.
$10 - $2 = $8 ( $8 taken away from the excess of $128)
Thus 128 divided by 8 = 16 ( 16 $2 notes are needed to take away the excess of $128)
Q5. There are a total of 128 wheels in a carpark. There are a total of 36 cars and motorcycles. How many motorcycles are there in the carpark?
Method 2: Supposition Suppose all the 36 vehicles are cars,
36 x 4 = 144
144 - 128 = 16 (excess wheels)
For every 1 motorcycle that replace 1 car, 2 wheels will be removed from the excess.
4 - 2 = 2 ( 2 wheels removed from the excess of 16)
Thus 16 divided by 2 = 8 ( 8 motorcycles are needed to remove the excess of 16 wheels)
Q6. Mrs Tan bought a total of 70 pens and files. Each pen cost $2 and each file cost $5. She paid a total of $293. How many pens did Mrs Tan buy?
Method 2: Supposition Suppose Mrs Tan bought 70 files,
70 x $5 = $350
$350 - $293 = $57 (excess)
For every 1 pen that replace 1 file, $3 will be removed from the excess.
$5 - $2 = $3 ( $3 removed from the excess of $57)
Thus 57 divided by 3 = 19 ( 19 pens are needed to remove the excess of $57)
Q7. Joshua scores a total of 33 points for attempting 15 questions in a quiz. For every correctly answered question, Joshua gets 5 points. For every wrong answer, he loses 2 points. How many questions has Joshua answered wrongly?
Method 1: Guess and Check
No. of correct ans
No. of points (+)
No. of wrong ans
No. of points (-)
Total no. of points
Check for 33 points
7 8 7 x 5 = 35 8 x 2 = 16 35 – 16 = 19 X
8 7 8 x 5 = 40 7 x 2 = 14 40 – 14 = 26 X
9 6 9 x 5 = 45 6 x 2 = 12 45 – 12 = 33
Q7. Joshua scores a total of 33 points for attempting 15 questions in a quiz. For every correctly answered question, Joshua gets 5 points. For every wrong answer, he loses 2 points. How many questions has Joshua answered wrongly?
Method 2: Supposition Suppose all the 15 questions are correctly answered,
15 x 5 = 75
75 – 33 = 42 (excess points)
For every 1 wrong answer to replace 1 correct answer, 7 points will be
removed from the excess.
5 – (-2) = 5 + 2 = 7
Thus 42 divided by 7 = 6 ( 6 wrong answers are needed to remove the
excess of 42 points)
Q8. Hafiq bought 24 red and blue balloons. He bought as many red balloons than blue balloons. Each red balloon cost $2 and each blue balloon cost $5. Hafiq spent $93 altogether. How many red balloons did he buy?
Method 1: Guess and Check
5
3
No. of red balloons
Amount spent on red balloons ($2)
No. of blue balloons
Amount spent on blue balloons ($5)
Total amount spent ($)
Check for $93
12 12 12 x $2 = $24 12 x $5 = $60 $24 + $60 = $84 X
3 5 3 x $2 = $6 5 x $5 = $25 $6 + $25 = $31 X
6 10 6 x $2 = $12 10 x $5 = $50 $12 + $50 = $62 X
9 15 9 x $2 = $18 15 x $5 = $75 $18 + $75 = $93
Joshua scores a total of 33 points for attempting 15 questions in a quiz. For every correctly answered question, Joshua gets 5 points. For every wrong answer, he loses 2 points. How many questions has Joshua answered wrongly?
Method 2: Supposition Suppose all 24 balloons are blue,
24 x 5 = 120
120 - 93 = 27 (excess money)
For every 1 blue balloon to replace 1 red balloon, $3 will be
removed from the excess.
5 – 2 = 3
Thus 27 divided by 3 = 9 ( 9 red balloons to remove the excess of $27)
Q8. Hafiq bought 24 red and blue balloons. He bought as many red balloons than blue balloons. Each red balloon cost $2 and each blue balloon cost $5. Hafiq spent $93 altogether. How many red balloons did he buy?
5
3
Q9. Sumei paid $828 for some wallets and handbags. Each wallet cost $22 and each handbag cost $4 more than each wallet. Sumei bought 6 more handbags than wallets. How many handbags did she buy?
Method 1: Guess and Check No. of wallets
Amount paid ($22)
No. of handbags
Amount paid ($26)
Total amount paid
Check for $828
10 16 10 x $22 = $220
16 x $26 = $416
$220 + $416 = $636
X
12 18 12 x $22 = $264
18 x $26 = $468
$264 + $468 = $732 X
14 20 14 x $22 = $308
20 x $26 = $520
$308 + $520 = $828
Q9. Sumei paid $828 for some wallets and handbags. Each wallet cost $22 and each handbag cost $4 more than each wallet. Sumei bought 6 more handbags than wallets. How many handbags did she buy?
Method 2: Model (Grouping)
6 more handbags = 6 x $26 = $156
$828 - $156 = $672
1 group of 1 wallet and 1 handbag = $22 + $26 = $48
$672 ÷ $48 = 14 (14 groups of wallets and handbags)
14 + 6 = 20
6 HB
W
• Monitor your child’s work.
- Study and
- Understand the problem.
- Plan a solution
- Execute the plan
- Review the answers
• Help your child develop good routines.
(using SUPER approach)
Please complete the survey using the QR code. (Heuristics)
Thank you for your Participation
Q & A