Thomas collected 85 $2 notes and $10 notes during Chinese ......during Chinese New Year. He...

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)

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Q & A